Superconductivity on a Quasiperiodic Lattice: Extended-to-Localized Crossover of Cooper Pairs

TL;DR

This paper investigates superconductivity in quasiperiodic Penrose lattices using the attractive Hubbard model, revealing an inhomogeneous superconducting phase with a crossover from extended to localized Cooper pairs.

Contribution

It introduces a real-space dynamical mean-field theory analysis of superconductivity on a quasiperiodic lattice, highlighting inhomogeneity and pairing crossover phenomena.

Findings

Superconducting phase exists at low temperatures on a Penrose lattice.

The superconducting state shows inhomogeneity due to nonperiodicity.

A crossover from extended to localized Cooper pairs is observed.

Abstract

We study a possible superconductivity in quasiperiodic systems, by portraying the issue within the attractive Hubbard model on a Penrose lattice. Applying a real-space dynamical mean-field theory to the model consisting of 4181 sites, we find a superconducting phase at low temperatures. Reflecting the nonperiodicity of the Penrose lattice, the superconducting state exhibits an inhomogeneity. According to the type of the inhomogeneity, the superconducting phase is categorized into three different regions which cross over each other. Among them, the weak-coupling region exhibits spatially extended Cooper pairs, which are nevertheless distinct from the conventional pairing of two electrons with opposite momenta.