  Gravitational wave (GW) emissions from extreme-mass-ratio inspirals (EMRIs)
are promising sources for low-frequency GW-detectors. They result from a
compact object, such as a stellar-mass black-hole (BH), captured by a
supermassive black hole (SMBH). Several physical processes have been proposed
to form EMRIs. In particular, weak two-body interactions over a long time scale
(i.e., relaxation processes) have been proposed as a likely mechanism to drive
the BH orbit to high eccentricity. Consequently, it is captured by the SMBH and
becomes an EMRI. Here we demonstrate that EMRIs are naturally formed in SMBH
binaries. Gravitational perturbations from an SMBH companion, known as the
eccentric Kozai-Lidov (EKL) mechanism, combined with relaxation processes,
yield a significantly more enhanced rate than any of these processes operating
alone. Since EKL is sensitive to the orbital configuration, two-body relaxation
can alter the orbital parameters, rendering the system in a more EKL-favorable
regime. As SMBH binaries are expected to be prevalent in the Universe, this
process predicts a substantially high EMRI rate.
