Theory of Little-Parks oscillations by vortices in two-dimensional superconductors

TL;DR

This paper presents a vortex-based mechanism for Little-Parks oscillations in 2D superconductors near the BKT transition, explaining half-quantum flux shifts without requiring unconventional pairing symmetries.

Contribution

It introduces a vortex-charge duality model and Monte Carlo simulations to explain half-quantum flux shifts in 2D superconducting rings.

Findings

Half-quantum flux shifts can occur without unconventional pairing.

Vortex screening causes oscillation shifts depending on sample geometry.

The model predicts LP oscillations induced by vortices near the BKT transition.

Abstract

The Little-Parks (LP) effect is a quantum phenomenon in which the superconducting transition temperature of a superconducting cylinder (or ring) oscillates periodically as a function of the magnetic flux threading the loop. Recently, multiple experiments have observed half-quantum flux shifts in measurements of LP oscillations, where the oscillations are globally shifted by half a flux quantum compared to conventional cases, a behavior referred to as a $\pi$-ring. Such observations are commonly linked to unconventional pairing symmetries. In this work, we demonstrate that half-quantum flux shifts can arise in two-dimensional (2D) superconducting rings without invoking unconventional pairing symmetry, provided that vortices near the Berezinskii-Kosterlitz-Thouless (BKT) transition are taken into account. Specifically, based on the vortex-charge duality theory near the BKT transition, we map the problem onto a Coulomb gas model, in which the magnetic flux is represented as a pair of opposite boundary charges (or vortices) at the two edges. The screening of these boundary charges by thermally excited vortex-antivortex pairs is investigated through explicit Monte Carlo simulations. Importantly, we demonstrate that the oscillation of the free-vortex density as a function of magnetic flux can exhibit an anomalous half-quantum flux shift, depending on the geometry of the sample. Our work thus predicts the LP oscillations induced by vortices in 2D superconducting rings near the BKT transition, which provides a new mechanism for generating $\pi$-rings.