Geometric effects in quantum tunneling

Geometric effects in quantum dynamics have gathered interest in condensed matter physics. It is well known that in adiabatic processes, the Berry phase cause nontrivial phenomena, but recently it is understood that geometric effects also play an important role in nonadiabatic processes. A typical example of nonadiabatic processes is quantum tunneling, which has various related phenomena such as electron-positron pair production in vacuum, tunnel ionization of atoms and molecules, and dielectric breakdown due to strong electric fields. In our study, we consider a twisted Landau-Zener Hamiltonian, in which a quadratic term additional to the normal Landau-Zener model produces nonadiabatic geometric effects. This system can be analyzed by a time-dependent unitary transformation, which modulates an effective mass. These effects give rise to nontrivial phenomena such as rectification, gapped perfect tunneling, and counter-diabaticity under fast sweeps. We apply our theory to two-dimensional Weyl electron systems irradiated by a circularly polarized laser and show that the excitation of electron-hole pair production is valley-dependent, i.e., light-induced valley polarization occurs. We also consider three-dimensional Dirac electron systems and show that the chiral current is generated by the circularly polarized laser.