Flat-band superconductivity in periodically strained graphene: mean-field and Berezinskii-Kosterlitz-Thouless transition

TL;DR

This paper investigates how periodically strained graphene with flat bands can host high-temperature superconductivity, analyzing superfluid properties and the BKT transition, and demonstrating potential for higher transition temperatures than twisted bilayer graphene.

Contribution

It extends the understanding of flat-band superconductivity in strained graphene to arbitrary periodic strains and calculates the BKT transition, highlighting the potential for high-temperature superconductivity.

Findings

Superconducting order parameter is strongly inhomogeneous.

Critical temperature and superfluid weight are approximately linear in interaction strength.

Realistic strain can significantly increase the BKT transition temperature.

Abstract

In the search of high-temperature superconductivity one option is to focus on increasing the density of electronic states. Here we study both the normal and $s$-wave superconducting state properties of periodically strained graphene, which exhibits approximate flat bands with a high density of states, with the flatness tunable by the strain profile. We generalize earlier results regarding a one-dimensional harmonic strain to arbitrary periodic strain fields, and further extend the results by calculating the superfluid weight and the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature $T_\text{BKT}$ to determine the true transition point. By numerically solving the self-consistency equation, we find a strongly inhomogeneous superconducting order parameter, similarly to twisted bilayer graphene. In the flat band regime the order parameter magnitude, critical chemical potential, critical temperature, superfluid weight, and BKT transition temperature are all approximately linear in the interaction strength, which suggests that high-temperature superconductivity might be feasible in this system. We especially show that by using realistic strain strengths $T_\text{BKT}$ can be made much larger than in twisted bilayer graphene, if using similar interaction strengths. We also calculate properties such as the local density of states that could serve as experimental fingerprints for the presented model.