  An enhanced rate of stellar tidal disruption events (TDEs) may be an
important characteristic of supermassive black hole (SMBH) binaries at close
separations. Here we study the evolution of the distribution of stars around a
SMBH binary due to the eccentric Kozai-Lidov (EKL) mechanism, including
octupole effects and apsidal precession caused by the stellar mass distribution
and general relativity. We identify a region around one of the SMBHs in the
binary where the EKL mechanism drives stars to high eccentricities, which
ultimately causes the stars to either scatter off the second SMBH or get
disrupted. For SMBH masses 10^7 Msun and 10^8 Msun, the TDE rate can reach
10^{-2} yr and deplete a region of the stellar cusp around the secondary SMBH
in ~0.5 Myr. As a result, the final geometry of the stellar distribution
between 0.01 and 0.1 pc around the secondary SMBH is a torus. These effects may
be even more prominent in nuclear stellar clusters hosting a supermassive and
an intermediate mass black hole.
