Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Thermally fluctuating superconductors in two dimensions

Subir Sachdev A, Oleg A. Starykh

Published Jan 1, 2000• 6 citations
OpenAlex

Abstract

Abstract In many two-dimensional superconducting systems1, 2, 3, 4, such as Josephson-junction arrays, granular superconducting films, and the high-temperature superconductors, it appears that the electrons bind into Cooper pairs below a pairing temperature (TP) that is well above the Kosterlitz–Thouless temperature (TKT, the temperature below which there is long-range superconducting order5, 6, 7, 8, 9, 10). The electron dynamics at temperatures between TKT and TP involve a complex interplay of thermal and quantum fluctuations, for which no quantitative theory exists. Here we report numerical results for this region, by exploiting its proximity to a T = 0 superconductor–insulator quantum phase transition11, 12. This quantum critical point need not be experimentally accessible for our results to apply. We characterize the static, thermodynamic properties by a single dimensionless parameter, γ(T). Quantitative and universal results are obtained for the frequency dependence of the conductivity, which are dependent only upon γ(T) and fundamental constants of nature.

Related papers

Universal scaling behavior of resistivity under two-dimensional superconducting phase fluctuations

Zongsheng Zhou, Kang Wang, Haijun Liao +2 more

Abstract In superconductors with relatively low superfluid density, such as cuprate high-$T_c$ superconductors, the phase fluctuations of the superconducting order parameter are remarkable, presumably playing a nonnegligible role in shaping many distinctive physical properties. Despite existing phenomenological arguments for many years, a comprehensive quantitative analysis of the electrical transport properties resulting from thermal superconducting phase fluctuations in two-dimensional superconductors has been lacking. This study employs Monte Carlo simulations to explore the numerically exact transport properties of a microscopic model of superconductivity, where the thermal phase fluctuations of the superconducting order parameter are described by the classical XY model. For both s-wave and d x 2 − y 2 -wave pairings, the electrical resistivity exhibits a universal scaling behavior at temperatures above the critical temperature T c . Our numerical results demonstrate that the scaling behavior of the quasiparticle lifetime is closely linked to the correlation length of the superconducting order parameter, yielding the universal scaling behavior of electrical resistivity determined by the Berezinskii-Kosterlitz-Thouless critical scaling of the correlation length. While this behavior aligns formally with the phenomenological framework of Halperin and Nelson in the critical region, our findings suggest that the resistivity scales with the inverse of the correlation length with a power less than one. Additionally, we examine the dependence of the electrical resistivity coefficient on the pairing amplitude and potential implications for recent transport experiments.

arXiv:2406.09944•npj Quantum Materials•Nov 25, 2025•1 citation

Universal conductivity of dirty bosons in two dimensions

S. M. Girvin, Mats Wallin, Erik Schwartz Sørensen +1 more

In contrast to the case of free fermions which have all states localized in two dimensions, dirty, repulsively-interacting bosons exhibit a zero-temperature localization phase transition between superconducting and insulating states as disorder is increased. The conductivity σ* = g (2 e ) 2 / h at the quantum critical point is a universal critical amplitude analogous to the universal jump in superfluid density at the classical Kosterlitz-Thouless transition. Using numerical Monte Carlo methods we compute the value of g for disorder-tuned transitions with and without long-range Coulomb interactions. We argue that this model is relevant to experiments on superconducting thin films and Josephson junction arrays.

Physica Scripta•Jan 1, 1992•8 citations

Tighter upper bounds on the critical temperature of two-dimensional superfluids and superconductors from the BCS to the Bose regime

Tingting Shi, Wei Zhang, C. A. R. Sá de Melo

Abstract We discuss standard and tighter upper bounds on the critical temperature T c of two-dimensional superfluids and superconductors versus particle density n or filling factor ν for continuum and lattice systems from the Bardeen–Cooper–Schrieffer (BCS) to the Bose regime. We consider only one-band Hamiltonians, where the transition from the normal to the superfluid (superconducting) phase is governed by the Berezinskii–Kosterlitz–Thouless (BKT) mechanism of vortex-antivortex binding, such that a direct relation between the superfluid density tensor and T c exists. The standard critical temperature upper bound T c up 1 is obtained from the Ferrell-Glover-Tinkham sum rule for the optical conductivity, which constrains the superfluid density tensor components. We demonstrate that it is imperative to consider at least the full effect of phase fluctuations of the order parameter for superfluidity (superconductivity) and use the renormalization group to obtain the phase-fluctuation critical temperature T c θ , a much tighter bound to the critical temperature supremum than T c up 1 over a wide range of densities or filling factors. We also discuss a fundamental difference between superfluids and superconductors in regards to the vortex core energy dependence on density. Going beyond phase fluctuations, we note that theories including modulus fluctuations of the order parameter or particle-hole fluctuations valid throughout the BCS-Bose evolution are still lacking, but the inclusion of these fluctuations can only produce a critical temperature that is lower than T c θ and thus produce an even tighter bound to the critical temperature supremum. We conclude by indicating that if the measured critical temperature exceeds T c θ in experiments involving two-dimensional single-band systems, then a non-BKT mechanism must be invoked to describe the superfluid (superconducting) transition.

New Journal of Physics•Aug 22, 2024•5 citations

Pairfield fluctuations of a 2D Hubbard model

Thomas Maier, Douglas J. Scalapino

Abstract At temperatures above the superconducting transition temperature, the pairfield susceptibility provides information on the nature of the pairfield fluctuations. Here, we study the d-wave pairfield susceptibility of a 2D Hubbard model for a doping which has a pseudogap (PG) and for a doping which does not. In both cases, there will be a region of Kosterlitz–Thouless fluctuations as the transition at TKT is approached. Above this region, we find evidence for pairfield-order parameter-phase fluctuations for dopings with a PG and BCS Cooper pair fluctuations for dopings without a PG.

arXiv:1810.10043•npj Quantum Materials•Jun 13, 2019•23 citations

Quantum vs thermal fluctuations in phase transitions of two-dimensional superconductors

Andrea Ponticelli, Francesco Giuseppe Capone, V. Cataudella +3 more

We investigate the impact of quantum and thermal phase fluctuations on the suppression of superconducting order in two-dimensional systems. Within the two-dimensional quantum XY model in the phase representation, where on-site interaction terms govern quantum phase fluctuations, we perform extensive path-integral quantum Monte Carlo simulations. The resulting temperature-interaction phase diagram establishes the presence of a well-defined critical line ending at a quantum critical point at vanishing temperature with no indication of reentrant behavior. We further demonstrate that the resistance above the critical line reproduces the two expected different critical behaviors. For stronger interactions, above the quantum critical point, the system exhibits a crossover to an insulating regime at low temperatures. Finally, Monte Carlo calculations of current-current correlation functions enable us to extract the frequency-dependent conductivity in both superconducting and normal regimes, revealing a finite-frequency response that we attribute to quantum phase fluctuations.

arXiv:2512.20476•Dec 23, 2025•0 citations

Microscopic scales and mechanism of quantum phase transitions in two-dimensional superconducting systems

Andrey Rogachev, Feldman, Samuel, Kevin Davenport

The superconducting ground state in many two-dimensional materials can be created or destroyed through quantum phase transitions (QPTs) controlled by non-thermal parameters such as carrier density or magnetic field. While various mechanisms for these QPTs have been proposed, it remains unclear which, if any, are applicable to a specific two-dimensional superconducting system. Here, we find that a pair-breaking mechanism which suppresses the Cooper pair density gives a unifying description of magnetic-field-driven QPTs in amorphous MoGe, Pb and TaN films, and the high-temperature superconductor La$_{1.92}$Sr$_{0.08}$CuO$_{4}$. This transition occurs within the superconducting subsystem and is masked by the dominant non-critical contribution of normal electrons. The discovery was enabled by the development of a QPT model that goes beyond the conventional determination of the critical exponents and incorporates into the analysis a microscopic length scale characterizing the transitions. We found that in the materials studied, and MoGe nanowires, this scale corresponds to the size of a Cooper pair. The model has also been successfully applied to QPTs in Josephson junction arrays and various non-superconducting materials. The observation that microscopic scales are encoded in the scaled experimental data of QPTs likely extends beyond equilibrium condensed matter physics and may reveal underlying principles of critical phenomena in a wide variety of systems.

arXiv:2309.00747•Sep 1, 2023•0 citations
Abstract In many two-dimensional superconducting systems1, 2, 3, 4, such as Josephson-junction arrays, granular superconducting films, and the high-temperature superconductors, it appears that the electrons bind into Cooper pairs below a pairing temperature (TP) that is well above the Kosterlitz–Thouless temperature (TKT, the temperature below which there is long-range superconducting order5, 6, 7, 8, 9, 10). The electron dynamics at temperatures between TKT and TP involve a complex interplay of thermal and quantum fluctuations, for which no quantitative theory exists. Here we report numerical results for this region, by exploiting its proximity to a T = 0 superconductor–insulator quantum phase transition11, 12. This quantum critical point need not be experimentally accessible for our results to apply. We characterize the static, thermodynamic properties by a single dimensionless parameter, γ(T). Quantitative and universal results are obtained for the frequency dependence of the conductivity, which are dependent only upon γ(T) and fundamental constants of nature.
Abstract In superconductors with relatively low superfluid density, such as cuprate high-TcT_cTc​ superconductors, the phase fluctuations of the superconducting order parameter are remarkable, presumably playing a nonnegligible role in shaping many distinctive physical properties. Despite existing phenomenological arguments for many years, a comprehensive quantitative analysis of the electrical transport properties resulting from thermal superconducting phase fluctuations in two-dimensional superconductors has been lacking. This study employs Monte Carlo simulations to explore the numerically exact transport properties of a microscopic model of superconductivity, where the thermal phase fluctuations of the superconducting order parameter are described by the classical XY model. For both s-wave and d x 2 − y 2 -wave pairings, the electrical resistivity exhibits a universal scaling behavior at temperatures above the critical temperature T c . Our numerical results demonstrate that the scaling behavior of the quasiparticle lifetime is closely linked to the correlation length of the superconducting order parameter, yielding the universal scaling behavior of electrical resistivity determined by the Berezinskii-Kosterlitz-Thouless critical scaling of the correlation length. While this behavior aligns formally with the phenomenological framework of Halperin and Nelson in the critical region, our findings suggest that the resistivity scales with the inverse of the correlation length with a power less than one. Additionally, we examine the dependence of the electrical resistivity coefficient on the pairing amplitude and potential implications for recent transport experiments.
In contrast to the case of free fermions which have all states localized in two dimensions, dirty, repulsively-interacting bosons exhibit a zero-temperature localization phase transition between superconducting and insulating states as disorder is increased. The conductivity σ* = g (2 e ) 2 / h at the quantum critical point is a universal critical amplitude analogous to the universal jump in superfluid density at the classical Kosterlitz-Thouless transition. Using numerical Monte Carlo methods we compute the value of g for disorder-tuned transitions with and without long-range Coulomb interactions. We argue that this model is relevant to experiments on superconducting thin films and Josephson junction arrays.
Abstract We discuss standard and tighter upper bounds on the critical temperature T c of two-dimensional superfluids and superconductors versus particle density n or filling factor ν for continuum and lattice systems from the Bardeen–Cooper–Schrieffer (BCS) to the Bose regime. We consider only one-band Hamiltonians, where the transition from the normal to the superfluid (superconducting) phase is governed by the Berezinskii–Kosterlitz–Thouless (BKT) mechanism of vortex-antivortex binding, such that a direct relation between the superfluid density tensor and T c exists. The standard critical temperature upper bound T c up 1 is obtained from the Ferrell-Glover-Tinkham sum rule for the optical conductivity, which constrains the superfluid density tensor components. We demonstrate that it is imperative to consider at least the full effect of phase fluctuations of the order parameter for superfluidity (superconductivity) and use the renormalization group to obtain the phase-fluctuation critical temperature T c θ , a much tighter bound to the critical temperature supremum than T c up 1 over a wide range of densities or filling factors. We also discuss a fundamental difference between superfluids and superconductors in regards to the vortex core energy dependence on density. Going beyond phase fluctuations, we note that theories including modulus fluctuations of the order parameter or particle-hole fluctuations valid throughout the BCS-Bose evolution are still lacking, but the inclusion of these fluctuations can only produce a critical temperature that is lower than T c θ and thus produce an even tighter bound to the critical temperature supremum. We conclude by indicating that if the measured critical temperature exceeds T c θ in experiments involving two-dimensional single-band systems, then a non-BKT mechanism must be invoked to describe the superfluid (superconducting) transition.
Abstract At temperatures above the superconducting transition temperature, the pairfield susceptibility provides information on the nature of the pairfield fluctuations. Here, we study the d-wave pairfield susceptibility of a 2D Hubbard model for a doping which has a pseudogap (PG) and for a doping which does not. In both cases, there will be a region of Kosterlitz–Thouless fluctuations as the transition at TKT is approached. Above this region, we find evidence for pairfield-order parameter-phase fluctuations for dopings with a PG and BCS Cooper pair fluctuations for dopings without a PG.
We investigate the impact of quantum and thermal phase fluctuations on the suppression of superconducting order in two-dimensional systems. Within the two-dimensional quantum XY model in the phase representation, where on-site interaction terms govern quantum phase fluctuations, we perform extensive path-integral quantum Monte Carlo simulations. The resulting temperature-interaction phase diagram establishes the presence of a well-defined critical line ending at a quantum critical point at vanishing temperature with no indication of reentrant behavior. We further demonstrate that the resistance above the critical line reproduces the two expected different critical behaviors. For stronger interactions, above the quantum critical point, the system exhibits a crossover to an insulating regime at low temperatures. Finally, Monte Carlo calculations of current-current correlation functions enable us to extract the frequency-dependent conductivity in both superconducting and normal regimes, revealing a finite-frequency response that we attribute to quantum phase fluctuations.
The superconducting ground state in many two-dimensional materials can be created or destroyed through quantum phase transitions (QPTs) controlled by non-thermal parameters such as carrier density or magnetic field. While various mechanisms for these QPTs have been proposed, it remains unclear which, if any, are applicable to a specific two-dimensional superconducting system. Here, we find that a pair-breaking mechanism which suppresses the Cooper pair density gives a unifying description of magnetic-field-driven QPTs in amorphous MoGe, Pb and TaN films, and the high-temperature superconductor La1.92_{1.92}1.92​Sr0.08_{0.08}0.08​CuO4_{4}4​. This transition occurs within the superconducting subsystem and is masked by the dominant non-critical contribution of normal electrons. The discovery was enabled by the development of a QPT model that goes beyond the conventional determination of the critical exponents and incorporates into the analysis a microscopic length scale characterizing the transitions. We found that in the materials studied, and MoGe nanowires, this scale corresponds to the size of a Cooper pair. The model has also been successfully applied to QPTs in Josephson junction arrays and various non-superconducting materials. The observation that microscopic scales are encoded in the scaled experimental data of QPTs likely extends beyond equilibrium condensed matter physics and may reveal underlying principles of critical phenomena in a wide variety of systems.