Electromagnetic response of time-reversal breaking metallic phases in two dimensions

Abstract

We explore two phases in two-dimensional electron fluids in which the time-reversal symmetry is broken spontaneously by using the method of higher dimensional bosonization. Mean-field calculations show that the order parameter is two two-component real vectors [Sun and Fradkin 2008]. There are two phases: the beta phase in which the two order parameters are perpendicular and the alpha phase in which they are parallel. This beta phase exhibits nonvanishing un-quantized anomalous Hall effect in the absence of external magnetic fields, which corresponds to the Berry curvature on the Fermi surface. The alpha phase does not have that property. To go beyond the mean-field, we introduce the machinery of higher dimensional bosonization. Our preliminary results show that in the mean field limit of the bosonized theory, the fluid spontaneously transforms into the time-reversal broken phase. It is evident from the result that the critical point we have is similar to that of Pomeranchuk instability. The quartic term in the dispersion expansion needed to be introduced to stabilize the theory. The correction coming from the higher order terms introduces the coupling to the curvature of the Fermi surfaces. The beta phase in the bosonized picture is not correct so we go back to the fermionic theory and integrate out the fermions in the symmetric phase directly to achieve an effective action. Finally, the full response polarization tensor is derived and its Ward identity is shown to be obeyed.