Nontrivial Bloch oscillation and Zener tunneling frequencies in helicoidal molecules due to spin-orbit coupling

Bloch oscillation and Zener tunneling are investigated in helicoidal molecules, with DNA as the representative example, in the presence of spin-orbit coupling induced by electrical charges accumulated along the structure of the molecule. We show that the presence of the spin-orbit coupling does not destroy the Bloch oscillations and, further, it induces the appearance of nontrivial Bloch oscillation frequencies associated with resonances among Wannier-Stark states. The Zener tunneling between the spin states is also studied here by looking at the time evolution of the polarization of the wave packet. The results show that the polarization also oscillates with nontrivial well-determined frequencies.