Topological phase transitions in glassy quantum matter

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5 Citations (Scopus)


Amorphous systems have rapidly gained attention as promising 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 critical properties of Chern and Z2 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 behavior of amorphous topological systems exhibit characteristic features not observed in disordered systems, motivating a wealth of interesting research directions.

Original languageEnglish
Article number013053
Number of pages9
Issue number1
Publication statusPublished - Jan 2020
Publication typeA1 Journal article-refereed

Publication forum classification

  • Publication forum level 1

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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