Fluctuation effect on Nonlinear Transport and Nernst-Ettingshausen Response in Two-Dimensional Superconductors under electric and magnetic field

TL;DR

This paper develops a theoretical framework for fluctuation-induced nonlinear transport and thermoelectric effects in 2D superconductors under electric and magnetic fields, revealing intrinsic S-shaped nonlinear responses and instability scales.

Contribution

It introduces a self-consistent Gaussian fluctuation theory incorporating electric field feedback, deriving explicit expressions for nonlinear current and resistance, and analyzing thermoelectric response in 2D superconductors.

Findings

Identification of an intrinsic S-shaped nonlinear $J$-$E$ characteristic.

Derivation of a criterion for the instability scale $B^{ ext{*}}$ where response becomes single-valued.

Validation of the theory through comparison with experimental data on $R(T)$, $I$-$V$, and $ ext{ extalpha}_{xy}$.

Abstract

In this paper, we present a unified theoretical study of fluctuation-dominated transport and transverse thermoelectric response in two-dimensional superconducting films subjected to out-of-plane magnetic fields and electric-field drive. Our approach is based on the time-dependent Ginzburg-Landau equation with Langevin thermal noise, in which interaction effects of fluctuating Cooper pairs are incorporated self-consistently at the Gaussian (Hartree) level. We derive closed-form expressions for the fluctuation-induced Cooper-pair density, the renormalized resistance $R(T,B_\perp)$, and the nonlinear current response $J(E,B_\perp)$, explicitly accounting for the feedback of the electric field on the fluctuation spectrum. A central result is the emergence of an intrinsic S-shaped nonlinear $J$-$E$ (or $I$-$V$) characteristic, featuring a negative-differential segment and multivalued solutions under voltage control. Within this framework, we introduce a physically transparent procedure to identify characteristic instability scales, such as the magnetic field $B^{\ast}$ (or equivalently $B_{\chi}$), which marks the terminal point of the S-shaped instability where the nonlinear response becomes single-valued. In parallel, we analyze the off-diagonal Peltier coefficient $\alpha_{xy}$ as a direct probe of the transverse thermoelectric response of superconducting fluctuations. The theory is validated through systematic comparisons with recent experimental measurements of multi-field $R(T)$ curves, nonlinear $I$-$V$ characteristics, and $\alpha_{xy}$ data across a broad range of thin-film superconducting materials.