Robustness of symmetry-protected topological states against time-periodic perturbations

Balabanov, Oleksandr; Johannesson, Henrik

doi:10.1103/physrevb.96.035149

Cited by 30 publications

(34 citation statements)

References 47 publications

(62 reference statements)

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“…Indeed, if ∆ V = 0, the unitary and Hermitian operatorwith being the vacuum state, fulfils the relation ΓH 0 Γ † = −H 0 . For the time-periodic part, it holdswhere t 0 = P/ 4 for the in-plane modulation and t 0 = 0 for the out-of-plane modulation, which implies chiral symmetry for Floquet systems (for a proof, see appendix A in 21 ). Being chirally symmetric, our system possesses a zero-energy Floquet mode that exhibits a vanishing amplitude on every second lattice site 21,31 .…”

Section: Methodsmentioning

confidence: 99%

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Limits of topological protection under local periodic driving

et al. 2019

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The bulk-edge correspondence guarantees that the interface between two topologically distinct insulators supports at least one topological edge state that is robust against static perturbations. Here, we address the question of how dynamic perturbations of the interface affect the robustness of edge states. We illuminate the limits of topological protection for Floquet systems in the special case of a static bulk. We use two independent dynamic quantum simulators based on coupled plasmonic and dielectric photonic waveguides to implement the topological Su-Schriefer-Heeger model with convenient control of the full space- and time-dependence of the Hamiltonian. Local time-periodic driving of the interface does not change the topological character of the system but nonetheless leads to dramatic changes of the edge state, which becomes rapidly depopulated in a certain frequency window. A theoretical Floquet analysis shows that the coupling of Floquet replicas to the bulk bands is responsible for this effect. Additionally, we determine the depopulation rate of the edge state and compare it to numerical simulations.

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Section: Methodsmentioning

confidence: 99%

“…In systems with time-periodic driving, the bulk-edge correspondence needs to be generalised, and anomalous edge modes can exist 19,20 . Time-periodic disorder at the boundary can also induce a shift in the energy of the topological edge state under certain conditions 21 .…”

Section: Introductionmentioning

confidence: 99%

Limits of topological protection under local periodic driving

et al. 2019

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“…We define nearly topological states in the sense that their energy eigenvalues remain the same even in the presence of disorder. [24] as robust states still appear in a system which breaks chiral symmetry [25][26][27].…”

Section: Robust Bulk Statesmentioning

confidence: 99%

Robust bulk states

Yüce

2019

Physics Letters A

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“…The value of η is vanishing for the Majorana states, (γ M = γ † M ), from which follows that u i = v * i . When the kicks are aperiodic, as studied in various topological systems [81][82][83][84], after a few kicks the quasi-energy spectrum in general becomes dense, the gaps are filled with states, and in the system considered in this work the criteria of small energies of NPRs become harder to distinguish the normal fermionic localized states from any surviving Majorana modes. Therefore the self-conjugacy is particularly useful to distinguish between the nature of the two states.…”

Section: Effects Of Dynamic Disorder On 1d Kitaev Modelmentioning

confidence: 99%

Static and Dynamic Disorder in Topological Systems: Localized, Critical and Extended States

2019

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Topological properties may be induced or changed by the action of disorder. We investigate two examples of this scenario: in the first, by showing that either trivial or topological two-dimensional superconductors, as a result of a static random distribution of magnetic impurities, display topological phases. The second one involves using timedependent perturbations, which also have the general effect of inducing topology and, under appropriate conditions, the appearance of topological properties is shown. In this case, we consider the effect on the topology of onedimensional systems, of time periodic or aperiodic perturbations consisting of kicks of spatially non-homogeneous potentials. One finds different regimes characterized by localized, critical, or extended non-equilibrium states, as a result of the time dependent perturbation. We further carry out the existence and characterization of the topological edge states that occur both in the case of a static and dynamic perturbations. In the case of the static disorder, the topological phases are characterized calculating the real space Chern number and various regimes for the low energy density of states are identified and explained in the context of general properties of the symmetry classes D and C. In the case of a time periodic perturbation (the Floquet regime) we contrast the dynamical localization, and its properties, when using kicks either in the quasiperiodic spatially inhomogeneous potentials of the Aubry-André type or in the case of kicks on the pairing amplitude in the presence of static Aubry-André quasi-disorder. In both, we make use of lattice sizes drawn from the Fibonacci sequence. We also show that aperiodicity in the sequence of time perturbations leads in general to delocalization, a regime characterized by a fully random matrix Hamiltonian with the appropriate symmetry.

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Robustness of symmetry-protected topological states against time-periodic perturbations

Cited by 30 publications

References 47 publications

Limits of topological protection under local periodic driving

Limits of topological protection under local periodic driving

Robust bulk states

Static and Dynamic Disorder in Topological Systems: Localized, Critical and Extended States

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