Floquet-Bloch Theory for Nonperturbative Response to a Static Drive
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arXiv
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| Format: | Preprint |
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2024
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| author | De Beule, Christophe Gassner, Steven Talkington, Spenser Mele, E. J. |
| author_facet | De Beule, Christophe Gassner, Steven Talkington, Spenser Mele, E. J. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17368 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Floquet-Bloch Theory for Nonperturbative Response to a Static Drive De Beule, Christophe Gassner, Steven Talkington, Spenser Mele, E. J. Mesoscale and Nanoscale Physics 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. |
| title | Floquet-Bloch Theory for Nonperturbative Response to a Static Drive |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2401.17368 |