Floquet-Bloch Theory for Nonperturbative Response to a Static Drive
arxiv(2024)
摘要
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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