Microwave Kerr/Faraday Resonance in Two-dimensional Chiral Superconductors

Abstract

We investigate the polar Kerr and Faraday effects in two-dimensional multiband chiral superconductors. We show that the clapping modes--the relative phase and amplitude oscillations between two chiral components of the superconducting order parameter--lie well within the quasiparticle excitation gap in multiband systems and dominate these magneto-optical responses in the microwave regime. The Kerr and Faraday rotation angles exhibit the resonant enhancement with sign reversals in the microwave regime as a function of the light frequency, reaching peak values on the order of 100 nrad--10 $μ$rad in thin films of candidate chiral superconductors. These resonances are accessible in superconducting atomic layer materials and provide a generic probe of chiral superconductivity in two-dimensional systems.

Figures (4)

• Figure 1: Diagrammatic representations of (a,b) the current-current correlation functions and (c) the effective interaction within the random phase approximation (RPA). Here, the dotted lines denote the electric current $J_{\mu}(\bm k)$ and $J_{\nu}(\bm k)$, the solid lines are the Gor'kov Green functions, and the thick (thin) wavy lines indicate the effective interaction $H_{\rm int}^{(\rm eff)}$ (the bare interaction $H_{\rm int}$).
• Figure 2: Crystal structure of the lattice model described by Eq. \ref{['HBdG']}. The black and grey circles represent the sublattices A and B, respectively.
• Figure 3: The $\omega$ dependence of the absolute values of the eigenvalues $\{\lambda_n (\omega)\}$ (dimensionless) of $1 + |V_{\rm int0}| \Pi^{\rm R}(\omega)$ for $t'/t=0.0, 5.0\times 10^{-2}, 5.0\times 10^{-1}$. In all panels (a-c), we set $t=1.25$ meV (bandwidth $E_{\mathrm B}\simeq8t=10\;\mathrm{meV}$; equivalently $E_{\mathrm B}/k_{\mathrm B}\simeq116\;\mathrm K$), $a=5$ Å, $T=0$ K, $M_z=0.5t$, $|V_{\rm int0}|=0.9t$, $\mu=2t$, and $\eta=1.0\times 10^{-4}t$. The gray shaded area indicates the quasiparticle continuum. The vertical lines indicate the Leggett (green, dotted), Higgs (blue, dashed), and clapping (red, solid) modes. Inset of panel (c) indicates the schematic image for the quasiparticle DOS, $N_s(\epsilon)$, with the smaller (larger) quasiparticle excitation gaps $2|\Delta_{\rm min}|$ ($2|\Delta_{\rm max}|$).
• Figure 4: The $\omega$-dependence of (a) the Kerr rotation angle and (b) Faraday rotation angle for $|V_{\rm int0}|/t=9.0\times 10^{-1},1.0,1.1,1.2$. The gray shaded area indicates the quasiparticle continuum. In all panels, we set $t=1.25\;\mathrm{meV}$ (bandwidth $E_{\mathrm B}\simeq8t=10\;\mathrm{meV}$), $a=5\;\text{\AA}$, $T=0\;\mathrm K$, $t'=M_z=0.5t$, $\mu=2t$, $\eta=1.0\times10^{-4}\;t$, and $n=1.45$.