Spontaneous symmetry breakings in two-dimensional kagome lattice

TL;DR

This paper investigates spontaneous symmetry breaking and topological phases in a two-dimensional kagome lattice with repulsive interactions, revealing infinitesimal instabilities at 1/3-filling and finite at 2/3-filling, and proposing a ferromagnetic quantum anomalous Hall state at half-filling.

Contribution

It demonstrates the conditions under which topological Mott insulator phases emerge or are suppressed in a kagome lattice with weak interactions, highlighting filling-dependent behaviors.

Findings

Infinitesimal instability and topological phases at 1/3-filling.

Finite instability and no topological phase at 2/3-filling.

Proposed ferromagnetic quantum anomalous Hall state at half-filling.

Abstract

We study spontaneous symmetry breakings for fermions (spinless and spinful) on a two-dimensional kagome lattice with nearest-neighbor repulsive interactions in weak coupling limit, and focus in particular on topological Mott insulator instability. It is found that at $\frac{1}{3}$-filling where there is a quadratic band crossing at $\Gamma$-point, in agreement with Ref. 1, the instabilities are infinitesimal and topological phases are dynamically generated. At $\frac{2}{3}$-filling where there are two inequivalent Dirac points, the instabilities are finite, and no topological phase is favored at this filling without breaking the lattice translational symmetry. A ferromagnetic quantum anomalous Hall state with infinitesimal instability is further proposed at half-filling of the bottom flat band.