Disorder effects in correlated topological insulators

Abstract

Using exact diagonalization and quantum Monte Carlo calculations we investigate the effects of disorder on the phase diagram of both non-interacting and interacting models of two-dimensional topological insulators. In the fermion sign problem-free interacting models we study, electron-electron interactions are described by an on-site repulsive Hubbard interaction and disorder is included via the one-body hopping operators. In both the non-interacting and interacting models we make use of recent advances in highly accurate real-space numerical evaluation of topological invariants to compute phase boundaries, and in the non-interacting models determine critical exponents of the transitions. We find different models exhibit distinct stability conditions of the topological phase with respect to interactions and disorder. We provide a general analytical theory that accurately predicts these trends.

arXiv comment13 pages, 5 figures

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• Stability of two-dimensional asymmetric materials with a quadratic band crossing point under four-fermion interaction and impurity scattering
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• Interaction-enhanced integer quantum Hall effect in disordered systems
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• Fermion-fermion interaction driven instability and criticality of quadratic band crossing systems with the breaking of time-reversal symmetry
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• Low-frequency and Moiré Floquet engineering: a review
• Emergent Weyl-like points in periodically modulated systems
• Recent progress on disorder-induced topological phases
• Critical fates induced by the interaction competition in three-dimensional tilted Dirac semimetals