Generating end modes in a superconducting wire by periodic driving of the hopping

The existence of gapless boundary states is a key attribute of any topological insulator. Topological band theory predicts that these states are robust against static perturbations that preserve the relevant symmetries. In this article, using Floquet theory, we examine how chiral symmetryprotection extends also to states subject to time-periodic perturbations − in one-dimensional Floquet topological insulators as well as in ordinary one-dimensional time-independent topological insulators. It is found that, in the case of the latter, the edge modes are resistant to a much larger class of time-periodic symmetry-preserving perturbations than in Floquet topological insulators. Notably, boundary states in chiral time-independent topological insulators also exhibit an unexpected resilience against a certain type of symmetry-breaking time-periodic perturbations. We argue that this is a generic property for topological phases protected by chiral symmetry. Implications for experiments are discussed.

show abstract

“…3). Similar states have been seen also in other 1D Floquet systems 30 . These boundary modes are not expected to be of a topological origin.…”

Section: Protection Against Symmetry-preserving Boundary Perturbationssupporting

confidence: 86%

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

Balabanov

Johannesson

2017

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…where U ad k (t f , 0) is the evolution operator in the adiabatic basis, and S T denotes the transpose of S. Using Eqs. (39) and (48), we may obtain the evolution operator for the system at t = t f in terms of r k (in Eqs. ( 46) and ( 47)) and ξ k (t 1 , t 2 ) (in Eq.…”

Section: Adiabatic-impulse Methodsmentioning

confidence: 99%

“…Sometimes we find end modes for which the eigenvalues of U (t) are not equal to ±1; these are called anomalous end modes 48 . Such modes always occur in pairs at each end of the system, with the eigenvalues of the pair being complex conjugates of each other.…”

Section: B End Modesmentioning

confidence: 99%

Low-frequency phase diagram of irradiated graphene and a periodically driven spin- 12 XY chain

et al. 2018

Self Cite

View full text Add to dashboard Cite

We study the Floquet phase diagram of two-dimensional Dirac materials such as graphene and the onedimensional (1D) spin-1/2 XY model in a transverse field in the presence of periodic time-varying terms in their Hamiltonians in the low drive frequency (ω) regime where standard 1/ω perturbative expansions fail. For graphene, such periodic time dependent terms are generated via the application of external radiation of amplitude A0 and time period T = 2π/ω, while for the 1D XY model, they result from a two-rate drive protocol with time-dependent magnetic field and nearest-neighbor couplings between the spins. Using the adiabatic-impulse method, whose predictions agree almost exactly with the corresponding numerical results in the low-frequency regime, we provide several semi-analytic criteria for the occurrence of changes in the topology of the phase bands (eigenstates of the evolution operator U ) of such systems. For irradiated graphene, we point out the role of the symmetries of the instantaneous Hamiltonian H(t) and the evolution operator U behind such topology changes. Our analysis reveals that at low frequencies, topology changes of irradiated graphene phase bands may also happen at t = T /3, 2T /3 (apart from t = T ) showing the necessity of analyzing the phase bands of the system for obtaining its phase diagrams. We chart out the phase diagrams at t = T /3, 2T /3, and T , where such topology changes occur, as a function of A0 and T using exact numerics, and compare them with the prediction of the adiabatic-impulse method. We show that several characteristics of these phase diagrams can be analytically understood from results obtained using the adiabatic-impulse method and point out the crucial contribution of the high-symmetry points in the graphene Brillouin zone to these diagrams. We study the modes which can appear at the edges of a finite-width strip of graphene and show that the change in the number of such modes agrees with the change in the Chern number of bulk graphene as we go across a phase band crossing. Finally we study the 1D XY model with a two-rate driving protocol. After studying the symmetries of the system, we use the adiabatic-impulse method and exact numerics to study its phase band crossing which occurs at t = T /2 and k = π/2. We also study the end modes generated by such a drive and show that there can be anomalous modes whose Floquet eigenvalues are not equal to ±1. We suggest experiments to test our theory. arXiv:1709.06554v1 [cond-mat.mes-hall]

show abstract

“…An interpolation with the symmetries given in Eq. (162) and Eq. (163) can be obtained by first finding an interpolation for λ ∈ [0, π], and then taking the interpolation for λ ∈ [−π, 0] as the mirror interpolation of [0, π].…”

Section: Even-integer (2z) Topological Invariantsmentioning

confidence: 99%

Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects

2017

View full text Add to dashboard Cite

Periodically driven (Floquet) systems have been under active theoretical and experimental investigations. This paper aims at a systematic study in the following aspects of Floquet systems: (i) A systematic formulation of topological invariants of Floquet systems based on the cooperation of topology and symmetries. Topological invariants are constructed for the ten symmetry classes in all spatial dimensions, for both homogeneous Floquet systems (Floquet topological insulators and superconductors) and Floquet topological defects. Meanwhile, useful representative Dirac Hamiltonians for all the symmetry classes are obtained and studied. (ii) A general theory of Floquet topological defects, based on the proposed topological invariants. (iii) Models and proposals of Floquet topological defects in low dimensions. Among other defect modes, we investigate Floquet Majorana zero modes and Majorana Pi modes in vortices of topologically trivial superconductors under a periodic drive. In addition, we clarified several notable issues about Floquet topological invariants. Among other issues, we prove the equivalence between the effective-Hamiltonian-based band topological invariants and the frequency-domain band topological invariants.

show abstract

Generating end modes in a superconducting wire by periodic driving of the hopping

Cited by 22 publications

References 64 publications

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

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

Low-frequency phase diagram of irradiated graphene and a periodically driven spin- 12 XY chain

Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects

Contact Info

Product

Resources

About