  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 non-existent. 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 YBCO, in
which intra-bilayer 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.
