Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing

Abstract

We investigate the stability of a quadratic band-crossing point (QBCP) in 2D fermionic systems. At the noninteracting level, we show that a QBCP exists and is topologically stable for a Berry flux +/-2pi if the point symmetry group has either fourfold or sixfold rotational symmetries. This putative topologically stable free-fermion QBCP is marginally unstable to arbitrarily weak short-range repulsive interactions. We consider both spinless and spin-1/2 fermions. Four possible ordered states result: a quantum anomalous Hall phase, a quantum spin Hall phase, a nematic phase, and a nematic-spin-nematic phase.

Quantum anomalous Hall state in bilayer graphene

“…The (4,0) and (3,1) states, which have M > = M < , thus exhibit a quantized Hall conductance at zero magnetic field-the hallmark of a QAH state. Because these states have σ xy = 0, they must spontaneously break time reversal symmetry.…”

“…These states are analogs of the 'topological Mott insulators' discussed in Refs. [2,3], and as such host topologically protected edge states. The counter-propagating valley modes for the QVH state were worked out in Ref.…”

“…Those include the 'longitudinal' fluctuation modes (L-modes) analogous to those discussed in Ref. [2,3], and also 'transverse' fluctuation modes (T-modes) which are unique to BLG. We find that these two types of modes have competing effects: while the L-modes favor the symmetry breaking multiplets, the T-modes favor the SU(4) invariant QAH state.…”

Spontaneous Quantum Hall Effect via a Thermally Induced Quadratic Fermi Point

“…Quantum Hall effect can also be induced by opening a gap at a topological Fermi point with a quadratic band dispersion [9]. These points are vortices carrying multiple topological charges n = ±2 in momentum space [10,11].…”

“…Because of its higher winding numbers, a quadratic Fermi point can decay into several elementary Dirac points while preserving the total topological charge [10]. Unlike Dirac points where interaction effects are suppressed due to a vanishing density of states (DOS), quadratic Fermi points are unstable against arbitrarily weak short-range interactions due to their finite DOS [9,12]. These Fermi points are usually protected in lattice models by C 4 or C 6 point group symmetries.…”