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arXiv:2008.03315 · Physical review. B./Physical review. B

Three-dimensional network model for strong topological insulator transitions

Jun Ho Son, S. Raghu

Published Sep 27, 2021• 4 citations
arXivHTMLPDF

Abstract

We construct a three-dimensional (3D), time-reversal symmetric generalization of the Chalker-Coddington network model for the integer quantum Hall transition. In addition to a weak topological insulator phase already accommodated by the network model framework in the preexisting literature, our network model hosts strong topological insulator phases. We unambiguously demonstrate that strong topological insulator phases emerge as intermediate phases between a trivial insulator phase and a weak topological phase. Additionally, we found a duality that relates a trivial insulator phase and a weak topological phase in our network model. Remarkably, strong topological phases are mapped to themselves under this duality. We show that upon adding sufficiently strong disorder, the strong topological insulator phases undergo phase transitions into a metallic phase. We numerically determine the critical exponent of the insulator-metal transition. Our network model explicitly shows how a semiclassical percolation picture of topological phase transitions in two dimensions can be generalized to 3D and opens up a venue for studying 3D topological phase transitions.

DOI
10.1103/physrevb.104.125142

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We investigate a symmetry-protected Z2{Z}_{2}Z2​ topological electron glass, a glassy equivalent of the Z2{Z}_{2}Z2​ topological band insulator in crystalline systems, and uncover associated quantum phase transitions in this three-dimensional amorphous network of atoms. Through explicit numerical calculations of the Witten effect, we show that the Z2{Z}_{2}Z2​ glass is characterized by an anomalous electromagnetic response, i.e., it can host dyons with 12\frac{1}{2}21​ electronic charge. We further study, using a variety of numerical diagnostics including such electromagnetic responses, the phase transitions of the Z2{Z}_{2}Z2​ glass into a metallic and/or a trivial insulating phase. We find that the phase transitions here are governed by subtle features of mobility edges and ``spectral inversion'' which are possibly unique to structurally amorphous systems. Our results provide a concrete setting to understand the general underpinnings of such phases, where strong structural disorder interplays with symmetry-protected topological order.
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