Eight fold quantum Hall phases in a time reversal symmetry broken tight binding model

TL;DR

This paper explores a modified Kane-Mele model with broken time reversal symmetry, revealing new topological phases including a quantum anomalous spin Hall insulator and complex multicritical points, with implications for experimental realization.

Contribution

It introduces a novel phase diagram of a TRS-broken Kane-Mele and Haldane model, uncovering a new QASHI phase and multicritical points, expanding understanding of topological insulators.

Findings

Discovery of quantum anomalous spin Hall insulator (QASHI) phase.

Identification of multicritical points where multiple topological phases meet.

Edge transport properties vary with topological phase, including spin-selective and spin-neutral modes.

Abstract

We consider a time reversal symmetry (TRS) broken Kane-Mele model superimposed with Haldane model and chart out the phase diagram using spin Chern number to investigate the fate of quantum anomalous Hall insulator (QAHI) and quantum spin Hall insulator (QSHI) phases. Interestingly, in addition to QSHI and QAHI phase, the phase diagram unveils quantum anomalous spin Hall insulator (QASHI) phase where only one spin sector is topological. We also find multicritical points where three / four topological phase boundaries coalesce. These topological phases are protected by an effective TRS and a composite anti-unitary particle-hole symmetry leading to remarkable properties of edge modes. We find spin-selective, spin-polarized and spin-neutral edge transport in QASHI, QSHI and QAHI phases respectively. Our study indicates that the robustness of the topological phase mainly depends on the spin gap which does not necessarily vanish at the Dirac points across a topological phase transition. We believe that our proposals can be tested in near future using recent experimental advancements in solid state and cold atomic systems.