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A mechanism is proposed for the tantalizing evidence of polar Kerr effect ina class of high temperature superconductors--the signs of the Kerr angle fromtwo opposite faces of the same sample are identical and magnetic field trainingis non-existent. The mechanism does not break global time reversal symmetry, asin an antiferromagnet, and results in zero Faraday effect. It is bestunderstood in a phenomenological model of bilayer cuprates, such as YBCO, inwhich intra-bilayer tunneling nucleates a chiral d-density wave such that theindividual layers have opposite chirality. Although specific to the chirald-density wave, the mechanism may be more general to any quasi-two-dimensionalorbital antiferromagnet in which time reversal symmetry is broken in eachplane, but not when averaged macroscopically.

A calculation for polar Kerr effect in high temperature cuprate superconductors