Flat bands in lattices with non-Hermitian coupling

Leykam, Daniel; Flach, Sergej; Chong, Yidong

doi:10.1103/physrevb.96.064305

Cited by 85 publications

(71 citation statements)

References 56 publications

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“…Another interesting interesting avenue for future research is the case of non-Hermitian Hamiltonians allowing for gain and loss terms in the Hamiltonian (2). Recently a number of works 57,58 analyzed flat bands in such systems or considered the fate of flat bands in the presence of non-Hermitian perturbations 50,59 and finding interesting results. Finally, non-Hermitian Hamiltonians have a larger parameter space suggesting richer classification as compared to the Hermitian case.…”

Section: Discussionmentioning

confidence: 99%

Universal d=1 flat band generator from compact localized states

2019

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The band structure of some translationally invariant lattice Hamiltonians contains strictly dispersionless flat bands(FB). These are induced by destructive interference, and typically host compact localized eigenstates (CLS) which occupy a finite number U of unit cells. FBs are important due to macroscopic degeneracy and consequently due to their high sensitivity and strong response to different types of weak perturbations. We use a recently introduced classification of FB networks based on CLS properties, and extend the FB Hamiltonian generator introduced in Phys. Rev. B 95, 115135 (2017) to an arbitrary number ν of bands in the band structure, and arbitrary size U of a CLS. The FB Hamiltonian is a solution to equations that we identify with an inverse eigenvalue problem. These can be solved only numerically in general. By imposing additional constraints, e.g. a chiral symmetry, we are able to find analytical solutions to the inverse eigenvalue problem.

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Section: Discussionmentioning

confidence: 99%

Universal d=1 flat band generator from compact localized states

2019

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“…The excitation of any superposition of CLSs is localized and diffractionless in the dynamical process. This dynamics is considerably different from that of a confined polynomial increase of excitation in the non-Hermitian lattices, where flat bands are entirely constituted by EPs [68,69]. Equations (21)-(23) are valid for the zero-energy flat band when J = 0.…”

Section: Compact Localized Statesmentioning

confidence: 94%

“…The renormalization coefficient is Ω = N j=1 |ζ j | 2 and ζ j is an arbitrary number. Antisymmetric excitation is diffractionless with a constant intensity [67], different from that in a non-Hermitian flat band entirely constituted by EPs [68,69].…”

Section: Flat Bandmentioning

confidence: 98%

Flat band induced by the interplay of synthetic magnetic flux and non-Hermiticity

Jin

2019

Phys. Rev. A

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A flat band is nondispersive and formed under destructive interference. Although flat bands are found in various Hermitian systems, to realize a flat band in non-Hermitian systems is an interesting task. Here, we propose a flat band in a parity-time symmetric non-Hermitian lattice. The proposed flat band has entirely real energy and is formed at an appropriate match between synthetic magnetic flux and non-Hermiticity. The flat band energy is tunable. At a weak intercell coupling, the flat band is isolated; whereas at a strong intercell coupling, it intersects with the dispersive band at the non-Hermitian phase transition point. The eigenstates of the flat band are compact localized states and are confined in one, two, or three unit cells at the edges or inside the non-Hermitian lattice.

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“…Flatband geometries [1][2][3][4][5][6][7][8][9][10][11][12] have attracted great interest in recent years due to the existence of at least one completely dispersionless band in their energy spectrum which bring new perspectives to the study of various fascinating phenomena, including fractional quantum Hall effect [13][14][15][16] , inverse Anderson localization [17][18][19][20][21][22] , conservative PT-symmetric compact solutions [23][24][25][26][27][28] , and nonlinear compact breathers [29][30][31][32] . Destructive interference is the essence of a flatband existence, and the associated eigenmodes are compact in real space -hence dubbed compact localized states (CLSs).…”

Section: Introductionmentioning

confidence: 99%

Observation of quincunx-shaped and dipole-like flatband states in photonic rhombic lattices without band-touching

et al. 2020

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We demonstrate experimentally the existence of compact localized states (CLSs) in a quasi-one-dimensional photonic rhombic lattice in presence of two distinct refractive-index gradients (i.e., a driven lattice ribbon) acting as external direct current (dc) electric fields. Such a lattice is composed of an array of periodically arranged evanescently coupled waveguides, which hosts a perfect flatband that touches both remaining dispersive bands when it is not driven. The external driving is realized by modulating the relative writing beam intensity of adjacent waveguides. We find that a y-gradient set perpendicularly to the ribbon preserves the flatband while removing the band-touching. The undriven CLS -which occupies two lattices sites over one unit cell -turns into a quincunx-shaped CLS spanned over two unit cells. Instead, an x-gradient acting parallel to the ribbon yields a Stark ladder of CLS whose spatial profile is unchanged with respect to the undriven case. We notably find that their superposition leads to Bloch-like oscillations in momentum space.

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Flat bands in lattices with non-Hermitian coupling

Cited by 85 publications

References 56 publications

Universal d=1 flat band generator from compact localized states

Universal d=1 flat band generator from compact localized states

Flat band induced by the interplay of synthetic magnetic flux and non-Hermiticity

Observation of quincunx-shaped and dipole-like flatband states in photonic rhombic lattices without band-touching

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