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Topological states modulation of Bi and Sb thin films by atomic adsorption Dongchao Wang,ab Li Chen,*ab Hongmei Liu,b Xiaoli Wang,b Guangliang Cui,b Pinhua Zhang,b Dapeng Zhaoc and Shuaihua Jic Based on first-principles calculations, we systematically investigated the topological surface states of Bi and Sb thin films of 1–5 bilayers in (111) orientation without and with H(F) adsorption, respectively.
Received 6th October 2014, Accepted 9th December 2014
We find that compared with clean Bi and Sb films, a huge band gap advantageous to observe the
DOI: 10.1039/c4cp04502e
quantum phase transition from trivial (non-trivial) to non-trivial (trivial) phase is induced for a three
quantum spin Hall effect can be opened in chemically decorated bilayer Bi and Sb films, and the bilayer Bi film and single (four) bilayer Sb film. Surface adsorption is an effective tool to manipulate the
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geometry, electronic structures and topological properties of film materials.
Introduction Topological insulators (TIs) as newly discovered quantum states have gained wide attention in condensed matter physics.1–4 Among them, two-dimensional (2D) TIs have been proposed as candidates to achieve the quantum spin Hall (QSH) effect, due to a unique spin-dependent conducting channel of edge states protected by time-reversal invariance. To date, some 2D layered film materials have been predicted to observe the QSH effect, such as planar graphene,5 low-buckled silicene and germanene.6 As a result of weak spin–orbit coupling (SOC) in the aforesaid elements, the band gap is just several meV too small to realize the QSH effect at room temperature (RT). As they show strong SOC, heavy metal bismuth (Bi)7,8 and antimony (Sb)9 films are attracting more interest and are proposed to be TIs. Experimentally, Bi10 and Sb11 films have been grown on various substrates. However, the above TIs have finite band gaps, theoretically 60–70 meV for a single bilayer (BL) Bi film opened by SOC, which is disadvantageous to observe the QSH phase experimentally at RT, preventing their applications in electronic devices. Therefore, devoting more effort to manipulating the electronic structure and enlarging the band gap of Bi and Sb films is expected. Previous work12–14 shows that introducing an external electric field and strain are useful ways to modulate the electronic structure and topological properties of Bi and Sb films, while the effect of electric field and strain is unapparent in increasing
a
School of Physics, Shandong University, Shandong 250100, China. E-mail: [email protected] b Institute of Condensed Matter Physics, Linyi University, Shandong 276000, China c State Key Laboratory of Low Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
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the bulk gap of 2D TIs. Moreover, the effect of substrate is an unavoidable factor during the experimental growth process. On various substrates, the Bi BL film will show different topological phases,15 i.e. it is a TI on hexagonal-BN and shows a metallic phase on a Si or Ge substrate. The topological edge states are preserved even after strong hybridization with the 3D TI Bi2Te2Se substrate,16 however, the band gap of the pristine Bi BL is replaced with a small hybridization gap. Recently, chemical decoration by hydrogen, halogens and other functional groups has been proposed to be an efficient way for both modulating the topological edge states and enlarging the bulk gap, as in graphane or fluorinated graphene compared with graphene. For example, with H edge adsorption, the transport properties of the topological edge states of Bi BL nanoribbons can be well enhanced,17 and depending on the concentration of adatoms, the edge states can be changed from localized to delocalized in real space.18 When the adatoms are adopted on both sides of the 2D film, functionalized germanene,19 stanene20 and Bi21 are found to have larger band gaps than the pristine cases, up to 0.3 eV for fluorinated stanene. In addition, a H terminated 1BL Ge film has been successfully synthesized,22 which provides inspiration to experimentally grow chemically modified Bi and Sb films with huge band gaps. However, the above decorations on 2D films are just for the single BL case. In our work, both single and multi-BL pristine and functionalized films of Bi and Sb are systematically investigated based on first-principles calculations. For pristine Bi and Sb films, the properties of surface and edge states change with the thickness of the films. Depending on atomic adsorption by H and F atoms, huge non-trivial band gaps can be opened in chemically decorated Bi and Sb films, and the quantum phase transition from trivial (non-trivial) to non-trivial (trivial) phase is induced for a 3BL Bi film and a 1BL (4BL) Sb film.
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Methods and parameters First-principles calculations based on density functional theory were performed by the Vienna ab initio simulation package (VASP).23 The Perdew–Burke–Ernzerhof (PBE)24 generalized gradient approximation (GGA) was used to describe the exchange–correlation potential. All calculations were carried out with an energy cutoff of 500 eV on the 18 18 1 k-point mesh. The vacuum layer was about 15 Å to eliminate the interactions between neighboring films. The structures were relaxed until the difference of the total free energy between two ionic steps was below 1 104 eV. The SOC was included in the self-consistent calculations of the electronic structure. To confirm the band topology and Z2 topological invariant, the ABINIT package was implemented.
Results and discussion Topological properties of Bi(111) thin films Geometry relaxation of free-standing Bi thin films in the range of 1 to 5BLs was primarily carried out. The top and side views of the stacked Bi(111) film structure is shown in Fig. 1(a). In such a structure, each Bi atom forms three equivalent covalent bonds with the three nearest-neighbor Bi atoms within the unit BL, while the interaction between neighboring BLs is through van der Waals forces.25 The optimized lattice constant of the Bi thin film as a function of film thickness is indicated by the black curve in Fig. 1(b). As the thickness increased, the values including lattice constant, buckling height and inter-BL distance will be much closer to those of the bulk geometry.26 This can be understood as follows: the thicker the film is, the stronger the coupling among different layers is, leading to reduced buckling height and inter-BL distance, and an increased corresponding lattice constant. Based on the optimized geometry of the Bi films, the dispersion relation is calculated as shown in Fig. 2. We find that both surface states of the 1BL and 2BL Bi films are semiconductors with positive band gaps as shown in Fig. 2(a) and (b). The direct and indirect band gaps are 0.635 eV and 0.543 eV for 1BL and 0.148 eV and 0.068 eV for 2BL, respectively. To detect the helical edge states clearly, we constructed nanoribbon structures with zigzag edges with preserved inversion symmetry for the 1BL and 2BL films, including 40 and 64 Bi atoms, respectively. The band structures
Fig. 1 (a) Top and side views of the layered Bi film. The dark red, light sea green and purple spheres indicate 1st, 2nd and 3rd layer Bi atoms, respectively. (b) Lattice constant of Bi (black) and Sb (red) films as a function of the film thickness.
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Fig. 2 (a) and (b) Band structures of the 1BL and 2BL Bi thin films, respectively. (c) and (d) Band structures of the zigzag nanoribbons of the 1BL and 2BL Bi thin films, respectively.
of the nanoribbons are shown in Fig. 2(c) and (d). Degenerate conducting edge states can be observed near the Fermi level in both the 1BL and 2BL Bi nanoribbons, indicated by the blue color. The helical edge states are robust against backscattering which is very helpful in applications for electronic devices. Insulating surface states and conducting edge states of the film systems show that both the 1BL and 2BL Bi films are intrinsic 2D TIs. However, when the thickness goes beyond 3BL the indirect band gap of the film becomes negative, showing a metallic character, unlike 1BL and 2BL.8 Although the 1BL and 2BL Bi films were theoretically confirmed to be 2D TIs above, on the experimental side, the band gaps are too small to achieve the QSH effect at RT. Therefore, finding a way to enhance the band gap but not change the topological nature is helpful to observe the QSH effect. Chemical decorating is an effective way to manipulate the lattice and electronic structure in both device design and material selection.19,20 There are 2 choices for surface adsorption of 2D films: single-side adsorption and double-side adsorption. When the adatoms are adopted only on one surface of the 2D film, a dipole electric field will be produced due to the charge transfer between the adatoms and film surface. However, if the adatoms are put on both surfaces of the film to reserve the inversion symmetry, the dipole field can be removed. Therefore, we here emulate the double-side case to preserve the inversion symmetry of the 2D TI films. Moreover, the choice of adatoms is of vital importance. Different adatoms will induce diverse reconfiguration of the lattice structure and the transition of the topological phase. It is skillful to realize 2D TIs with huge band gaps and other properties via choosing suitable adatoms. Given the preexisting experience and experimental availability, H and F atoms are good options to emulate surface adsorption.22,29 We chose H and F atoms as the chemical functional groups, which easily saturate the dangling bonds from the sp3 hybridized Bi atoms as shown in the top and side views of the single BL case in Fig. 3(a) and (b), respectively. The H(F) atoms are bonded to the Bi atoms on both sides of the BL slab in an alternating way.
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mentioned above. For the 2D TI phase, the topological invariant is calculated from the parities of the Bloch wave functions for occupied bands at all time-reversal invariant points, one G and three M points, as di ¼
N Y
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m¼1
Fig. 3 Lattice geometry of the decorated 1BL Bi thin film from the (a) top view and (b) side view. The blue balls represent the Bi atoms and the celadon balls indicate the H(F) atoms. Band structures of the 1BL Bi thin films with (c) H and (d) F adsorption. The solid red lines and solid black lines indicate the calculations without SOC and with SOC, respectively.
All the new configurations of the chemically decorated Bi thin films are optimized to obtain stable structures. It is found that the H adsorbed 1BL Bi film has a quasi-planar structure for which the buckling height is 0.073 Å, much smaller than that of the pristine 1BL Bi thin film discussed above, while the lattice constant of the Bi film with H adsorption is 5.56 Å, enlarged 27.5% relative to the pristine Bi film. In addition, the Bi–H bond length is optimized to 1.823 Å. Based on the structural relaxation, the band structure of the H adsorbed Bi film in Fig. 3(c) is calculated without and with SOC which plays an important role in TIs. Noticeably, when SOC is excluded, a Dirac point appears at the Fermi level at the K point, indicated by the solid red lines. When SOC is switched on, one splitting at the Dirac point at the K point is observed in the solid black lines shown. Such splitting is a result of the first order relativistic effect related to Bi elements, which is robust against perturbation.21 According to partial band projections, the states without SOC around the Fermi level at the G point are mainly influenced by the atomic px and py orbitals of the Bi atoms. As the SOC effect is taken into account, the degeneracy of the energy level is lifted, opening two band gaps above and below the Fermi level. This originates from the variation of the atomic orbital component of the splitting bands. Taking the two splitting bands above the Fermi level as an example, the upper one at G remains composed of px and py orbitals, while the weight of the s orbital is added in the lower one as well as the original px and py orbitals. Therefore, such variation leads to a change of band potential that reshapes the band configuration at the G point. It is also because the s, px and py orbitals are mixed in the lower of the two splitting bands below the Fermi level. The band reshaping at the K and G points around the Fermi level induces an indirect SOC band gap of 1.08 eV, which is largely increased compared with that of the pristine Bi film. The presence of insulating surface states makes it possible for the decorated Bi thin film to be a 2D TI. Another effective way to distinguish non-trivial TIs from ordinary insulators is by calculating the topological invariant n proposed by Fu and Kane,28 except for simulating the edge states of the nanoribbons
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xi2m ðKi Þ; ð1Þn ¼
4 Y
di ¼ dðGÞd3 ðMÞ;
(1)
i¼1
where x2m = 1 denotes parity eigenvalues and N is the number of occupied bands. n = 0 characterizes a trivial insulator, while n = 1 indicates a non-trivial phase. Thus, the topological invariant mentioned above is calculated to determine the topological phase of the 1BL Bi film with adsorbed H atoms. The results show that the H adsorbed Bi film has a non-trivial band topology with the topological invariant v = 1. This non-trivial topological phase is similar to that of graphene with SOC taken into account, which is one kind of Kane–Mele type QSH phase. However, for the pristine 1BL Bi film the non-trivial band topology is due to band inversion undergoing gap closing at certain SOC strengths. Given the feasibility of observing the QSH effect at RT, the Bi hydride with a huge SOC gap should be one of the preferential candidates. Among the adopted atoms, the halogens are also a good choice because of their active chemical properties. The lattice constant of the 1BL Bi film with F adsorption is reduced to 5.39 Å, compared with 5.56 Å for the H adsorbed Bi film. Since the electronegativity of F is larger than that of H, the bonding between Bi and F is stronger than that between Bi and H. The buckling height is decreased to 0.407 Å compared with the freestanding Bi film, meaning that a low buckled geometry is more stable for the fluorinated Bi film. The Bi–F bond length slightly increases to 2.114 Å due to the larger covalent bond radius of F atoms. Subsequently, the band structures are also calculated based on the optimized lattice structure without and with SOC as shown in Fig. 3(d). As for H adsorption, a Dirac point also appears at the Fermi level at the K point in the Brillouin zone for the F adsorbed Bi film without SOC, denoted by the solid red lines. The bands at the Dirac point and the G point split away when the SOC is taken into consideration, as shown by the solid black lines, inducing an indirect SOC gap of 1.04 eV which is slightly less than that of the H adsorbed Bi film. According to partial band projections we find that, different from H adsorption, the states without SOC near the Fermi level contain the px and py orbitals of the F atoms besides those of the Bi atoms. The band splitting at the G point induced by SOC results from the additional s and pz orbitals of the F atoms, along with the px and py orbitals of the F and Bi atoms in the lower band, leading to different energy levels. Consequently, the band splitting at G in the F adsorbed Bi film is slightly larger than that in the H adsorbed film. Based on analysis of the total parities of the occupied bands, the topological invariant v is 1, indicating a non-trivial topological state for the Bi film decorated by F atoms. Therefore, it is also possible to realize the QSH effect in the 2D low buckled F adsorbed Bi film with a sizable bulk band gap. In the same way, the H atoms are adsorbed on both surfaces of the 2BL Bi film. Compared with the pristine case, the film structure is reshaped. The lattice constant changes from 4.52 Å
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to 5.27 Å, while both the intra-BL and inter-BL distances decrease by B0.7 Å, meaning stronger coupling between neighboring layers. In terms of structure, the influence of H atoms on the 2BL Bi film is obviously less than that of 1BL. Then, the band structure of the 2BL film modified by H atoms with SOC is calculated, which shows that there is an indirect band gap of 0.09 eV. The geometry of the 2BL Bi film decorated by F adsorption is slightly compressed at the surface but expanded vertically, which is like the case of the 1BL with adsorbed H and F atoms. By calculating and analyzing the band structure of the 2BL Bi film adsorbed by F atoms, the top of the valence bands and the bottom of the conduction bands overlap indirectly, showing metallic character. To sum up, H and F adsorption has a great influence on the geometries and band structures of the Bi films, and the effect of H adsorption is slightly stronger than that of F adsorption. Although the bulk gap has been enlarged by H adsorption relative to the free-standing 2BL Bi film, it is much less than that of the H adsorbed 1BL Bi film, too small to observe the QSH effect. In previous studies, most work chose the 1BL Bi film as an object to modulate the electronic structure and edge state.15–17,21 However, the modulation of multilayer films is still very important for device choice and design for various applications. With the thickness increased, we find that the effect of adatoms on the geometry of the Bi film becomes weaker and weaker. Unlike the 1BL and 2BL films, the 3BL case is just slightly reconfigured by H adsorption. However, the band structure is largely changed. Compared with the free-standing 3BL film which is semimetallic with a negative indirect band gap as shown in Fig. 4(a), the film with H adsorption becomes a semiconductor with the bands at the G point opened and the bands at the K point becoming close to each other as shown in Fig. 4(b), inducing an indirect gap of 0.33 eV. The topological invariant calculated from the parities of the occupied bands is 1, indicating a non-trivial band topology. When the F atoms are adsorbed on the top and bottom surfaces of the 3BL Bi film, the geometry parameters are much closer to those of the pristine film. Although the intrinsic character is not varied, the band structure is reshaped. As shown in Fig. 4(c), the bottom of the conduction bands at the K and M points shift downward below the Fermi level, while the top of the valence bands shifts upward above the Fermi level, keeping the semimetallic properties. With the thickness increased, the influence of adatoms on
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the lattice structure of the multi-BL films beyond 3BL is limited. When H atoms are adopted on the surfaces of the 4BL and 5BL films, a negative indirect gap appears with the bands shifted to overlap around the Fermi level with respect to the decorated 3BL film, showing a clear sign of a semimetal, though the shape of the bands is similar to the 3BL case. When the F atoms are adsorbed, the band structures of the 4BL and 5BL films are like that of 3BL, showing semimetallic properties. On the whole, by investigating systematically single and multi BL Bi films without and with chemical decorating, surface adsorption is proposed to be an effective tool to modulate the topological surface states of 2D films for device applications. Topological properties of Sb(111) thin films Sb, being in the same group as Bi, also has strong SOC. The Sb(111) film geometry is analogous to the Bi(111) film geometry of buckling hexagonal honeycomb shown in Fig. 1(a). From the structural relaxation, the lattice constants of the 1–5BL films are shown in Fig. 1(b) as the red curve, which are generally smaller than those of the Bi films due to the smaller atomic radius of Sb. The parameters obtained from the optimization are in good agreement with an earlier study.27 Then, the band structures of the 1–5BL Sb films were calculated, which are shown in Fig. 5. For the 1BL Sb thin film in Fig. 5(a), the bulk gap is very large, up to 2.621 eV, and the surface splitting indicated in blue reaches 1.324 eV at the G point. The direct gaps of surface splitting in the 2–5BL films as shown in Fig. 5(d), are 0.323 eV, 0.039 eV, 0.016 eV and 0.008 eV, respectively. It is essential for a well-defined Z2 number that the direct gap always remains open at the G point. According to the parity analysis, the topological invariant n = 0 for the 1–3BL films, meaning they are ordinary insulators, while n = 1 for the 4–5BL films showing that they are non-trivial insulators. The same chemical decorating is employed for the Sb films with different thicknesses, since Sb has strong SOC being in the same group as Bi. Firstly, the lattice structure of a single BL Sb film with H atoms adsorbed on both surfaces is optimized. A quasi-planar geometry is also confirmed to be stable with the buckling height of 0.081 Å, which is slightly larger than that of the Bi film with H adsorption. The lattice constant of the H adsorbed Sb film is 5.29 Å, much larger than that of the pristine Sb film (4.12 Å), indicating that the bonding between Sb atoms becomes weaker due to the H atomic adsorption. Owing to the
Fig. 4 Band structures of the 3BL Bi thin films: (a) the pristine case, (b) with adsorbed H atoms, and (c) with adsorbed F atoms.
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Fig. 5 Band structures of (a) 1BL, (b) 2BL and (c) 4BL Sb thin films. The blue curves indicate the surface states of the Sb thin films within the bulk gap. The inset in (c) is the enlargement of the surface states at G. (d) Surface splitting as a function of film thickness.
smaller covalent bond radius of Sb atoms, the Sb–H bond length decreases to 1.733 Å relative to that of the Bi film with H adsorption. As for the H adsorbed Bi film, the SOC effect on the H adsorbed Sb film was also researched. In Fig. 6(a), the band structure is shown without SOC and with SOC, denoted by the solid red and black lines, respectively. Obviously, the Dirac point which is closed without SOC at the K point is opened by the SOC effect, inducing a direct bulk band gap of 0.48 eV.
Fig. 6 Band structures of the 1BL Sb thin film with adsorbed (a) H atoms and (b) F atoms, the 2BL Sb thin film with adsorbed (c) H atoms and (d) F atoms, and the 4BL Sb thin film with adsorbed (e) H atoms and (f) F atoms. The solid red lines and solid black lines indicate the calculations without SOC and with SOC, respectively.
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The results of calculating the parities show that the topological invariant shifts from 0 in the pristine Sb film to 1 in the single BL Sb film with H adsorption. This results in a quantum phase transition from an ordinary insulator to a non-trivial topological phase driven by H adsorption. Then, the H atoms are replaced with F atoms bonded on the 1BL Sb film. After the geometry is fully optimized, the obtained lattice constant, buckling height and Sb–F bond length are 5.16 Å, 0.279 Å and 1.977 Å, respectively. The structural reconfiguration follows the rule discussed above in the H and F adsorbed 1BL Bi films. The band structures are calculated without and with SOC as shown in Fig. 6(b). The direct SOC gap is 0.39 eV at the K point, slightly less than that of the Sb film with H adsorption. Analysis of the parities also shows that the topological invariant is 1, indicating that the 1BL Sb film with F adsorption is also in a non-trivial topological state, like that with H adsorption. Compared with the pristine Sb film in Fig. 5(a), the band structure of the films with H and F adsorption is largely changed with the direct gap shifted from the G point to K point. Surface adsorption that induces topological phase transition from a trivial to non-trivial insulator is proved to be useful for modulating the topological phase. For the 2BL Sb film with H and F adsorption, the geometry is also fully relaxed, and the reconfiguration follows the rule discussed above. Based on the optimized structures, the dispersion relation of H and F adsorption including SOC is plotted in Fig. 6(c) and (d), respectively. We find that the band gap opened previously in the pristine film closes between the K and G point, inducing a semimetallic state for both H and F adsorption. Compared with the Bi film, the effect of surface adsorption is relatively weak in the Sb film due to the stronger SOC of Bi. The same calculation is employed for the 3BL and 4BL Sb films. As the thickness increases, the bonding between neighboring layers becomes strengthened. Therefore, the structural reconfiguration by H and F adsorption is not apparent as for 1BL and 2BL. However, the effect of H and F adsorption on the electronic structure is still as great as that of 1BL and 2BL. The 3BL Sb film is transformed from a normal insulator to a semimetal with the band gap closed by adatoms like in 2BL. On the other hand, the 4BL film with H and F adsorption turns into a semimetal, as shown in Fig. 6(e) and (f), from a 2D TI, losing the non-trivial band topology. It is proven once again that surface adsorption can realize the mutual transition between the trivial and non-trivial phase. For the 5BL film, the effect of H and F adsorption is different. In the presence of F adsorption, there is a negative band gap like for 3BL and 4BL, showing a semimetallic character, whereas the gap is enlarged by H adsorption up to 0.07 eV. The topological invariant is also calculated, showing a non-trivial band topology for the 5BL film with H adsorption. This also shows that the effect of H adsorption on the electronic properties is slightly stronger than that of F adsorption to reach our desired purpose. Previous studies8 showed that the Bi(111) film represents a special class of system having an intermediate inter-BL coupling strength, which has a significant influence on its topological properties. The stronger the inter-BL coupling is, the larger the band gap becomes. In our study, the inter-BL coupling strength will be changed for the Bi and Sb thin films by atomic adsorption,
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correspondingly leading to changes in the topological properties. Here, we take the 2BL and 3BL Bi films as an example. For the pristine 2BL film, the intra-BL and inter-BL distances are 1.72 Å and 3.00 Å, which means a weak inter-BL coupling regime. When H atoms are adsorbed on the Bi atoms of both surfaces, these two distances are 1.03 Å and 2.3 Å, which are decreased largely, meaning a stronger intra-BL and inter-BL coupling. Therefore, the enhanced coupling strength induces a larger band gap than that of the pristine film. Similarly, the phenomenon is also observed in the 3BL film. The intra-BL and inter-BL distances of the pristine film are 1.69 Å and 2.72 Å, respectively. They are 1.58 Å and 2.50 Å in the H adsorbed film, meaning slightly stronger inter-BL coupling in the adsorbed configuration. Furthermore, the influence of H and F adsorption on the same BL film is also diverse. For the 2BL Bi film, the intra-BL and inter-BL distances after F adsorption are 1.59 Å and 2.35 Å, slightly larger than those after H adsorption. For the 1BL Sb film, the interlayer coupling driven by surface adsorption is more obvious. In the pristine case, the Sb film has a buckling height of 1.65 Å, while it becomes much flatter for the H or F adsorbed film. The interlayer coupling strength is so strong that the band structure is drastically reshaped and then the parities of the occupied bands are inverted, leading to a non-trivial phase. On the other hand, the atomic orbitals and the SOC effect result in the difference in the properties of the H and F adsorbed film, as discussed above. Such analysis can be extended to other multi-BL Bi films and multi-BL Sb films. Taking the 4BL Sb film as an example, the bands around the Fermi level between the K and G points after F adsorption contain a greater contribution from the pz orbital of the F atoms, pushing the bands down more than after H adsorption. Compared with the pristine film, due to the introduction of the s orbital of the H atoms or the pz orbital of the F atoms, the bands near the Fermi level away from the G point are warped, leading to a semimetal. For the 5BL Sb film after H adsorption, more subbands turn into the same energy window than in the 4BL film. Stronger band hybridizations interplay, shifting the bands towards the Fermi level. There is a greater s orbital component in the lower states near the Fermi level between the K and G points, opening a small indirect band gap. The F adsorbed 5BL Sb film also becomes a semimetal like the F adsorbed 4BL film, with the bands between the K and G points shifting down below the Fermi level coupling by the contribution of the pz orbital of the F atoms. Therefore, both H and F adsorption play an important role in the electronic structure and quantum phase transition of film systems. More research is expected to be carried out with Cl, Br, I and other gaseous functional groups in the future. Experimentally, although the halides of Bi and Sb (F, Cl, Br and I) have been synthesized in 3-dimensions, such 3D halides are not stable once the temperature is beyond the experimental one such as room temperature.30–33 As far as we know, chemically decorated Bi and Sb films have not been experimentally reported. Recently, pristine Bi and Sb ultrathin films have been grown on Bi2Te3(111)10,34 and Si(111)11,35 substrates, respectively. Therefore, chemically decorated Bi and Sb films may be realized by exposing pristine Bi and Sb
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films to atomic and molecular gases or by chemical reaction in solvents, which is analogous to germanene.22 The effective use of chemical functional groups is a significant tool to modulate the lattice and electronic structures and the topological properties of various insulating and conducting materials.
Conclusions In conclusion, we have systematically studied the topological surface states of pristine and chemically decorated Bi and Sb thin films of 1–5BLs in the (111) orientation without and with atomic (H and F) adsorption. The results show that a huge band gap, beneficial for observing the QSH effect at RT, is induced in the 1BL Bi and Sb films after H and F adsorption. On the other hand, the topological phase transition from a trivial (nontrivial) to non-trivial (trivial) insulator is driven by both H and F adsorption in the 3BL Bi film and 1BL (4BL) Sb film. For the other BL Bi and Sb films, the analogous quantum phase transition is also driven from semiconductor to semimetal, such as the F adsorbed 2BL Bi film, along with the H(F) adsorbed 2BL and 3BL Sb films. Therefore, atomic adsorption is proposed to be an effective method to enlarge the band gap of 2D TIs and modulate the topological phase transition of Bi and Sb thin films. More novel properties may be discovered by using other chemical functional groups, such as gases and transition metals. The artificial modulation of electronic properties will be helpful for the potential applications of Bi and Sb thin films in nanoscale devices.
Acknowledgements We thank the financial support from the National Natural Science Foundation of China (Grant No. 51431004, 11274151, 11147007, 11204120 and 11404058), from the Open Research Program of the State Key Laboratory of Low-Dimensional Quantum Physics of Tsinghua University (Grant No. 20120924) and the Key Disciplines of Condensed Matter Physics of Linyi University.
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11 G. Bian, T. Miller and T. C. Chiang, Phys. Rev. Lett., 2011, 107, 036802. 12 L. Chen, Z. F. Wang and F. Liu, Phys. Rev. B: Condens. Matter Mater. Phys., 2013, 87, 235420. 13 D. C. Wang, L. Chen, H. M. Liu and X. L. Wang, J. Phys. Soc. Jpn., 2013, 82, 094712. 14 D. C. Wang, L. Chen, H. M. Liu and X. L. Wang, EPL, 2013, 104, 57011. 15 Z. Q. Huang, F. C. Chuang, C. H. Hsu, Y. T. Liu, H. R. Chang, H. Lin and A. Bansil, Phys. Rev. B: Condens. Matter Mater. Phys., 2013, 88, 165301. 16 S. H. Kim, K. H. Jin, J. Park, J. S. Kim, S. H. Jhi, T. H. Kim and H. W. Yeom, Phys. Rev. B: Condens. Matter Mater. Phys., 2014, 89, 155436. 17 Z. F. Wang, L. Chen and F. Liu, Nano Lett., 2014, 14, 2879. 18 L. Chen, G. L. Cui, P. H. Zhang, X. L. Wang, H. M. Liu and D. C. Wang, Phys. Chem. Chem. Phys., 2014, 16, 17206. 19 C. Si, J. W. Liu, Y. Xu, J. Wu, B. L. Gu and W. H. Duan, Phys. Rev. B: Condens. Matter Mater. Phys., 2014, 89, 115429. 20 Y. Xu, B. H. Yan, H. J. Zhang, J. Wang, G. Xu, P. Z. Tang, W. H. Duan and S. C. Zhang, Phys. Rev. Lett., 2013, 111, 136804. 21 Z. G. Song, C. C. Liu, J. B. Yang, J.Z. Han, M. Ye, B. T. Fu, Y. C. Yang, Q. Niu, J. Lu, Y. G. Yao, 2014, arXiv:1402.2399 [cond-mat.mtrl-sci]. 22 E. Bianco, S. Butler, S. S. Jiang, O. D. Restrepo, W. Windl and J. E. Goldberger, ACS Nano, 2013, 7, 4414.
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23 G. Kresse and J. Furthmuller, Comput. Mater. Sci., 1996, 6, 15. 24 J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865. ¨nig, J. Sun, Yu. M. Koroteev, G. Bihlmayer, J. Wells, 25 H. Mo E. V. Chulkov, K. Pohl and Ph. Hofmann, Phys. Rev. B: Condens. Matter Mater. Phys., 2005, 72, 085410. 26 Ph. Hofmann, Prog. Surf. Sci., 2006, 81, 191. 27 X. Gonze, J. P. Michenaud and J. P. Vigneron, Phys. Rev. B: Condens. Matter Mater. Phys., 1990, 41, 11827. 28 L. Fu and C. L. Kane, Phys. Rev. B: Condens. Matter Mater. Phys., 2007, 76, 045302. 29 J. Zhou, M. M. Wu, X. Zhou and Q. Sun, Appl. Phys. Lett., 2009, 95, 103108. 30 N. C. Norman, Chemistry of arsenic, antimony, and bismuth, Springer, 1998, pp. 67–84. ISBN 0-7514-0389-X. 31 N. Wiberg, A. F. Holleman and E. Wiberg, Inorganic chemistry, Academic Press, 2001, ISBN 0-12-352651-5. 32 H. J. Emeleus and A. G. Sharp, Advances in Inorganic Chemistry and Radiochemistry, Academic Press, 1975, pp. 77–78. ISBN 0-12-023617-6. 33 N. N. Greenwood and A. Earnshaw, Chemistry of the Elements, Butterworth-Heinemann, 2nd edn, 1997, ISBN 0-7506-3365-4. 34 C. Sabater, D. Goslbez-Martnez, J. Fernndez-Rossier, J. G. Rodrigo, C. Untiedt and J. J. Palacios, Phys. Rev. Lett., 2013, 110, 176802. 35 G. Bian, X. X. Wang, Y. Liu, T. Miller and T.-C. Chiang, Phys. Rev. Lett., 2012, 108, 176401.
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Cite this: DOI: 10.1039/c4cp04502e
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Topological states modulation of Bi and Sb thin films by atomic adsorption Dongchao Wang,ab Li Chen,*ab Hongmei Liu,b Xiaoli Wang,b Guangliang Cui,b Pinhua Zhang,b Dapeng Zhaoc and Shuaihua Jic Based on first-principles calculations, we systematically investigated the topological surface states of Bi and Sb thin films of 1–5 bilayers in (111) orientation without and with H(F) adsorption, respectively.
Received 6th October 2014, Accepted 9th December 2014
We find that compared with clean Bi and Sb films, a huge band gap advantageous to observe the
DOI: 10.1039/c4cp04502e
quantum phase transition from trivial (non-trivial) to non-trivial (trivial) phase is induced for a three
quantum spin Hall effect can be opened in chemically decorated bilayer Bi and Sb films, and the bilayer Bi film and single (four) bilayer Sb film. Surface adsorption is an effective tool to manipulate the
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geometry, electronic structures and topological properties of film materials.
Introduction Topological insulators (TIs) as newly discovered quantum states have gained wide attention in condensed matter physics.1–4 Among them, two-dimensional (2D) TIs have been proposed as candidates to achieve the quantum spin Hall (QSH) effect, due to a unique spin-dependent conducting channel of edge states protected by time-reversal invariance. To date, some 2D layered film materials have been predicted to observe the QSH effect, such as planar graphene,5 low-buckled silicene and germanene.6 As a result of weak spin–orbit coupling (SOC) in the aforesaid elements, the band gap is just several meV too small to realize the QSH effect at room temperature (RT). As they show strong SOC, heavy metal bismuth (Bi)7,8 and antimony (Sb)9 films are attracting more interest and are proposed to be TIs. Experimentally, Bi10 and Sb11 films have been grown on various substrates. However, the above TIs have finite band gaps, theoretically 60–70 meV for a single bilayer (BL) Bi film opened by SOC, which is disadvantageous to observe the QSH phase experimentally at RT, preventing their applications in electronic devices. Therefore, devoting more effort to manipulating the electronic structure and enlarging the band gap of Bi and Sb films is expected. Previous work12–14 shows that introducing an external electric field and strain are useful ways to modulate the electronic structure and topological properties of Bi and Sb films, while the effect of electric field and strain is unapparent in increasing
a
School of Physics, Shandong University, Shandong 250100, China. E-mail: [email protected] b Institute of Condensed Matter Physics, Linyi University, Shandong 276000, China c State Key Laboratory of Low Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
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the bulk gap of 2D TIs. Moreover, the effect of substrate is an unavoidable factor during the experimental growth process. On various substrates, the Bi BL film will show different topological phases,15 i.e. it is a TI on hexagonal-BN and shows a metallic phase on a Si or Ge substrate. The topological edge states are preserved even after strong hybridization with the 3D TI Bi2Te2Se substrate,16 however, the band gap of the pristine Bi BL is replaced with a small hybridization gap. Recently, chemical decoration by hydrogen, halogens and other functional groups has been proposed to be an efficient way for both modulating the topological edge states and enlarging the bulk gap, as in graphane or fluorinated graphene compared with graphene. For example, with H edge adsorption, the transport properties of the topological edge states of Bi BL nanoribbons can be well enhanced,17 and depending on the concentration of adatoms, the edge states can be changed from localized to delocalized in real space.18 When the adatoms are adopted on both sides of the 2D film, functionalized germanene,19 stanene20 and Bi21 are found to have larger band gaps than the pristine cases, up to 0.3 eV for fluorinated stanene. In addition, a H terminated 1BL Ge film has been successfully synthesized,22 which provides inspiration to experimentally grow chemically modified Bi and Sb films with huge band gaps. However, the above decorations on 2D films are just for the single BL case. In our work, both single and multi-BL pristine and functionalized films of Bi and Sb are systematically investigated based on first-principles calculations. For pristine Bi and Sb films, the properties of surface and edge states change with the thickness of the films. Depending on atomic adsorption by H and F atoms, huge non-trivial band gaps can be opened in chemically decorated Bi and Sb films, and the quantum phase transition from trivial (non-trivial) to non-trivial (trivial) phase is induced for a 3BL Bi film and a 1BL (4BL) Sb film.
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Methods and parameters First-principles calculations based on density functional theory were performed by the Vienna ab initio simulation package (VASP).23 The Perdew–Burke–Ernzerhof (PBE)24 generalized gradient approximation (GGA) was used to describe the exchange–correlation potential. All calculations were carried out with an energy cutoff of 500 eV on the 18 18 1 k-point mesh. The vacuum layer was about 15 Å to eliminate the interactions between neighboring films. The structures were relaxed until the difference of the total free energy between two ionic steps was below 1 104 eV. The SOC was included in the self-consistent calculations of the electronic structure. To confirm the band topology and Z2 topological invariant, the ABINIT package was implemented.
Results and discussion Topological properties of Bi(111) thin films Geometry relaxation of free-standing Bi thin films in the range of 1 to 5BLs was primarily carried out. The top and side views of the stacked Bi(111) film structure is shown in Fig. 1(a). In such a structure, each Bi atom forms three equivalent covalent bonds with the three nearest-neighbor Bi atoms within the unit BL, while the interaction between neighboring BLs is through van der Waals forces.25 The optimized lattice constant of the Bi thin film as a function of film thickness is indicated by the black curve in Fig. 1(b). As the thickness increased, the values including lattice constant, buckling height and inter-BL distance will be much closer to those of the bulk geometry.26 This can be understood as follows: the thicker the film is, the stronger the coupling among different layers is, leading to reduced buckling height and inter-BL distance, and an increased corresponding lattice constant. Based on the optimized geometry of the Bi films, the dispersion relation is calculated as shown in Fig. 2. We find that both surface states of the 1BL and 2BL Bi films are semiconductors with positive band gaps as shown in Fig. 2(a) and (b). The direct and indirect band gaps are 0.635 eV and 0.543 eV for 1BL and 0.148 eV and 0.068 eV for 2BL, respectively. To detect the helical edge states clearly, we constructed nanoribbon structures with zigzag edges with preserved inversion symmetry for the 1BL and 2BL films, including 40 and 64 Bi atoms, respectively. The band structures
Fig. 1 (a) Top and side views of the layered Bi film. The dark red, light sea green and purple spheres indicate 1st, 2nd and 3rd layer Bi atoms, respectively. (b) Lattice constant of Bi (black) and Sb (red) films as a function of the film thickness.
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Fig. 2 (a) and (b) Band structures of the 1BL and 2BL Bi thin films, respectively. (c) and (d) Band structures of the zigzag nanoribbons of the 1BL and 2BL Bi thin films, respectively.
of the nanoribbons are shown in Fig. 2(c) and (d). Degenerate conducting edge states can be observed near the Fermi level in both the 1BL and 2BL Bi nanoribbons, indicated by the blue color. The helical edge states are robust against backscattering which is very helpful in applications for electronic devices. Insulating surface states and conducting edge states of the film systems show that both the 1BL and 2BL Bi films are intrinsic 2D TIs. However, when the thickness goes beyond 3BL the indirect band gap of the film becomes negative, showing a metallic character, unlike 1BL and 2BL.8 Although the 1BL and 2BL Bi films were theoretically confirmed to be 2D TIs above, on the experimental side, the band gaps are too small to achieve the QSH effect at RT. Therefore, finding a way to enhance the band gap but not change the topological nature is helpful to observe the QSH effect. Chemical decorating is an effective way to manipulate the lattice and electronic structure in both device design and material selection.19,20 There are 2 choices for surface adsorption of 2D films: single-side adsorption and double-side adsorption. When the adatoms are adopted only on one surface of the 2D film, a dipole electric field will be produced due to the charge transfer between the adatoms and film surface. However, if the adatoms are put on both surfaces of the film to reserve the inversion symmetry, the dipole field can be removed. Therefore, we here emulate the double-side case to preserve the inversion symmetry of the 2D TI films. Moreover, the choice of adatoms is of vital importance. Different adatoms will induce diverse reconfiguration of the lattice structure and the transition of the topological phase. It is skillful to realize 2D TIs with huge band gaps and other properties via choosing suitable adatoms. Given the preexisting experience and experimental availability, H and F atoms are good options to emulate surface adsorption.22,29 We chose H and F atoms as the chemical functional groups, which easily saturate the dangling bonds from the sp3 hybridized Bi atoms as shown in the top and side views of the single BL case in Fig. 3(a) and (b), respectively. The H(F) atoms are bonded to the Bi atoms on both sides of the BL slab in an alternating way.
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mentioned above. For the 2D TI phase, the topological invariant is calculated from the parities of the Bloch wave functions for occupied bands at all time-reversal invariant points, one G and three M points, as di ¼
N Y
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m¼1
Fig. 3 Lattice geometry of the decorated 1BL Bi thin film from the (a) top view and (b) side view. The blue balls represent the Bi atoms and the celadon balls indicate the H(F) atoms. Band structures of the 1BL Bi thin films with (c) H and (d) F adsorption. The solid red lines and solid black lines indicate the calculations without SOC and with SOC, respectively.
All the new configurations of the chemically decorated Bi thin films are optimized to obtain stable structures. It is found that the H adsorbed 1BL Bi film has a quasi-planar structure for which the buckling height is 0.073 Å, much smaller than that of the pristine 1BL Bi thin film discussed above, while the lattice constant of the Bi film with H adsorption is 5.56 Å, enlarged 27.5% relative to the pristine Bi film. In addition, the Bi–H bond length is optimized to 1.823 Å. Based on the structural relaxation, the band structure of the H adsorbed Bi film in Fig. 3(c) is calculated without and with SOC which plays an important role in TIs. Noticeably, when SOC is excluded, a Dirac point appears at the Fermi level at the K point, indicated by the solid red lines. When SOC is switched on, one splitting at the Dirac point at the K point is observed in the solid black lines shown. Such splitting is a result of the first order relativistic effect related to Bi elements, which is robust against perturbation.21 According to partial band projections, the states without SOC around the Fermi level at the G point are mainly influenced by the atomic px and py orbitals of the Bi atoms. As the SOC effect is taken into account, the degeneracy of the energy level is lifted, opening two band gaps above and below the Fermi level. This originates from the variation of the atomic orbital component of the splitting bands. Taking the two splitting bands above the Fermi level as an example, the upper one at G remains composed of px and py orbitals, while the weight of the s orbital is added in the lower one as well as the original px and py orbitals. Therefore, such variation leads to a change of band potential that reshapes the band configuration at the G point. It is also because the s, px and py orbitals are mixed in the lower of the two splitting bands below the Fermi level. The band reshaping at the K and G points around the Fermi level induces an indirect SOC band gap of 1.08 eV, which is largely increased compared with that of the pristine Bi film. The presence of insulating surface states makes it possible for the decorated Bi thin film to be a 2D TI. Another effective way to distinguish non-trivial TIs from ordinary insulators is by calculating the topological invariant n proposed by Fu and Kane,28 except for simulating the edge states of the nanoribbons
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xi2m ðKi Þ; ð1Þn ¼
4 Y
di ¼ dðGÞd3 ðMÞ;
(1)
i¼1
where x2m = 1 denotes parity eigenvalues and N is the number of occupied bands. n = 0 characterizes a trivial insulator, while n = 1 indicates a non-trivial phase. Thus, the topological invariant mentioned above is calculated to determine the topological phase of the 1BL Bi film with adsorbed H atoms. The results show that the H adsorbed Bi film has a non-trivial band topology with the topological invariant v = 1. This non-trivial topological phase is similar to that of graphene with SOC taken into account, which is one kind of Kane–Mele type QSH phase. However, for the pristine 1BL Bi film the non-trivial band topology is due to band inversion undergoing gap closing at certain SOC strengths. Given the feasibility of observing the QSH effect at RT, the Bi hydride with a huge SOC gap should be one of the preferential candidates. Among the adopted atoms, the halogens are also a good choice because of their active chemical properties. The lattice constant of the 1BL Bi film with F adsorption is reduced to 5.39 Å, compared with 5.56 Å for the H adsorbed Bi film. Since the electronegativity of F is larger than that of H, the bonding between Bi and F is stronger than that between Bi and H. The buckling height is decreased to 0.407 Å compared with the freestanding Bi film, meaning that a low buckled geometry is more stable for the fluorinated Bi film. The Bi–F bond length slightly increases to 2.114 Å due to the larger covalent bond radius of F atoms. Subsequently, the band structures are also calculated based on the optimized lattice structure without and with SOC as shown in Fig. 3(d). As for H adsorption, a Dirac point also appears at the Fermi level at the K point in the Brillouin zone for the F adsorbed Bi film without SOC, denoted by the solid red lines. The bands at the Dirac point and the G point split away when the SOC is taken into consideration, as shown by the solid black lines, inducing an indirect SOC gap of 1.04 eV which is slightly less than that of the H adsorbed Bi film. According to partial band projections we find that, different from H adsorption, the states without SOC near the Fermi level contain the px and py orbitals of the F atoms besides those of the Bi atoms. The band splitting at the G point induced by SOC results from the additional s and pz orbitals of the F atoms, along with the px and py orbitals of the F and Bi atoms in the lower band, leading to different energy levels. Consequently, the band splitting at G in the F adsorbed Bi film is slightly larger than that in the H adsorbed film. Based on analysis of the total parities of the occupied bands, the topological invariant v is 1, indicating a non-trivial topological state for the Bi film decorated by F atoms. Therefore, it is also possible to realize the QSH effect in the 2D low buckled F adsorbed Bi film with a sizable bulk band gap. In the same way, the H atoms are adsorbed on both surfaces of the 2BL Bi film. Compared with the pristine case, the film structure is reshaped. The lattice constant changes from 4.52 Å
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to 5.27 Å, while both the intra-BL and inter-BL distances decrease by B0.7 Å, meaning stronger coupling between neighboring layers. In terms of structure, the influence of H atoms on the 2BL Bi film is obviously less than that of 1BL. Then, the band structure of the 2BL film modified by H atoms with SOC is calculated, which shows that there is an indirect band gap of 0.09 eV. The geometry of the 2BL Bi film decorated by F adsorption is slightly compressed at the surface but expanded vertically, which is like the case of the 1BL with adsorbed H and F atoms. By calculating and analyzing the band structure of the 2BL Bi film adsorbed by F atoms, the top of the valence bands and the bottom of the conduction bands overlap indirectly, showing metallic character. To sum up, H and F adsorption has a great influence on the geometries and band structures of the Bi films, and the effect of H adsorption is slightly stronger than that of F adsorption. Although the bulk gap has been enlarged by H adsorption relative to the free-standing 2BL Bi film, it is much less than that of the H adsorbed 1BL Bi film, too small to observe the QSH effect. In previous studies, most work chose the 1BL Bi film as an object to modulate the electronic structure and edge state.15–17,21 However, the modulation of multilayer films is still very important for device choice and design for various applications. With the thickness increased, we find that the effect of adatoms on the geometry of the Bi film becomes weaker and weaker. Unlike the 1BL and 2BL films, the 3BL case is just slightly reconfigured by H adsorption. However, the band structure is largely changed. Compared with the free-standing 3BL film which is semimetallic with a negative indirect band gap as shown in Fig. 4(a), the film with H adsorption becomes a semiconductor with the bands at the G point opened and the bands at the K point becoming close to each other as shown in Fig. 4(b), inducing an indirect gap of 0.33 eV. The topological invariant calculated from the parities of the occupied bands is 1, indicating a non-trivial band topology. When the F atoms are adsorbed on the top and bottom surfaces of the 3BL Bi film, the geometry parameters are much closer to those of the pristine film. Although the intrinsic character is not varied, the band structure is reshaped. As shown in Fig. 4(c), the bottom of the conduction bands at the K and M points shift downward below the Fermi level, while the top of the valence bands shifts upward above the Fermi level, keeping the semimetallic properties. With the thickness increased, the influence of adatoms on
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the lattice structure of the multi-BL films beyond 3BL is limited. When H atoms are adopted on the surfaces of the 4BL and 5BL films, a negative indirect gap appears with the bands shifted to overlap around the Fermi level with respect to the decorated 3BL film, showing a clear sign of a semimetal, though the shape of the bands is similar to the 3BL case. When the F atoms are adsorbed, the band structures of the 4BL and 5BL films are like that of 3BL, showing semimetallic properties. On the whole, by investigating systematically single and multi BL Bi films without and with chemical decorating, surface adsorption is proposed to be an effective tool to modulate the topological surface states of 2D films for device applications. Topological properties of Sb(111) thin films Sb, being in the same group as Bi, also has strong SOC. The Sb(111) film geometry is analogous to the Bi(111) film geometry of buckling hexagonal honeycomb shown in Fig. 1(a). From the structural relaxation, the lattice constants of the 1–5BL films are shown in Fig. 1(b) as the red curve, which are generally smaller than those of the Bi films due to the smaller atomic radius of Sb. The parameters obtained from the optimization are in good agreement with an earlier study.27 Then, the band structures of the 1–5BL Sb films were calculated, which are shown in Fig. 5. For the 1BL Sb thin film in Fig. 5(a), the bulk gap is very large, up to 2.621 eV, and the surface splitting indicated in blue reaches 1.324 eV at the G point. The direct gaps of surface splitting in the 2–5BL films as shown in Fig. 5(d), are 0.323 eV, 0.039 eV, 0.016 eV and 0.008 eV, respectively. It is essential for a well-defined Z2 number that the direct gap always remains open at the G point. According to the parity analysis, the topological invariant n = 0 for the 1–3BL films, meaning they are ordinary insulators, while n = 1 for the 4–5BL films showing that they are non-trivial insulators. The same chemical decorating is employed for the Sb films with different thicknesses, since Sb has strong SOC being in the same group as Bi. Firstly, the lattice structure of a single BL Sb film with H atoms adsorbed on both surfaces is optimized. A quasi-planar geometry is also confirmed to be stable with the buckling height of 0.081 Å, which is slightly larger than that of the Bi film with H adsorption. The lattice constant of the H adsorbed Sb film is 5.29 Å, much larger than that of the pristine Sb film (4.12 Å), indicating that the bonding between Sb atoms becomes weaker due to the H atomic adsorption. Owing to the
Fig. 4 Band structures of the 3BL Bi thin films: (a) the pristine case, (b) with adsorbed H atoms, and (c) with adsorbed F atoms.
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Fig. 5 Band structures of (a) 1BL, (b) 2BL and (c) 4BL Sb thin films. The blue curves indicate the surface states of the Sb thin films within the bulk gap. The inset in (c) is the enlargement of the surface states at G. (d) Surface splitting as a function of film thickness.
smaller covalent bond radius of Sb atoms, the Sb–H bond length decreases to 1.733 Å relative to that of the Bi film with H adsorption. As for the H adsorbed Bi film, the SOC effect on the H adsorbed Sb film was also researched. In Fig. 6(a), the band structure is shown without SOC and with SOC, denoted by the solid red and black lines, respectively. Obviously, the Dirac point which is closed without SOC at the K point is opened by the SOC effect, inducing a direct bulk band gap of 0.48 eV.
Fig. 6 Band structures of the 1BL Sb thin film with adsorbed (a) H atoms and (b) F atoms, the 2BL Sb thin film with adsorbed (c) H atoms and (d) F atoms, and the 4BL Sb thin film with adsorbed (e) H atoms and (f) F atoms. The solid red lines and solid black lines indicate the calculations without SOC and with SOC, respectively.
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The results of calculating the parities show that the topological invariant shifts from 0 in the pristine Sb film to 1 in the single BL Sb film with H adsorption. This results in a quantum phase transition from an ordinary insulator to a non-trivial topological phase driven by H adsorption. Then, the H atoms are replaced with F atoms bonded on the 1BL Sb film. After the geometry is fully optimized, the obtained lattice constant, buckling height and Sb–F bond length are 5.16 Å, 0.279 Å and 1.977 Å, respectively. The structural reconfiguration follows the rule discussed above in the H and F adsorbed 1BL Bi films. The band structures are calculated without and with SOC as shown in Fig. 6(b). The direct SOC gap is 0.39 eV at the K point, slightly less than that of the Sb film with H adsorption. Analysis of the parities also shows that the topological invariant is 1, indicating that the 1BL Sb film with F adsorption is also in a non-trivial topological state, like that with H adsorption. Compared with the pristine Sb film in Fig. 5(a), the band structure of the films with H and F adsorption is largely changed with the direct gap shifted from the G point to K point. Surface adsorption that induces topological phase transition from a trivial to non-trivial insulator is proved to be useful for modulating the topological phase. For the 2BL Sb film with H and F adsorption, the geometry is also fully relaxed, and the reconfiguration follows the rule discussed above. Based on the optimized structures, the dispersion relation of H and F adsorption including SOC is plotted in Fig. 6(c) and (d), respectively. We find that the band gap opened previously in the pristine film closes between the K and G point, inducing a semimetallic state for both H and F adsorption. Compared with the Bi film, the effect of surface adsorption is relatively weak in the Sb film due to the stronger SOC of Bi. The same calculation is employed for the 3BL and 4BL Sb films. As the thickness increases, the bonding between neighboring layers becomes strengthened. Therefore, the structural reconfiguration by H and F adsorption is not apparent as for 1BL and 2BL. However, the effect of H and F adsorption on the electronic structure is still as great as that of 1BL and 2BL. The 3BL Sb film is transformed from a normal insulator to a semimetal with the band gap closed by adatoms like in 2BL. On the other hand, the 4BL film with H and F adsorption turns into a semimetal, as shown in Fig. 6(e) and (f), from a 2D TI, losing the non-trivial band topology. It is proven once again that surface adsorption can realize the mutual transition between the trivial and non-trivial phase. For the 5BL film, the effect of H and F adsorption is different. In the presence of F adsorption, there is a negative band gap like for 3BL and 4BL, showing a semimetallic character, whereas the gap is enlarged by H adsorption up to 0.07 eV. The topological invariant is also calculated, showing a non-trivial band topology for the 5BL film with H adsorption. This also shows that the effect of H adsorption on the electronic properties is slightly stronger than that of F adsorption to reach our desired purpose. Previous studies8 showed that the Bi(111) film represents a special class of system having an intermediate inter-BL coupling strength, which has a significant influence on its topological properties. The stronger the inter-BL coupling is, the larger the band gap becomes. In our study, the inter-BL coupling strength will be changed for the Bi and Sb thin films by atomic adsorption,
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correspondingly leading to changes in the topological properties. Here, we take the 2BL and 3BL Bi films as an example. For the pristine 2BL film, the intra-BL and inter-BL distances are 1.72 Å and 3.00 Å, which means a weak inter-BL coupling regime. When H atoms are adsorbed on the Bi atoms of both surfaces, these two distances are 1.03 Å and 2.3 Å, which are decreased largely, meaning a stronger intra-BL and inter-BL coupling. Therefore, the enhanced coupling strength induces a larger band gap than that of the pristine film. Similarly, the phenomenon is also observed in the 3BL film. The intra-BL and inter-BL distances of the pristine film are 1.69 Å and 2.72 Å, respectively. They are 1.58 Å and 2.50 Å in the H adsorbed film, meaning slightly stronger inter-BL coupling in the adsorbed configuration. Furthermore, the influence of H and F adsorption on the same BL film is also diverse. For the 2BL Bi film, the intra-BL and inter-BL distances after F adsorption are 1.59 Å and 2.35 Å, slightly larger than those after H adsorption. For the 1BL Sb film, the interlayer coupling driven by surface adsorption is more obvious. In the pristine case, the Sb film has a buckling height of 1.65 Å, while it becomes much flatter for the H or F adsorbed film. The interlayer coupling strength is so strong that the band structure is drastically reshaped and then the parities of the occupied bands are inverted, leading to a non-trivial phase. On the other hand, the atomic orbitals and the SOC effect result in the difference in the properties of the H and F adsorbed film, as discussed above. Such analysis can be extended to other multi-BL Bi films and multi-BL Sb films. Taking the 4BL Sb film as an example, the bands around the Fermi level between the K and G points after F adsorption contain a greater contribution from the pz orbital of the F atoms, pushing the bands down more than after H adsorption. Compared with the pristine film, due to the introduction of the s orbital of the H atoms or the pz orbital of the F atoms, the bands near the Fermi level away from the G point are warped, leading to a semimetal. For the 5BL Sb film after H adsorption, more subbands turn into the same energy window than in the 4BL film. Stronger band hybridizations interplay, shifting the bands towards the Fermi level. There is a greater s orbital component in the lower states near the Fermi level between the K and G points, opening a small indirect band gap. The F adsorbed 5BL Sb film also becomes a semimetal like the F adsorbed 4BL film, with the bands between the K and G points shifting down below the Fermi level coupling by the contribution of the pz orbital of the F atoms. Therefore, both H and F adsorption play an important role in the electronic structure and quantum phase transition of film systems. More research is expected to be carried out with Cl, Br, I and other gaseous functional groups in the future. Experimentally, although the halides of Bi and Sb (F, Cl, Br and I) have been synthesized in 3-dimensions, such 3D halides are not stable once the temperature is beyond the experimental one such as room temperature.30–33 As far as we know, chemically decorated Bi and Sb films have not been experimentally reported. Recently, pristine Bi and Sb ultrathin films have been grown on Bi2Te3(111)10,34 and Si(111)11,35 substrates, respectively. Therefore, chemically decorated Bi and Sb films may be realized by exposing pristine Bi and Sb
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films to atomic and molecular gases or by chemical reaction in solvents, which is analogous to germanene.22 The effective use of chemical functional groups is a significant tool to modulate the lattice and electronic structures and the topological properties of various insulating and conducting materials.
Conclusions In conclusion, we have systematically studied the topological surface states of pristine and chemically decorated Bi and Sb thin films of 1–5BLs in the (111) orientation without and with atomic (H and F) adsorption. The results show that a huge band gap, beneficial for observing the QSH effect at RT, is induced in the 1BL Bi and Sb films after H and F adsorption. On the other hand, the topological phase transition from a trivial (nontrivial) to non-trivial (trivial) insulator is driven by both H and F adsorption in the 3BL Bi film and 1BL (4BL) Sb film. For the other BL Bi and Sb films, the analogous quantum phase transition is also driven from semiconductor to semimetal, such as the F adsorbed 2BL Bi film, along with the H(F) adsorbed 2BL and 3BL Sb films. Therefore, atomic adsorption is proposed to be an effective method to enlarge the band gap of 2D TIs and modulate the topological phase transition of Bi and Sb thin films. More novel properties may be discovered by using other chemical functional groups, such as gases and transition metals. The artificial modulation of electronic properties will be helpful for the potential applications of Bi and Sb thin films in nanoscale devices.
Acknowledgements We thank the financial support from the National Natural Science Foundation of China (Grant No. 51431004, 11274151, 11147007, 11204120 and 11404058), from the Open Research Program of the State Key Laboratory of Low-Dimensional Quantum Physics of Tsinghua University (Grant No. 20120924) and the Key Disciplines of Condensed Matter Physics of Linyi University.
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