Spontaneous Quantum Hall Effect in chiral d-density waves

TL;DR

This paper investigates how a chiral d-density wave state exhibits a spontaneous quantum Hall effect due to topological Chern-Simons terms arising from parity and time-reversal symmetry breaking.

Contribution

It demonstrates the emergence of Chern-Simons terms in the effective action of a chiral d-density wave, linking topological properties to observable Hall effects.

Findings

Chern-Simons terms are induced in the electromagnetic response.

The Hall conductance is quantized due to topological origin.

Electric and magnetic fields are coupled in the chiral state.

Abstract

We study the electromagnetic response of a chiral ${\rm d_{xy}+id_{x^2-y^2}}$ charge density wave state. Due to parity (${\cal P}$) and time reversal (${\cal T}$) violation, Chern-Simons terms emerge in the effective action of the U(1) gauge field. As a consequence electric and magnetic fields are coupled providing the possibility of observing the Spontaneous Quantum Hall Effect i.e. generation of Hall voltage via the sole application of an electric field. We show how the Chern-Simons terms are induced and discuss the topological origin of the quantization of Hall conductance.