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The measurement of Higgs self-coupling is one of the most crucial physicsgoals at the future colliders. At the LHC, the di-Higgs production is a mainway to measure the Higgs trilinear coupling. As a complementary to the di-Higgsproduction, $t \bar{t} hh$ process may open a new avenue to measure di-Higgsphysics at the LHC and a future 100 TeV $pp$ collider or a high energy $e^+e^-$collider since the extra $t\bar t$ in the final states may efficiently suppressthe backgrounds. However, such a kind of process is also controlled by thetop-Higgs coupling. In this work, we investigate the impact of CP-violatingtop-Higgs coupling on $t\bar{t}hh$ production at the LHC, ILC and a 100 TeVhadron collider under the current Higgs data. Within 2$\sigma$ Higgs dataallowed parameter region, we find that the cross section of $t\bar{t}hh$ at theLHC-14 TeV, ILC-1 TeV and VHE-LHC/SPPC-100 TeV can be enhanced up to 2.1 timesthe SM predictions. The future precise measurement of Higgs coupling willreveal the nature of top-Higgs interaction and improve the sensitivity of thedetermination of Higgs self-coupling through $t\bar{t}hh$ production.

Enhancing $t\bar{t}hh$ production through CP-violating top-Higgs interaction at the LHC, ILC and a 100 TeV collider