Floquet band structure of a semi-Dirac system

Chen, Qi; Du, Liang; Fiete, Gregory A.

doi:10.1103/physrevb.97.035422

Cited by 52 publications

(45 citation statements)

References 91 publications

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“…To study the J 1 -J 2 models in Eqs. (35), (39) and their approximate counterparts in Eqs. (48), (51) we employ exact diagonalization [97].…”

Section: Flow Equation Approach For the Xy-spin Chain With Anti-symmementioning

confidence: 99%

“…In non-interacting systems H F can be used to dynamically engineer interesting and topological band structures [29][30][31][32][33][34][35][36][37][38], most notably Floquet topological insulators [39][40][41][42][43][44]. Our main interest, however, is interacting systems where H F can be engineered to drive phase transitions [45,46], or, in the case of Floquet-MBL systems, realize new phases without equilibrium analogs [18,19,[47][48][49].…”

Section: Introductionmentioning

confidence: 99%

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Flow Equation Approach to Periodically Driven Quantum Systems

et al. 2019

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We present a theoretical method to generate a highly accurate time-independent Hamiltonian governing the finite-time behavior of a time-periodic system. The method exploits infinitesimal unitary transformation steps, from which renormalization group-like flow equations are derived to produce the effective Hamiltonian. Our tractable method has a range of validity reaching into frequencyand drive strength-regimes that are usually inaccessible via high frequency ω expansions in the parameter h/ω, where h is the upper limit for the strength of local interactions. We demonstrate exact properties of our approach on a simple toy-model, and test an approximate version of it on both interacting and non-interacting many-body Hamiltonians, where it offers an improvement over the more well-known Magnus expansion and other high frequency expansions. For the interacting models, we compare our approximate results to those found via exact diagonalization. While the approximation generally performs better globally than other high frequency approximations, the improvement is especially pronounced in the regime of lower frequencies and strong external driving. This regime is of special interest because of its proximity to the resonant regime where the effect of a periodic drive is the most dramatic. Our results open a new route towards identifying novel non-equilibrium regimes and behaviors in driven quantum many-particle systems.

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“…To study the J 1 -J 2 models in Eqs. (35), (39) and their approximate counterparts in Eqs. (48), (51) we employ exact diagonalization [97].…”

Section: Flow Equation Approach For the Xy-spin Chain With Anti-symmementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Flow Equation Approach to Periodically Driven Quantum Systems

et al. 2019

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“…By tuning the intensity and frequency of the radiation, one can dynamically tune these photon-dressed bands and hence control the properties of the irradiated system. Besides the control of direct exchange coupling already mentioned, Floquet dynamics also strongly influence transport properties [35][36][37], optical properties [38][39][40], topological phases [41][42][43], and interlayer tunneling [44,45].…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium RKKY interaction in irradiated graphene

Modi

Asmar

Tse

2020

Phys. Rev. Research

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We demonstrate that the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in graphene can be strongly modified by a time-periodic driving field even in the weak drive regime. This effect is due to the opening of a dynamical band gap at the Dirac points when graphene is exposed to circularly polarized light. Using Keldysh-Floquet Green's functions, we develop a theoretical framework to calculate the time-averaged RKKY coupling under weak periodic drives, and we show that its magnitude in undoped graphene can be decreased controllably by increasing the driving strength, while mostly maintaining its ferromagnetic or antiferromagnetic character. In doped graphene, we find RKKY oscillations with a period that is tunable by the driving field. When a sufficiently strong drive is turned on that brings the Fermi level completely within the dynamically opened gap, the behavior of the RKKY coupling changes qualitatively from that of doped to undoped irradiated graphene.

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“…At the noninteracting level, dramatic changes in the band structure can occur, including a change from a non-topological band structure to a topological one. [8][9][10][11][12][13][14][15][16][17][18][19][20][21] Two commonly discussed physical scenarios for periodically driven systems include periodic changes in the laser fields that establish the optical lattice potential for cold atom systems, 22,23 and solid state systems that are driven by a monochromatic laser field. [24][25][26][27][28][29][30][31] The effect of light on the Hofstadter butterfly has not been studied extensively.…”

Section: Introductionmentioning

confidence: 99%

Floquet Hofstadter butterfly on the kagome and triangular lattices

Chen

Barr

et al. 2018

Phys. Rev. B

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In this work we use Floquet theory to theoretically study the influence of monochromatic circularly and linearly polarized light on the Hofstadter butterfly-induced by a uniform perpendicular magnetic field-for both the kagome and triangular lattices. In the absence of the laser light, the butterfly has fractal structure with inversion symmetry about magnetic flux φ = 1/4, and reflection symmetry about φ = 1/2. As the system is exposed to an external laser, we find circularly polarized light deforms the butterfly by breaking the mirror symmetry at flux φ = 1/2. By contrast, linearly polarized light deforms the original butterfly while preserving the mirror symmetry at flux φ = 1/2. We find the inversion symmetry is always preserved for both linear and circular polarized light. For linearly polarized light, the Hofstadter butterfly depends on the polarization direction. Further, we study the effect of the laser on the Chern number of lowest band in the off-resonance regime (laser frequency is larger than the bandwidth). For circularly polarized light, we find that low laser intensity will not change the Chern number, but beyond a critical intensity the Chern number will change. For linearly polarized light, the Chern number depends on the polarization direction. Our work highlights the generic features expected for the periodically driven Hofstadter problem on different lattices.

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Floquet band structure of a semi-Dirac system

Cited by 52 publications

References 91 publications

Flow Equation Approach to Periodically Driven Quantum Systems

Flow Equation Approach to Periodically Driven Quantum Systems

Nonequilibrium RKKY interaction in irradiated graphene

Floquet Hofstadter butterfly on the kagome and triangular lattices

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