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Extreme mass ratio inspirals (EMRIs) are compact binary systems characterizedby a mass-ratio $q=m/M$ in the range $~10^{-9}-10^{-4}$ and represent primarygravitational wave (GW) sources for the forthcoming Laser Interferometer SpaceAntenna (LISA). While their standard formation channel involves relaxationprocesses deflecting compact objects on very low angular momentum orbits aroundthe central massive black hole, a number of alternative formation channels hasbeen proposed, including binary tidal break-up, migration in accretion disksand secular and chaotic dynamics around a massive black hole binary (MBHB). Inthis work, we take an extensive closer look at this latter scenario,investigating how EMRIs can be triggered by a MBHBs, formed in the aftermath ofgalaxy mergers. By employing a suite of relativistic three-body simulations, weevaluate the efficiency of EMRI formation for different parameters of the MBHB,assessing the importance of both secular and chaotic dynamics. By modelling thedistribution of compact objects in galaxy nuclei, we estimate the resultingEMRI formation rate, finding that EMRI are produced in a sharp burst, with peakrates that are 10-100 times higher than the standard two-body relaxationchannel, lasting for 10$^6$--10$^8$ years. By coupling our results with anestimate of the cosmic MBHB merger rate, we finally forecast that LISA couldobserve ${\cal O}(10)$ EMRIs per year formed by this channel.

Extreme Mass Ratio Inspirals triggered by Massive Black Hole Binaries: from Relativistic Dynamics to Cosmological Rates