Generalized superconductors and holographic optics

Abstract

Abstract:We study generalized holographic s-wave superconductors in four dimensional R-charged black hole and Lifshitz black hole backgrounds, in the probe limit. We first establish the superconducting nature of the boundary theories, and then study their optical properties. Numerical analysis indicates that a negative Depine-Lakhtakia index may appear at low frequencies in the theory dual to the R-charged black hole, for certain temperature ranges, for specific values of the charge parameter. The corresponding cut-off values for these are numerically established in several cases. Such effects are seen to be absent in the Lifshitz background where this index is always positive.

Refractive index in generalized superconductors with Born–Infeld electrodynamics

“…Obviously, Re( ) and Re(μ) are not simultaneously negative, which may be a signal of the negative refraction [23]. However, just as pointed out in [19,22,29], Im(μ) < 0 could imply some problem in the − μ approach, although we have defined an effective magnetic permeability that is not an observable. We will not comment on this further since this delicate issue is beyond the scope and the purpose of our work.…”

“…The behaviors of (23) is not very strictly satisfied and the caveat may be related to the appearance of a negative imaginary part of the magnetic permeability, just as pointed out in [22,29]. Though Markel proposed that Im(μ) (the loss term in the permeability) can in fact be negative for diamagnetic materials [70], it is worthwhile to have a better understanding of this point in our holographic approach.…”

“…When the Born-Infeld parameter b → 0, the model (3) reduces to the generalized holographic superconductors with the usual Maxwell electrodynamics investigated in [20][21][22].…”

“…However, in the fully backreacted spacetime, Amariti et al showed that the negative refraction is allowed in the superconducting phase [19]. Extending the investigation to the generalized holographic superconductors in which the spontaneous breaking of a global U (1) symmetry occurs via the Stückelberg mechanism [20,21], Mahapatra et al observed that a negative Depine-Lakhtakia index may appear at low frequencies in the theory dual to the R-charged black hole, which indi-cates that the system exhibits negative refraction even in the probe limit [22]. Other investigations based on the refractive index in the holographic dual models can be found, for example, in Refs.…”

Electromagnetic response of strongly coupled plasmas

“…The former implies that the electromagnetic energy flux and the phase velocity of an electromagnetic wave through the medium propagate in opposite directions [6,[12][13][14][15][16][17][18][19][20][21][22]; the latter means that, even if isotropic, a medium supports multiple electromagnetic waves with the same frequency but different wave-vectors [7][8][9][10][11]. Following these results, various authors investigated these topics in a wide variety of different setups, see for example [26][27][28][29][30][31][32][33][34][35][36]. In particular [37] provides an analysis of the actual signature of the abovementioned phenomena in condensed matter systems and it proposes suitable experiments to measure such effects.…”