Electronic instabilities in Penrose quasi-crystals: competition, coexistence and collaboration of order

TL;DR

This paper investigates electronic instabilities in Penrose quasicrystals using a real-space functional renormalization group, revealing complex phase behavior including competing, coexisting, and collaborating orders beyond traditional crystal physics.

Contribution

It introduces an unbiased, beyond-mean-field approach to study electronic phases in quasicrystals, uncovering rich and novel ordering phenomena.

Findings

Identification of antiferromagnetic and charge density wave phases

Discovery of coexisting and collaborating orders in quasicrystals

Highlighting the importance of beyond-mean-field methods for quasicrystal physics

Abstract

Quasicrystals lack translational symmetry, but can still exhibit long-ranged order, promoting them to candidates for unconventional physics beyond the paradigm of crystals. Here, we apply a real-space functional renormalization group approach to the prototypical quasicrystalline Penrose tiling Hubbard model treating} competing electronic instabilities in an unbiased, beyond-mean-field fashion. {\color{red} Our work reveals a delicate interplay between charge and spin degrees of freedom in quasicrystals}. Depending on the range of interactions and hopping amplitudes, we unveil a rich phase diagram including antiferromagnetic orderings, charge density waves and subleading, superconducting pairing tendencies. For certain parameter regimes we find a competition of phases, which is also common in crystals, but additionally encounter phases coexisting in a spatially separated fashion and ordering tendencies which mutually collaborate to enhance their strength. We therefore establish that quasicrystalline structures open up a route towards this rich ordering behavior uncommon to crystals and that an unbiased, beyond-mean-field approach is essential to describe this physics of quasicrystals correctly.