Brillouin-Wigner theory for high-frequency expansion in periodically driven systems: Application to Floquet topological insulators

Takahiro Mikami, Sota Kitamura, Kenji Yasuda, Naoto Tsuji, Takashi Oka, and Hideo Aoki
Phys. Rev. B 93, 144307 – Published 29 April 2016; Erratum Phys. Rev. B 99, 019902 (2019)

Abstract

We construct a systematic high-frequency expansion for periodically driven quantum systems based on the Brillouin-Wigner (BW) perturbation theory, which generates an effective Hamiltonian on the projected zero-photon subspace in the Floquet theory, reproducing the quasienergies and eigenstates of the original Floquet Hamiltonian up to desired order in 1/ω, with ω being the frequency of the drive. The advantage of the BW method is that it is not only efficient in deriving higher-order terms, but even enables us to write down the whole infinite series expansion, as compared to the van Vleck degenerate perturbation theory. The expansion is also free from a spurious dependence on the driving phase, which has been an obstacle in the Floquet-Magnus expansion. We apply the BW expansion to various models of noninteracting electrons driven by circularly polarized light. As the amplitude of the light is increased, the system undergoes a series of Floquet topological-to-topological phase transitions, whose phase boundary in the high-frequency regime is well explained by the BW expansion. As the frequency is lowered, the high-frequency expansion breaks down at some point due to band touching with nonzero-photon sectors, where we find numerically even more intricate and richer Floquet topological phases spring out. We have then analyzed, with the Floquet dynamical mean-field theory, the effects of electron-electron interaction and energy dissipation. We have specifically revealed that phase transitions from Floquet-topological to Mott insulators emerge, where the phase boundaries can again be captured with the high-frequency expansion.

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  • Received 23 November 2015
  • Revised 13 April 2016

DOI:https://doi.org/10.1103/PhysRevB.93.144307

©2016 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Erratum

Erratum: Brillouin-Wigner theory for high-frequency expansion in periodically driven systems: Application to Floquet topological insulators [Phys. Rev. B 93, 144307 (2016)]

Takahiro Mikami, Sota Kitamura, Kenji Yasuda, Naoto Tsuji, Takashi Oka, and Hideo Aoki
Phys. Rev. B 99, 019902 (2019)

Authors & Affiliations

Takahiro Mikami1, Sota Kitamura1, Kenji Yasuda1,*, Naoto Tsuji1,†, Takashi Oka2,‡, and Hideo Aoki1

  • 1Department of Physics, University of Tokyo, Hongo, Tokyo, 113-0033, Japan
  • 2Department of Applied Physics, University of Tokyo, Hongo, Tokyo 113-8656, Japan

  • *Present address: Department of Applied Physics, University of Tokyo, Hongo, Tokyo 113-8656, Japan.
  • Present address: RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan.
  • Present address: Max-Planck-Institut für Physik komplexer Systeme and Max Planck Institut für Chemische Physik fester Stoffe, D-01187 Dresden, Germany.

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Issue

Vol. 93, Iss. 14 — 1 April 2016

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