Apparent double-$T_c$ from a single BKT transition in anisotropic phase-only models

TL;DR

This study shows that apparent double transition temperatures in 2D superconductors can arise from finite-size and dynamic effects in models, not necessarily indicating true thermodynamic splitting.

Contribution

We demonstrate that anisotropic Josephson-junction array models exhibit a single BKT transition, with apparent double-$T_c$ arising from finite-size and dynamic effects, not multiple true transitions.

Findings

Equilibrium model exhibits a single BKT transition.

Out-of-equilibrium effects reshape $R$--$T$ curves, causing apparent double-$T_c$.

Critical scaling criteria remain consistent with a single $T_{ ext{BKT}}$.

Abstract

Transport experiments on two-dimensional superconductors often yield direction-dependent transition temperatures, raising the question of whether such a ``double-$T_c$'' reflects a true thermodynamic splitting or a transport artifact. To establish a baseline, we study a minimal anisotropic phase-only Josephson-junction array in equilibrium and under resistively shunted junction dynamics with fluctuating twist boundary conditions. The equilibrium model exhibits a single Berezinskii--Kosterlitz--Thouless (BKT) transition. Out of equilibrium, anisotropic Josephson couplings and anisotropic dissipation reshape the linear $R$--$T$ curves in a finite-size, finite-current crossover regime, so that curve-shape criteria such as Halperin--Nelson fits and fixed-resistance thresholds yield an apparent double-$T_c$. In contrast, critical-scaling criteria -- the universal exponent $\alpha=3$ and dynamic finite-size scaling -- remain consistent with the single $T_{\mathrm{BKT}}$. A robust splitting that persists in the nonlinear critical scaling, such as that recently reported at KTaO$_3$ interfaces, therefore points to physics beyond this clean anisotropic baseline.