Intrinsic Nernst Effect from Berry Curvature in Superconductors

Abstract

The Nernst effect in superconductors is typically linked to fluctuating Cooper pairs above $T_c$ or vortex motion below $T_c$. We show instead that Berry curvature of Bogoliubov quasiparticles can generate an intrinsic Nernst response in a clean, vortex-free superconducting state. Focusing on two-dimensional (2D) systems with Ising spin-orbit coupling, relevant to transition-metal dichalcogenides, we identify two regimes: an intervalley $s$-wave paired state where a weak magnetic field activates the effect, and an intravalley chiral $p$-wave paired state that exhibits a spontaneous charge or spin Nernst response without a field. We propose an experimental setup that circumvents screening and provide estimates of the signal magnitude. Our results establish the Nernst effect as a direct probe of Berry curvature and pairing symmetry in 2D spin-orbit-coupled superconductors.

Figures (3)

• Figure 1: (a) Schematic of the proposed geometry for measuring Nernst effect in the superconducting state. A radial thermal gradient $\nabla_{\bf r} T\neq 0$ induces a transversal loop current ${\bf j}$, which generates a detectable out-of-plane magnetic flux $\Phi_{\rm th}$. (b) Intervalley $s$-wave and (c) intravalley $p$-wave pairings of the dominant low-energy bands in a type-II Ising superconductor. $K$ and $K'$ are time-reversal-related valleys, and $\mu$ is the chemical potential. In panel (b), the subscripts of $\mu$ label three distinct doping regimes discussed in the text and in Fig. \ref{['fig2']}.
• Figure 2: Properties of intervalley $s$-wave pairing. Upper panels: (a) $\alpha_H(\lambda_{\rm so}k_0,\mu)$ with $k_0=\lambda_{\rm so}/2t$, $\beta_{\rm so}=7$, $t=500$ , $T=1$, $\Delta=1$ and $h=0.5$. (b)-(d) $\alpha_H(\lambda_{\rm so}k_0,\beta_{\rm so})$ with the same parameters as in (a), but with chemical potentials $\mu_1 = 4 - \beta_{\rm so}$, $\mu_2=0$, $\mu_3 = 2 + \beta_{\rm so}$, corresponding respectively to the three doping regimes in Fig. \ref{['fig1']}(b). The dashed line in (b) marks $\beta_{\rm so}=\lambda_{\rm so}k_0$. Lower panels: (a) Berry curvature $\Omega_k$ ($\Omega_k^{K,K'}=\pm|\Omega_k^{K,K'}|$) and (b)-(d) the energy dispersion $E_k$ for the K (solid) and K' (dashed) valleys in the lower BdG band, with parameters matching the blue markers in the upper panels. Units: meV for energies, $a^{-1}$ ($a$ lattice constant) for $k$, $a^{-2}$ for $\Omega_k$, ${\rm meV}\cdot a^2$ for $t$, and $\alpha_0$ for $\alpha_H$.
• Figure 3: Properties of intravalley chiral $p$-wave pairing. (a) Berry curvature and (b) the corresponding lower BdG band near the $K$ valley, with the Fermi momentum $k_F=0.1$ and color indicating the quasiparticle charge $\rho_k$, calculated using the parameters of the blue triangle in (c). (c) $\alpha_H$ for $\beta_{\rm so}<0$, $T=1$, $t=500$, and $\lambda_{\rm so}=h=0$. Units: meV for energies, $a^{-1}$ for $k$, $a^{-2}$ for $\Omega_k$, ${\rm meV}\cdot a^2$ for $t$, and $\alpha_0$ for $\alpha_H$.