Calculation for polar Kerr effect in high-temperature cuprate superconductors

A mechanism is proposed for the tantalizing evidence of polar Kerr effect in a class of high-temperature superconductors: the signs of the Kerr angle from two opposite faces of the same sample are identical and magnetic field training is nonexistent. The mechanism does not break global time-reversal symmetry, as in an antiferromagnet, and results in zero Faraday effect. It is best understood in a phenomenological model of bilayer cuprates, such as YBa2Cu3O6+δ, in which intrabilayer tunneling nucleates a chiral d-density wave such that the individual layers have opposite chirality. Although specific to the chiral d-density wave, the mechanism may be more general to any quasi-two-dimensional orbital antiferromagnet in which time-reversal symmetry is broken in each plane, but not when averaged macroscopically.