New aspects of Nonadiabatic Geometric Effects --- Application to Twisted Schwinger Effect in Dirac and Weyl Fermions

We study geometric effects in nonadiabatic quantum tunneling and derive the tunneling formula within the quadratic expansion of the Hamiltonian. In addition to the rectification effect known previously, we find two novel effects, namely perfect tunneling and counterdiabaticity at fast sweep speed. As an application, we study the twisted Schwinger effect, i.e., nonadiabatic pair production of particles induced by a rotating electric field. In 2D and 3D Dirac and Weyl fermions, this gives a nonperturbative generation mechanism for valley polarization and current.