Time-reversal symmetry breaking by a $(d+id)$ density-wave state in underdoped cuprate superconductors

It was proposed that the $id_{x^2-y^2}$ density-wave state (DDW) may be responsible for the pseudogap behavior in the underdoped cuprates. Here we show that the admixture of a small $d_{xy}$ component to the order parameter of the DDW state breaks macroscopic time reversal symmetry, leading to a non-zero polar Kerr effect. The $d_{xy}$ component breaks the symmetry between the counter-propagating orbital currents of the DDW state, which is ultimately responsible for the non-zero Kerr signal. From the results of the recent experiments by Xia \textit{et al.}, arXiv:0711.2494, we deduce that the amplitude of the $d_{xy}$ admixture is quite small compared to the ordered DDW component. \\ Reference: S. Tewari, C. Zhang, V. M. Yakovenko, S. Das Sarma, arXiv:0711.2329.