Dirac materials under linear polarized light: quantum wave function time evolution and topological Berry phases as classical charged particles trajectories under electromagnetic fields

Abstract

The response of electrons under linearly polarized light in Dirac materials as borophene or graphene is analyzed in a continuous wave regime for an arbitrary intense field. Using a rotation and a time-dependent phase transformation, the wave function evolution is shown to be governed by a spinor-component decoupled Whittaker-Hill equation. The numerical solution of these equations enables to find the quasienergy spectrum. For borophene it reveals a strong anisotropic response. By applying an extra unitary transformation, the wave functions are proven to follow an Ince equation. The evolution of the real and imaginary parts of the wave function is interpreted as the trajectory of a classical charged particle under oscillating electric and magnetic field. The topological properties of this forced quantum system are studied using this analogy. In particular, in the adiabatic driving regime, the system is described with an effective Matthieu equation while in the non-adiabatic regime the full Whittaker-Hill equation is needed. From there, it is possible to separate the dynamical and Berry phase contributions to obtain the topological phase diagram due to the driving. Therefore, a different path to perturbation theory is developed to obtain time-driven topological phases.

Time domain photonic hook beam for manipulating nanoparticles along curved trajectories

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Wigner transport in linear electromagnetic fields

“…The analysis of charged quantum particles in electromagnetic fields is, among others, particularly important to nanoelectronics [1][2][3][4][5][6][7][8]. The established Wigner formulation of quantum mechanics [9] (see recent reviews [10,11] and book [12]) defines the Wigner function by applying the Weyl transform to the density matrix [13]:…”

Floquet engineering of tilted and gapped Dirac bandstructure in 1T$$^\prime$$-MoS$$_2$$

“…Another example where Floquet engineering plays an important role is provided by the optical control of magnetic properties 16 – 19 . In contrast, a linearly-polarized optical field leads to an in-plane anisotropy and could affect the sequential-tunneling current of doped electrons for a non-zero polarization angle 20 , 21 . Additionally, a band gap could also be produced in a high-intensity field regime for circularly-polarized irradiation 22 .…”