Topological phase transitions in glassy quantum matter

Isac Sahlberg,Alex Westström,Teemu Ojanen,Kim Pöyhönen

doi:10.1103/physrevresearch.2.013053

Abstract

Amorphous systems have rapidly gained promise as novel platforms for topological matter. In this work we establish a scaling theory of amorphous topological phase transitions driven by the density of lattice points in two dimensions. By carrying out a finite-size scaling analysis of topological invariants averaged over discrete and continuum random geometries, we discover unique critical properties of Chern and $\mathbb{Z}_2$ glass transitions. Even for short-range hopping models the Chern glass phase may persist down to the fundamental lower bound given by the classical percolation threshold. While the topological indices accurately satisfy the postulated one-parameter scaling, they do not generally flow to the closest integer value in the thermodynamic limit. Furthermore, the value of the critical exponent describing the diverging localization length varies continuously along the phase boundary and is not fixed by the symmetry class of the Hamiltonian. We conclude that the critical behaviour of amorphous topological systems exhibit characteristic features not observed in disordered systems, motivating a wealth of new research directions.

Highlights

While topological classification of matter is in principle completely independent of the symmetry-breaking classification, much recent literature is devoted to the increasingly subtle interplay of topology and spatial order [1]
It is remarkable that the topological phase may persist all the way down to the classical percolation threshold
Motivated by the rising interest in amorphous topological states, we introduced a scaling theory of density-driven topological phase transitions in glassy systems

Summary

Introduction

While topological classification of matter is in principle completely independent of the symmetry-breaking classification, much recent literature is devoted to the increasingly subtle interplay of topology and spatial order [1]. By adopting a completely complementary starting point, a number of recent studies have identified amorphous systems without reference to a band structure as fruitful platforms for topological states [2,3,4,5,6,7,8] This crucial property sets amorphous topological systems apart from disordered and Anderson topological insulators [9,10], where nontrivial topology relies on residual spatial order. The possibility of fabricating topological states through randomly located dopants could allow access to a whole new class of designer topological systems This aspect was recently highlighted in concrete proposals for amorphous topological superconductors [11] and insulators [12]. The existence of amorphous topological states has become a well-established fact with a rapidly growing number of novel proposals

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Conclusion