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

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 $π$-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 $π$-rings.

💡 Research Summary

The Little‑Parks (LP) effect—periodic oscillations of the superconducting transition temperature with magnetic flux Φ threading a cylinder or ring—has long been understood within Ginzburg‑Landau theory as a manifestation of the Aharonov‑Bohm phase of the order‑parameter. Recent experiments on thin‑film materials such as β‑Bi₂Pd, α‑BiPd, TaS₂, and others have reported a half‑quantum (π) shift of the LP oscillations, i.e., the resistance minima occur at Φ = (n + ½) Φ₀ instead of the conventional integer multiples of the flux quantum Φ₀ = h/2e. These observations have been interpreted as signatures of unconventional pairing (spin‑triplet, chiral) that can generate an intrinsic π‑phase winding.

However, all reported measurements were performed on quasi‑two‑dimensional flakes at temperatures close to the onset of finite resistance, i.e., near the Berezinskii‑Kosterlitz‑Thouless (BKT) transition. Near BKT, thermally excited vortex‑antivortex pairs proliferate, and free (unbound) vortices dominate the dissipative response. The authors therefore ask whether the half‑quantum shift can arise purely from vortex physics without invoking exotic pairing symmetries.

To answer this, they construct a vortex‑charge duality description of a 2D superconductor near the BKT point. Starting from the phase‑only action S = ∫dτ d²r J