Abstract
Interaction-driven topological phases 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 instability 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 sheds new light on the theoretical understanding of the interaction-driven phases in QBT systems.
Highlights
Topological phases of matter in the band structure with nontrivial topological Berry phase become an exciting research area of modern physics, culminating in the experimental observations of Haldane-honeycomb insulator[1] and the quantum anomalous Hall (QAH) effect in topological insulator.[2]
It has been identified that a quadratic band touching (QBT) point has topological feature, and can be driven towards a QAH phase with time-reversal symmetry (TRS) breaking even under arbitrary weak interactions, while strong interactions may lead to other competing phases.[18,19]
For weak interactions V < V1, by applying the HellmannFeynman theorem, we demonstrate the emergence of interactiondriven QAH phase whose topological properties are featured by two degenerate TRS breaking ground states arising from a pair of Kramers degenerate states with opposite chiralities and integer quantized topological Hall conductances
Summary
Topological phases of matter in the band structure with nontrivial topological Berry phase become an exciting research area of modern physics, culminating in the experimental observations of Haldane-honeycomb insulator[1] and the quantum anomalous Hall (QAH) effect in topological insulator.[2]. For topologically trivial band structures with zero Chern number[5–8], it was proposed that the strong correlation between electrons can induce spontaneous TRS breaking at mean field level[9,10] and lead to QAH effect in Dirac semimetals. These interaction-induced topological phases are interesting, since they can significantly enrich the class of topological materials.[11–13].
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