Spontaneous Quantum Hall Effect in chiral d-density waves

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.