Thermally fluctuating superconductors in two dimensions

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

T. Schneider, D. Ariosa

R. Rossignoli, Juan P. Zagorodny

Subir Sachdev A, Oleg A. Starykh

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.

Oscar Viyuela, A Rivas, M A Martin-Delgado

We have applied the recently developed theory of topological Uhlmann numbers to a representative model of a topological insulator in two dimensions, the Qi–Wu–Zhang model. We have found a stable symmetry-protected topological phase under external thermal fluctuations in two dimensions. A complete phase diagram for this model is computed as a function of temperature and coupling constants in the original Hamiltonian. It shows the appearance of large stable phases of matter with topological properties compatible with thermal fluctuations or external noise and the existence of critical lines separating abruptly trivial phases from topological phases. These novel critical temperatures represent thermal topological phase transitions. The initial part of the paper comprises a self-contained explanation of the Uhlmann geometric phase needed to understand the topological properties that it may acquire when applied to topological insulators and superconductors.

Oscar Viyuela, ́Angel Rivas, Martin-Delgado Alcántara, Miguel Ángel

We have applied the recently developed theory of topological Uhlmann numbers to a representative model of a topological insulator in two dimensions, the Qi-Wu-Zhang model. We have found a stable symmetry-protected topological phase under external thermal fluctuations in two dimensions. A complete phase diagram for this model is computed as a function of temperature and coupling constants in the original Hamiltonian. It shows the appearance of large stable phases of matter with topological properties compatible with thermal fluctuations or external noise and the existence of critical lines separating abruptly trivial phases from topological phases. These novel critical temperatures represent thermal topological phase transitions. The initial part of the paper comprises a self-contained explanation of the Uhlmann geometric phase needed to understand the topological properties that it may acquire when applied to topological insulators and superconductors.