Quantum Geometric Contributions to the BKT Transition: Beyond Mean Field Theory

TL;DR

This paper investigates how quantum geometric effects influence the BKT transition temperature in 2D superconductors, highlighting their role beyond mean field theory and their potential experimental signatures.

Contribution

It introduces a framework incorporating quantum geometry into the understanding of the BKT transition, emphasizing the role of pair effective mass and geometric effects in 2D superconductivity.

Findings

Quantum geometry affects the pair effective mass and raises $T_{BKT}$.

Geometric contributions can be estimated from the ratio of $T^*$ to $T_{BKT}$.

Preliminary estimates suggest significant geometric effects in twisted bilayer graphene.

Abstract

We study quantum geometric contributions to the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature, $T_{\mathrm{BKT}}$, in the presence of fluctuations beyond BCS theory. Because quantum geometric effects become progressively more important with stronger pairing attraction, a full understanding of 2D multi-orbital superconductivity requires the incorporation of preformed pairs. We find it is through the effective mass of these pairs that quantum geometry enters the theory and this suggests that the quantum geometric effects are present in the non-superconducting pseudogap phase as well. Increasing these geometric contributions tends to raise $T_{\mathrm{BKT}}$ which then competes with fluctuation effects that generally depress it. We argue that a way to physically quantify the magnitude of these geometric terms is in terms of the ratio of the pairing onset temperature $T^*$ to $T_{\mathrm{BKT}}$. Our paper calls attention to an experimental study demonstrating how both temperatures and, thus, their ratio may be currently accessible. They can be extracted from the same voltage-current measurements which are generally used to establish BKT physics. We use these observations to provide rough preliminary estimates of the magnitude of the geometric contributions in, for example, magic angle twisted bilayer graphene.