Low-energy effective theory and symmetry classification of flux phases on the kagome lattice

Motivated by recent experiments on AV(3)Sb(5) (A = K, Rb, Cs), the chiral flux phase has been proposed to explain time-reversal symmetry breaking. To fully understand the physics behind the chiral flux phase, we construct a low-energy effective theory based on the van Hove points around the Fermi surface. The possible symmetry-breaking states and their classifications of the low-energy effective theory are completely studied, especially the flux phases on the kagome lattice. In addition, we discuss the relations between the low-energy symmetry breaking orders, the chiral flux, and charge bond orders. We find all possible 183 flux phases on the kagome lattice within a 2*2 unit cell by brute-force approach and classify them by point-group symmetry. Among the 183 phases, we find 3 classes in a 1*1 unit cell, 8 classes in a 1*2 unit cell, and 18 classes in a 2*2 unit cell, respectively. These results provide a full picture of the time-reversal symmetry breaking in kagome lattices.