Time-reversal symmetry breaking and spontaneous anomalous Hall effect in Fermi fluids

We study the spontaneous nonmagnetic time-reversal symmetry breaking in a two-dimensional Fermi liquid without breaking either the translation symmetry or the U(1) charge symmetry. Assuming the low-energy physics is described by fermionic quasiparticle excitations, we identified an “emergent” local U(1)^N symmetry in momentum space for an N-band model. For a large class of models, including all one-band and two-band models, we found that the time-reversal and chiral symmetry breaking can be described by the U(1)^N gauge theory associated with this emergent local U(1)^N symmetry. This conclusion enables the classification of the time-reversal symmetry-breaking states as types I and II, depending on the type of accompanying spatial symmetry breaking. The properties of each class are studied. In particular, we show that the states breaking both time reversal and chiral symmetries are described by spontaneously generated Berry phases. We also show examples of the time-reversal symmetry-breaking phases in several different microscopically motivated models and calculate their associated Hall conductance within a mean-field approximation. The fermionic nematic phase with time-reversal symmetry breaking is also presented and the possible realizations in strongly correlated models such as the Emery model are discussed.