Floquet-surface bound states in the continuum in a resonantly driven one-dimensional tilted defect-free lattice

Zhu, Bo; Ke, Yongguan; Liu, Wenjie; Zhou, Zheng; Zhong, Honghua

doi:10.1103/physreva.102.023303

Cited by 6 publications

(2 citation statements)

References 38 publications

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“…The states of a periodically driven system are labeled by the eigenvalues of U T . It is possible for states localized near the boundaries to have Floquet eigenvalues which lie within the continuum of eigenvalues of the bulk states; these are called Floquet bound states in a continuum [49][50][51]. When we numerically find states which appear to be candidates for such bound states, we have to study their wave functions carefully to decide if they are true bound states (with normalizable wave functions) or if they merely have large values in some restricted regions of space but are not normalizable (for an infinite system size) because their wave functions do not go to zero fast enough outside those regions.…”

Section: Introductionmentioning

confidence: 99%

Floquet engineering of edge states in the presence of staggered potential and interactions

Sur

Sen

2021

Phys. Rev. B

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We study the effects of a periodically driven electric field applied to a variety of tight-binding models in one dimension. We first consider a noninteracting system with or without a staggered on-site potential, and we find that periodic driving can generate states localized completely or partially near the ends of a finite-sized system. Depending on the system parameters, such states have Floquet eigenvalues lying either outside or inside the continuum of eigenvalues of the bulk states. In the former case, we find that these states are completely localized at the ends and are true edge states, while in the latter case, the states are not completely localized at the ends although the localization can be made almost perfect by tuning the driving parameters. We then consider a system of two bosonic particles which have an on-site Hubbard interaction and show that a periodically driven electric field can generate two-particle states which are localized at the ends of the system. We show that many of these effects can be understood using a Floquet perturbation theory which is valid in the limit of a large staggered potential or large interaction strength. Some of these effects can also be understood qualitatively by considering time-independent Hamiltonians which have a potential at the sites at the edges; Hamiltonians of these kinds effectively appear in a Floquet-Magnus analysis of the driven problem. Finally, we discuss how the edge states produced by periodic driving of a noninteracting system of fermions can be detected by measuring the differential conductance of the system.

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Section: Introductionmentioning

confidence: 99%

Floquet engineering of edge states in the presence of staggered potential and interactions

Sur

Sen

2021

Phys. Rev. B

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“…In a periodically driven system, however, we must label states by the eigenvalues of the Floquet operator; these are phases which correspond to points lying on a unit circle. It is possible that bound states will have Floquet eigenvalues which lie within the continuum of eigenvalues of the bulk states; these are called 'Floquet bound states in a continuum' [46][47][48] . When we numerically find states which appear to be candidates for such bound states, we have to study their wave functions carefully to decide if they are really bound states (with normalizable wave functions) or if they merely have large values in some restricted regions of space but are not normalizable (for an infinite system size) because their wave functions do not go to zero fast enough outside those regions.…”

Section: Introductionmentioning

confidence: 99%

Floquet engineering of edge states in the presence of staggered potential and interactions

Sur,

Sen

2020

Preprint

View full text Add to dashboard Cite

We study the effects of a periodically driven electric field applied to a variety of tight-binding models in one dimension. We first consider a non-interacting system with or without a staggered on-site potential, and we find that that periodic driving can generate states localized completely or partially near the ends of a finite-sized system. Depending on the system parameters, such states have Floquet eigenvalues lying either outside or inside the continuum of eigenvalues of the bulk states; only in the former case we find that these states are completely localized at the ends and are true edge states. We then consider a system of two bosonic particles which have an on-site Hubbard interaction and show that a periodically driven electric field can generate two-particle states which are localized at the ends of the system. We show that many of these effects can be understood using a Floquet perturbation theory which is valid in the limit of large staggered potential or large interaction strength. Some of these effects can also be understood qualitatively by considering time-independent Hamiltonians which have a potential at the sites at the edges; Hamiltonians of these kind effectively appear in a Floquet-Magnus analysis of the driven problem. Finally, we discuss how the edge states produced by periodic driving of a non-interacting system of fermions can be detected by measuring the differential conductance of the system.

show abstract

Edge states in quantum spin chains: The interplay among interaction, gradient magnetic field, and Floquet engineering

et al. 2021

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Floquet-surface bound states in the continuum in a resonantly driven one-dimensional tilted defect-free lattice

Cited by 6 publications

References 38 publications

Floquet engineering of edge states in the presence of staggered potential and interactions

Floquet engineering of edge states in the presence of staggered potential and interactions

Floquet engineering of edge states in the presence of staggered potential and interactions

Edge states in quantum spin chains: The interplay among interaction, gradient magnetic field, and Floquet engineering

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