Quantum Anomalous Hall Insulator Stabilized By Competing Interactions

Abstract

We study the quantum phases driven by interaction in a semimetal with a quadratic band touching at the Fermi level. By combining the density matrix renormalization group (DMRG), analytical power expanded Gibbs potential method, and the weak coupling renormalization group, we study a spinless fermion system on a checkerboard lattice at half-filling, which has a quadratic band touching in the absence of interaction. In the presence of strong nearest-neighbor ($V_1$) and next-nearest-neighbor ($V_2$) interactions, we identify a site nematic insulator phase, a stripe insulator phase, and a phase separation region, in agreement with the phase diagram obtained analytically in the strong coupling limit (i.e. in the absence of fermion hopping). In the intermediate interaction regime, we establish a quantum anomalous Hall phase in the DMRG as evidenced by the spontaneous time-reversal symmetry breaking and the appearance of a quantized Chern number $C=1$. For weak interaction, we utilize the power expanded Gibbs potential method that treats $V_1$ and $V_2$ on equal footing, as well as the weak coupling renormalization group. Our analytical results reveal that not only the repulsive $V_1$ interaction, but also the $V_2$ interaction (both repulsive and attractive), can drive the quantum anomalous Hall phase. We also determine the phase boundary in the $V_1$-$V_2$ plane that separates the semimetal from the quantum anomalous Hall state. Finally, we show that the nematic semimetal, which was proposed for $|V_2|\gg V_1$ at weak coupling in a previous study, is absent, and the quantum anomalous Hall state is the only weak coupling instability of the spinless quadratic band touching semimetal.

arXiv comment25 pages, 19 figures

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Cited by in corpus (19)

• Realization of Topological Mott Insulator in a Twisted Bilayer Graphene Lattice Model
• Tunning topological phase and quantum anomalous Hall effect by interaction in quadratic band touching systems
• Quantum critical behavior of two-dimensional Fermi systems with quadratic band touching
• DMRG study of strongly interacting ${\mathbb{Z}}_2$ flatbands: a toy model inspired by twisted bilayer graphene
• Thermodynamic Response and Neutral Excitations in Integer and Fractional Quantum Anomalous Hall States Emerging from Correlated Flat Bands
• Self-Trapped Polarons and Topological Defects in a Topological Mott Insulator
• Quantum anomalous Hall phase in synthetic bilayers via twistless twistronics
• Quantum Anomalous Hall Phase Stabilized via Realistic Interactions on a Kagome Lattice
• Quantum Phases of Kagome Electron System with Half-Filled Flat Bands
• Superconductivity due to fluctuating loop currents
• Interaction-driven quantum anomalous Hall insulator in Dirac semimetal
• Multiple insulating phases due to the interplay of strong correlations and lattice geometry in a single-orbital Hubbard model
• Soluble Fermionic Quantum Critical Point in Two Dimensions
• Interaction Driven Topological Phase Transition in Monolayer CrCl${}_2$(pyrazine)${}_2$
• Ubiquitous nematic Dirac semimetal emerging from interacting quadratic band touching system
• Spin loop-current textures in Hubbard models
• Bound states in two-dimensional Fermi systems with quadratic band touching
• Correlated Hopf insulators
• Quantum anomalous Hall domains in a Quenched Topological Mott Insulator