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Quantum topological transition in hyperbolic metamaterials based on high Tc superconductors
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 305701 (http://iopscience.iop.org/0953-8984/26/30/305701) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 132.203.227.63 This content was downloaded on 10/07/2014 at 08:32
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 305701 (6pp)
doi:10.1088/0953-8984/26/30/305701
Quantum topological transition in hyperbolic metamaterials based on high Tc superconductors Igor I Smolyaninov Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742, USA E-mail: [email protected] Received 11 March 2014, revised 18 May 2014 Accepted for publication 9 June 2014 Published 8 July 2014 Abstract
Hyperbolic metamaterials are known to exhibit a transition in the topology of the photon iso-frequency surface from a closed ellipsoid to an open hyperboloid, resulting in a considerable increase of the photonic density of states. This topological transition may also be described as a change of metric signature of the effective optical space. Here we demonstrate that high Tc superconductors exhibit hyperbolic metamaterial behavior in the far infrared and THz frequency ranges. In the THz range the hyperbolic behavior occurs only in the normal state, while no propagating photon modes exist in the superconducting state. Thus, a quantum topological transition may be observed for THz photons at zero temperature as a function of the external magnetic field, in which the effective Minkowski spacetime arises in the mixed state of the superconductor at some critical value of the external magnetic field. Nucleation of effective Minkowski spacetime occurs via the formation of quantized Abrikosov vortices. Keywords: superconductivity, metamaterial, topological transition (Some figures may appear in colour only in the online journal)
take into account its topology and symmetries, the language of ‘effective Minkowski spacetime’ appears to be quite convenient. In addition, this language establishes a connection between hyperbolic metamaterials and other condensed matter analogue models of gravity (see the recent extensive review [4] and the references therein). In some sense, hyperbolic metamaterials offer an interesting experimental window into the physics of Minkowski spacetimes [5–8]. However, because of the different natures of metamaterial and cosmological systems, there are no direct implications of metamaterial research on gravitational physics. Here we analyze electromagnetic properties of high Tc superconductors and demonstrate that they may exhibit hyperbolic metamaterial behavior in the far infrared and THz frequency ranges. Moreover, according to the calculations presented below, in the THz range the hyperbolic behavior occurs only in the normal state, while no propagating photon modes exist in the superconducting state. Therefore, we predict that a novel quantum topological transition may be observed for
Recent advances in electromagnetic metamaterials have revealed such fascinating optical effects as negative refraction and electromagnetic cloaking. Even more consequential for condensed matter physics appears to be the recent observation that hyperbolic metamaterials may exhibit a drastic transition in the topology of the photon iso-frequency surface, from a closed ellipsoid to an open hyperboloid [1]. This novel topological transition results in a considerable increase of the photonic density of states, which deeply affects both optical and electronic properties of the material. This topological transition may also be described as a change of metric signature of the effective ‘optical space’, via its metric signature transition [2]. Indeed, propagation of monochromatic extraordinary light inside a hyperbolic metamaterial is described by a wave equation, which exhibits 2 + 1 dimensional Lorentz symmetry. The role of time in the corresponding effective 3D Minkowski spacetime is played by the spatial coordinate, which is oriented along the optical axis of the metamaterial [2, 3]. Since the best description of a physical system must 0953-8984/14/305701+6$33.00
1
© 2014 IOP Publishing Ltd Printed in the UK
I I Smolyaninov
J. Phys.: Condens. Matter 26 (2014) 305701
THz photons in high Tc superconductors at zero temperature as a function of the external magnetic field. As a result of this quantum topological transition an effective Minkowski spacetime arises in the mixed state of the superconductor at some critical value of the external magnetic field. Nucleation of this effective Minkowski spacetime occurs via formation of quantized Abrikosov vortices. These results appear to be even more interesting given the fact that the actual physical Minkowski vacuum behaves as a somewhat similar superconducting hyperbolic metamaterial when subjected to very strong magnetic field [9, 10]. As a first step, let us demonstrate that the wave equation describing propagation of monochromatic extraordinary light inside a hyperbolic metamaterial does indeed exhibit 2 + 1 dimensional Lorentz symmetry. A detailed derivation of this result can be found in [2, 3]. We assume that the metamaterial in question is uniaxial and non-magnetic (µ = 1), so that the electromagnetic field inside the metamaterial may be separated into ordinary and extraordinary waves. Vector E ⃗ of the extraordinary light wave is parallel to the plane defined by the k–vector of the wave and the optical axis of the metamaterial. Since hyperbolic metamaterials typically exhibit strong temporal dispersion, we will work in the frequency domain and assume that in some frequency bands around ω = ω0 the metamaterial may be described by anisotropic dielectric tensor, having the diagonal components εxx = εyy = ε1 > 0 and εzz = ε2
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My IOPscience
Quantum topological transition in hyperbolic metamaterials based on high Tc superconductors
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 305701 (http://iopscience.iop.org/0953-8984/26/30/305701) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 132.203.227.63 This content was downloaded on 10/07/2014 at 08:32
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 305701 (6pp)
doi:10.1088/0953-8984/26/30/305701
Quantum topological transition in hyperbolic metamaterials based on high Tc superconductors Igor I Smolyaninov Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742, USA E-mail: [email protected] Received 11 March 2014, revised 18 May 2014 Accepted for publication 9 June 2014 Published 8 July 2014 Abstract
Hyperbolic metamaterials are known to exhibit a transition in the topology of the photon iso-frequency surface from a closed ellipsoid to an open hyperboloid, resulting in a considerable increase of the photonic density of states. This topological transition may also be described as a change of metric signature of the effective optical space. Here we demonstrate that high Tc superconductors exhibit hyperbolic metamaterial behavior in the far infrared and THz frequency ranges. In the THz range the hyperbolic behavior occurs only in the normal state, while no propagating photon modes exist in the superconducting state. Thus, a quantum topological transition may be observed for THz photons at zero temperature as a function of the external magnetic field, in which the effective Minkowski spacetime arises in the mixed state of the superconductor at some critical value of the external magnetic field. Nucleation of effective Minkowski spacetime occurs via the formation of quantized Abrikosov vortices. Keywords: superconductivity, metamaterial, topological transition (Some figures may appear in colour only in the online journal)
take into account its topology and symmetries, the language of ‘effective Minkowski spacetime’ appears to be quite convenient. In addition, this language establishes a connection between hyperbolic metamaterials and other condensed matter analogue models of gravity (see the recent extensive review [4] and the references therein). In some sense, hyperbolic metamaterials offer an interesting experimental window into the physics of Minkowski spacetimes [5–8]. However, because of the different natures of metamaterial and cosmological systems, there are no direct implications of metamaterial research on gravitational physics. Here we analyze electromagnetic properties of high Tc superconductors and demonstrate that they may exhibit hyperbolic metamaterial behavior in the far infrared and THz frequency ranges. Moreover, according to the calculations presented below, in the THz range the hyperbolic behavior occurs only in the normal state, while no propagating photon modes exist in the superconducting state. Therefore, we predict that a novel quantum topological transition may be observed for
Recent advances in electromagnetic metamaterials have revealed such fascinating optical effects as negative refraction and electromagnetic cloaking. Even more consequential for condensed matter physics appears to be the recent observation that hyperbolic metamaterials may exhibit a drastic transition in the topology of the photon iso-frequency surface, from a closed ellipsoid to an open hyperboloid [1]. This novel topological transition results in a considerable increase of the photonic density of states, which deeply affects both optical and electronic properties of the material. This topological transition may also be described as a change of metric signature of the effective ‘optical space’, via its metric signature transition [2]. Indeed, propagation of monochromatic extraordinary light inside a hyperbolic metamaterial is described by a wave equation, which exhibits 2 + 1 dimensional Lorentz symmetry. The role of time in the corresponding effective 3D Minkowski spacetime is played by the spatial coordinate, which is oriented along the optical axis of the metamaterial [2, 3]. Since the best description of a physical system must 0953-8984/14/305701+6$33.00
1
© 2014 IOP Publishing Ltd Printed in the UK
I I Smolyaninov
J. Phys.: Condens. Matter 26 (2014) 305701
THz photons in high Tc superconductors at zero temperature as a function of the external magnetic field. As a result of this quantum topological transition an effective Minkowski spacetime arises in the mixed state of the superconductor at some critical value of the external magnetic field. Nucleation of this effective Minkowski spacetime occurs via formation of quantized Abrikosov vortices. These results appear to be even more interesting given the fact that the actual physical Minkowski vacuum behaves as a somewhat similar superconducting hyperbolic metamaterial when subjected to very strong magnetic field [9, 10]. As a first step, let us demonstrate that the wave equation describing propagation of monochromatic extraordinary light inside a hyperbolic metamaterial does indeed exhibit 2 + 1 dimensional Lorentz symmetry. A detailed derivation of this result can be found in [2, 3]. We assume that the metamaterial in question is uniaxial and non-magnetic (µ = 1), so that the electromagnetic field inside the metamaterial may be separated into ordinary and extraordinary waves. Vector E ⃗ of the extraordinary light wave is parallel to the plane defined by the k–vector of the wave and the optical axis of the metamaterial. Since hyperbolic metamaterials typically exhibit strong temporal dispersion, we will work in the frequency domain and assume that in some frequency bands around ω = ω0 the metamaterial may be described by anisotropic dielectric tensor, having the diagonal components εxx = εyy = ε1 > 0 and εzz = ε2
