Time-Reversal Symmetry Breaking and Spontaneous Anomalous Hall Effect in Fermi Fluids

Understand

We study the spontaneous non-magnetic time-reversal symmetry breaking in a two-dimensional Fermi liquid without breaking either the translation symmetry or the U(1) charge symmetry.

• Assuming that 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.