Nematic, topological and Berry phases when a flat and a parabolic band touch

Abstract

A (single flavor) quadratic band crossing in two dimensions is known to have a generic instability towards a quantum anomalous Hall (QAH) ground state for infinitesimal repulsive interactions. Here we introduce a generalization of a quadratic band crossing which is protected only by rotational symmetry. By focusing on the representative case of a parabolic and flat band touching, which also allows for a straightforward lattice realization, the interaction induced nematic phase is found generally to compete successfully with the QAH insulator, and to become the dominant instability in certain parts of the phase diagram already at weak coupling. The full phase diagram of the model, together with its topological properties, is mapped out using a perturbative renormalization group, strong coupling analysis, the mean-field theory. Interestingly, the Berry flux varies continuously in the single flavour limit with various control parameters.

5 pages, 3 figures

References in corpus (8)

• Topological Mott Insulators
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• Quantum Anomalous Hall State in Bilayer Graphene
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• Pseudo-magnetic catalysis of the time-reversal symmetry breaking in graphene
• Interaction-induced anomalous quantum Hall state on the honeycomb lattice
• Spontaneous quantum Hall effect via thermally induced quadratic Fermi point
• Majorana mass, time reversal symmetry, and the dimension of space

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