Quadratic band touching points and flat bands in two-dimensional topological Floquet systems

Du, Liang; Zhou, Xiaoting; Fiete, Gregory A.

doi:10.1103/physrevb.95.035136

Cited by 44 publications

(48 citation statements)

References 99 publications

(134 reference statements)

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“…Other contexts include high-temperature superconductivity 11,12 , Wigner crystalisation 13,14 , realising higher-spin analogs of Weylfermions 15 , bands with chiral character 16 , lattice supersolids 17 , fractal geometries 18 , magnets with dipolarinteractions 19 , and Floquet physics 20,21 . Flat bands of magnons also play a crucial role in determining the behaviour of quantum magnets in magnetic fields [22][23][24][25] .…”

Section: Introductionmentioning

confidence: 99%

Disordered flat bands on the kagome lattice

Bilitewski

Moessner

2018

Phys. Rev. B

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We study two models of correlated bond-and site-disorder on the kagome lattice considering both translationally invariant and completely disordered systems. The models are shown to exhibit a perfectly flat ground state band in the presence of disorder for which we provide exact analytic solutions. Whereas in one model the flat band remains gapped and touches the dispersive band, the other model has a finite gap, demonstrating that the band touching is not protected by topology alone. Our model also displays fully saturated ferromagnetic groundstates in the presence of repulsive interactions, an example of disordered flat band ferromagnetism. arXiv:1809.10726v2 [cond-mat.str-el]

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Section: Introductionmentioning

confidence: 99%

Disordered flat bands on the kagome lattice

Bilitewski

Moessner

2018

Phys. Rev. B

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“…The reflection symmetry about the flux φ = 1/2 is observed E(φ) = E(1 − φ), where we used E(φ) to denote the energy spectrum of Hamiltonian [Eq. (20)] with magnetic flux φ. This is because the reflection symmetry about φ = 1/2 is preserved by time-reversal symmetry and changing the lattice will not break the symmetry.…”

Section: Hofstadter Butterfly On the Kagome Latticementioning

confidence: 99%

“…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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“…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%

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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Quadratic band touching points and flat bands in two-dimensional topological Floquet systems

Cited by 44 publications

References 99 publications

Disordered flat bands on the kagome lattice

Disordered flat bands on the kagome lattice

Floquet Hofstadter butterfly on the kagome and triangular lattices

Flow Equation Approach to Periodically Driven Quantum Systems

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