Unconventional superfluidity of superconductivity on Penrose lattice

TL;DR

This paper explores how superconductivity behaves on a Penrose lattice, revealing unique properties like persistent paramagnetic superfluid density and enhanced transition temperature with disorder, differing from periodic systems.

Contribution

It provides a theoretical analysis of superconductivity on a Penrose lattice, highlighting unconventional superfluid properties and the effects of disorder on transition temperature.

Findings

Paramagnetic superfluid density remains finite in the thermodynamic limit.

Superfluid density and transition temperature increase with disorder strength.

Superconductivity is influenced by the extended nature of single particle states.

Abstract

We theoretically investigate the gap function, superfluid density and the transition temperature of the superconductivity (SC) on semi-periodic Penrose lattice, where an attractive Hubbard model is adopted as an example. Firstly, we clarify that the gap function, density of states and superfluid density are all positively correlate to the extended degree of single particle states around the Fermi energy. Secondly, we identify that the paramagnetic component of the superfluid density does not decay to zero in the thermodynamic limit, which is completely different from the periodic system. The difference between the diamagnetic and paramagnetic currents keeps stable with whatever scaling, which is consistent with recent experimental results that although the superfluid density is lower than that of the periodic system, the system has bulk SC. Thirdly, we find that both the superfluid density and SC transition temperature can be boosted with the increase of disorder strength, which should be general to quasicrystal but unusual to periodic systems, reflecting the interplay between the underlying geometry and disorder.