Quasiperiodic pairing in graphene quasicrystals

TL;DR

This paper explores how twisted bilayer graphene quasicrystals exhibit distinct superconducting behaviors in periodic and quasiperiodic energy ranges, revealing quasiperiodic superconductivity linked to local density of states variations.

Contribution

It introduces the concept of quasiperiodic superconductivity in graphene quasicrystals and explains its origin related to local density of states distribution.

Findings

Superconductivity in periodic energy ranges is a superposition of two monolayer superconductors.

Quasiperiodic energy ranges exhibit enhanced, non-uniform superconductivity due to LDOS inhomogeneity.

The study explains superconductivity observed in recent moiré quasicrystals.

Abstract

We investigate the superconducting instabilities of twisted bilayer graphene quasicrystals (TBGQC) obtained by stacking two monolayer graphene sheets with a $30^\circ$ relative twisting. The electronic energy spectrum of TBGQC contains periodic energy ranges (PER) and quasiperiodic energy ranges (QER), where the underlying local density of states (LDOS) exhibits periodic and quasiperiodic distribution, respectively. We found that superconductivity in the PER is a simple superposition of two monolayer superconductors. This is because, particularly near the charge neutrality point of TBGQC, the two layers are weekly coupled, leading to pairing instabilities with uniform distribution in real space. On the other hand, within QER, the inhomogeneous distribution of the LDOS enhances the superconducting instability with a non-uniform distribution of pairing amplitudes, leading to quasiperiodic superconductivity. Our study can qualitatively explain the superconductivity in recently discovered moir\'e quasicrystals, which show superconductivity in its QER.