Tunning topological phase and quantum anomalous Hall effect by interaction in quadratic band touching systems

TL;DR

This paper investigates how interactions influence topological phases in quadratic band touching systems, revealing a transition from quantum anomalous Hall to nematic charge-density-wave phases with an intermediate bond-ordered critical phase.

Contribution

It introduces a detailed phase diagram for interacting spinless fermions on a checkerboard lattice, identifying a novel intermediate bond-ordered phase and the interaction-driven transition mechanisms.

Findings

Weak interactions induce quantum anomalous Hall effect.

Strong interactions lead to nematic charge-density-wave phase.

An intermediate bond-ordered critical phase exists between QAH and CDW.

Abstract

Interaction driven topological phases can significantly enrich the class of topological materials and thus are of great importance. Here, we study the phase diagram of interacting spinless fermions filling the two-dimensional checkerboard lattice with a quadratic band touching (QBT) point. By developing new diagnosis based on the state-of-the-art density-matrix renormalization group and exact diagonalization, we determine accurate quantum phase diagram for such a system at half-filling with three distinct phases. For weak nearest-neighboring interactions, we demonstrate the instablity of the QBT towards an interaction-driven spontaneous quantum anomalous Hall (QAH) effect. For strong interactions, the system breaks the rotational symmetry realizing a nematic charge-density-wave (CDW) phase. Interestingly, for intermediate interactions we discover a symmetry-broken bond-ordered critical phase sandwiched in between the QAH and CDW phases, which splits the QBT into two Dirac points driven by interaction. Instead of the direct transition between QAH and CDW phases, our identification of an intermediate phase shed new light on the theoretical understanding of the interaction-driven phases in QBT systems.