Reveals Half-Flux Shifts in Little-Parks Oscillations of 2D Superconductors

Researchers are revisiting the Little-Parks effect, a periodic oscillation in the superconducting transition temperature of rings subjected to magnetic flux, to explain recently observed anomalies. Ying-Ming Xie and Naoto Nagaosa, both from the RIKEN Center for Emergent Matter Science, alongside et al., demonstrate that shifts in these oscillations, known as half-flux shifts or ‘-rings’ , do not necessarily require unconventional pairing symmetries within the superconducting material. Their work establishes a novel mechanism where these shifts arise from the behaviour of vortices near the Berezinskii-Kosterlitz-Thouless transition in two-dimensional superconducting rings, offering a new understanding of how these intriguing quantum effects manifest and potentially broadening the scope for designing novel superconducting devices.

Half-quantum flux shifts emerge from vortex screening in superconducting rings, creating unique magnetic properties

Scientists have demonstrated that half-quantum flux shifts, previously linked to unconventional pairing symmetries in superconductors, can arise in two-dimensional superconducting rings without requiring such exotic mechanisms. The research, published on February 2, 2026, establishes a new understanding of the Little-Parks (LP) effect, a quantum phenomenon where the superconducting transition temperature oscillates with changes in magnetic flux.
The team achieved this breakthrough by focusing on the behaviour of vortices near the Berezinskii-Kosterlitz-Thouless (BKT) transition, a critical point in 2D superconductivity. Specifically, the researchers employed vortex-charge duality theory, mapping the problem onto a Coulomb gas model where magnetic flux is represented by opposite boundary charges at the edges of the superconducting ring.

Through explicit Monte Carlo simulations, they investigated how these boundary charges are screened by thermally excited vortex-antivortex pairs. This approach allowed them to demonstrate that the oscillation of free-vortex density as a function of magnetic flux can exhibit an anomalous half-quantum flux shift, dependent on the sample’s geometry.

The study unveils a mechanism for generating π-rings, superconducting rings exhibiting the half-quantum flux shift, driven by vortex dynamics near the BKT transition. This work predicts LP oscillations induced by vortices in 2D superconducting rings, offering a novel explanation for experimental observations in materials like β-Bi2Pd, α-BiPd, TaS2, Bi/Ni bilayers, CsV3Sb5, and 2M-WS2.

The findings thus provide a new pathway for understanding and potentially controlling superconducting behaviour in thin-film devices and quantum circuits. This research establishes that the anomalous half-quantum flux shift can be driven by BKT physics without the need for unconventional pairing. The team constructed a vortex-charge duality theory and mapped the problem onto a two-dimensional neutral Coulomb gas model, representing magnetic flux as boundary charges.

By performing Monte Carlo simulations, they investigated the effects of these boundary charges, revealing that the free-vortex density oscillates periodically with magnetic flux, leading to LP behaviour. Importantly, the simulations demonstrated that the half-quantum flux shift can occur across a wide range of parameters through field-modified vortex dynamics near the BKT transition.

Modelling half-flux quantum shifts via thermally activated vortex-antivortex pair distributions reveals interesting phenomena

Scientists investigated the Little-Parks (LP) effect in two-dimensional (2D) superconducting rings, focusing on unexplained half-flux shifts observed in recent experiments. The study aimed to demonstrate that these shifts, indicative of unconventional pairing symmetries, could arise from vortex dynamics near the Berezinskii-Kosterlitz-Thouless (BKT) transition, without requiring exotic pairing mechanisms.

Researchers mapped the problem onto a Coulomb gas model, representing magnetic flux as pairs of opposite boundary charges located at the edges of the ring. To investigate the screening of these boundary charges, the team performed explicit Monte Carlo simulations to model thermally excited vortex-antivortex pairs.

The simulations calculated the bulk net charge distribution, ρ(y) = ρ+(y)−ρ−(y), induced by the boundary charges along the x-direction, using parameters chosen to yield a BKT transition temperature of approximately 0.18. Boundary charges were set to -0.5 and 0.5 at y = 0 and y = Ly respectively, and the length unit in simulations corresponded to the superconducting coherence length ξ.

Analysis of the charge distribution revealed a near-exponential decay away from the boundaries, suppressed as the ring length, Lx, increased. The temperature dependence of ρ(y) showed a rapid increase with temperature due to thermally excited charge pairs, maintaining overall charge neutrality. Researchers then analytically obtained the charge density profile using a Debye, Hückel approximation, confirming agreement with numerical results.

They defined the boundary-induced charge, Qbnd, and bulk-induced charge, Qbulk, to compare contributions from each region, finding they became comparable at Ly ∼20. Further experiments focused on the oscillation of free charge density, ∆nfree, as a function of magnetic flux, Φ/Φ0, to directly observe LP oscillations near the BKT transition.

A charge was defined as free if the distance to the nearest opposite charge exceeded a cutoff distance of 0.7, ensuring clear visibility of the LP oscillations. The team calculated nfree as the average number of free vortices over Monte Carlo measurements, revealing a crossover from 0-ring to π-ring behaviour as Ly varied, thus predicting a new mechanism for generating -rings.

Half-flux shifts emerge from vortex screening near the BKT transition temperature

Scientists have demonstrated that half-flux shifts, observed in Little-Parks (LP) oscillations of superconducting rings, can arise without requiring unconventional pairing symmetries. The research team investigated two-dimensional (2D) superconducting rings near the Berezinskii-Kosterlitz-Thouless (BKT) transition, utilising vortex-charge duality theory to map the problem onto a Coulomb gas model.

This approach represents the magnetic flux as pairs of opposite boundary charges, or vortices, at the edges of the ring. Experiments involved Monte Carlo simulations to investigate the screening of these boundary charges by thermally excited vortex-antivortex pairs. Results demonstrate that the oscillation of free-vortex density as a function of magnetic flux can exhibit an anomalous half-flux shift, dependent on the sample’s geometry.

The corresponding BKT transition temperature was measured to be approximately 0.18, with simulations conducted using parameters around this value. Detailed analysis of the bulk net charge distribution, ρ(y), revealed exponential decay away from the boundaries due to the presence of boundary charges. The team found that ρ(y) increases rapidly at higher temperatures, consistent with the excitation of positive and negative charge pairs, and always satisfies ρ(y) = −ρ(−y), confirming overall charge neutrality.

Analytical modelling using the Debye, Hückel approximation aligned well with numerical results, identifying a bulk region where ρ(y) varies linearly with y and a boundary region extending approximately 2 units of the superconducting coherence length, ξ. Measurements of the ratio between boundary-induced charge, Qbnd, and bulk-induced charge, Qbulk, showed they become comparable at a length Ly of approximately 20.

The team then investigated the free charge density, nfree, as a function of magnetic flux, Φ, to directly observe LP oscillations near the BKT transition. Oscillations of the free charge density, ∆nfree, were measured for varying Ly, revealing a crossover from 0-ring to π-ring behaviour around Qbnd/Qbulk ∼1. This crossover indicates a shift in the LP effect, demonstrating the potential to generate π-rings through vortex dynamics near the BKT transition.

Vortex dynamics explain half-flux shifts in superconducting rings near the BKT transition temperature

Scientists have demonstrated that half-flux shifts, observed in Little-Parks (LP) oscillations of superconducting rings, can arise without the need to invoke unconventional pairing symmetries. These shifts, known as -rings, are typically associated with exotic superconducting states, but this work establishes an alternative explanation rooted in the behaviour of vortices near the Berezinskii-Kosterlitz-Thouless (BKT) transition.

Researchers mapped the problem onto a Coulomb gas model, representing magnetic flux as boundary charges and investigating their screening by thermally excited vortex-antivortex pairs using Monte Carlo simulations. Specifically, the oscillation of free-vortex density as a function of magnetic flux was shown to exhibit anomalous half-flux shifts dependent on sample geometry.

This provides a new mechanism for generating -rings, linking LP oscillations to vortex dynamics in two-dimensional superconductors near the BKT transition. The findings suggest that the observed π-ring behaviour is robust across a range of parameters, including varying ring perimeter and temperature. The authors acknowledge a limitation in their current model, noting that the evolution of LP oscillations between the temperature regimes near the BKT transition and the mean-field transition temperature remains an open question.

Future research could explore this transition and investigate how supercurrents modify the observed LP oscillations. Preliminary experimental studies are anticipated to validate the theoretical framework and provide valuable insights into the interplay between LP oscillations and BKT physics, furthering our understanding of superconductivity in two-dimensional systems.