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arXiv · 2401.17368

Floquet-Bloch Theory for Nonperturbative Response to a Static Drive

Christophe De Beule·Steven Gassner·Spenser Talkington·E. J. Mele
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Abstract

We develop the Floquet-Bloch theory of noninteracting fermions on a periodic lattice in the presence of a constant electric field. As long as the field lies along a reciprocal lattice vector, time periodicity of the Bloch Hamiltonian is inherited from the evolution of momentum in the Brillouin zone. The corresponding Floquet quasienergies yield the Wannier-Stark ladder with interband couplings included to all orders. These results are compared to perturbative results where the lowest-order interband correction gives the field-induced polarization shift in terms of the electric susceptibility. Additionally, we investigate electronic transport by coupling the system to a bath within the Floquet-Keldysh formalism. We then study the breakdown of the band-projected theory from the onset of interband contributions and Zener resonances in the band-resolved currents. In particular, we consider the transverse quantum-geometric response in two spatial dimensions due to the Berry curvature. In the strong-field regime, the semiclassical theory predicts a plateau of the geometric response as a function of field strength. Here, we scrutinize the conditions under which the semiclassical results continue to hold in the quantum theory.

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Christophe De Beule, Steven Gassner, Spenser Talkington, E. J. Mele. 2024-01-30. Floquet-Bloch Theory for Nonperturbative Response to a Static Drive. https://doi.org/10.1103/physrevb.109.235421

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