Negative refraction and superconductivity

Abstract

We discuss exotic properties of charged hydrodynamical systems, in the broken superconducting phase, probed by electromagnetic waves. Motivated by general arguments from hydrodynamics, we observe that negative refraction, namely the propagation in opposite directions of the phase velocities and of the energy flux, is expected for low enough frequencies. We corroborate this general idea by analyzing a holographic superconductor in the AdS/CFT correspondence, where the response functions can be explicitly computed. We study the dual gravitational theory both in the probe and in the backreacted case. We find that, while in the first case the refractive index is positive at every frequency, in the second case there is negative refraction at low enough frequencies. This is in agreement with hydrodynamic considerations.

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.…”

“…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. Interestingly, the inclusion of the backreaction can make Im(μ) positive [19,29,31]. We will leave this subject for future research.…”

“…Using the shooting method, we can solve the equations of motion (19) and (20) numerically and then examine the effect of the Born-Infeld electrodynamics on the negative refraction. For concreteness, we will set ξ = 0.2 for the fixed mass of the scalar field m 2 = −2.…”

“…Using the AdS/CFT correspondence, Gao and Zhang investigated the optical properties in the s-wave superconductors and found that the negative refraction does not appear in these holographic models in the probe limit [18]. 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].…”

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.…”