Floquet Topological Superfluid and Majorana Zero Modes in Two-Dimensional Periodically Driven Fermi Systems

Yang, X. M.; Huang, Beibing; Wang, Zhengling

doi:10.1038/s41598-018-20604-w

Cited by 13 publications

(8 citation statements)

References 62 publications

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“…19, 20, and 22. In this phase, the Z 2 flux excitations carry pairs of localized Majorana modes at quasi-energies 0 and π/T , where T is the driving period, protected by the time periodicity of the fermionic Hamiltonian. 54 We show that upon exchange, the two Majorana modes behave as two independent non-Abelian Ising anyons.…”

Section: Introductionmentioning

confidence: 82%

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Topology and localization of a periodically driven Kitaev model

et al. 2019

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Periodically driven quantum many-body systems support anomalous topological phases of matter, which cannot be realized by static systems. In many cases, these anomalous phases can be manybody localized, which implies that they are stable and do not heat up as a result of the driving. What types of anomalous topological phenomena can be stabilized in driven systems, and in particular, can an anomalous phase exhibiting non-Abelian anyons be stabilized? We address this question using an exactly solvable, stroboscopically driven 2D Kitaev spin model, in which anisotropic exchange couplings are boosted at consecutive time intervals. The model shows a rich phase diagram which contains anomalous topological phases. We characterize these phases using weak and strong scattering-matrix invariants defined for the fermionic degrees of freedom. Of particular importance is an anomalous phase whose zero flux sector exhibits fermionic bands with zero Chern numbers, while a vortex binds a pair of Majorana modes, which as we show support non-Abelian braiding statistics. We further show that upon adding disorder, the zero flux sector of the model becomes localized. However, the model does not remain localized for a finite density of vortices. Hybridization of Majorana modes bound to vortices form "vortex bands", which delocalize by either forming Chern bands or a thermal metal phase. We conclude that while the model cannot be many-body localized, it may still exhibit long thermalization times, owing to the necessity to create a finite density of vortices for delocalization to occur.

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Section: Introductionmentioning

confidence: 82%

“…19, 20, and 22. In this phase, the Z 2 flux excitations carry pairs of localized Majorana modes at quasi-energies 0 and π/T , where T is the driving period, protected by the time periodicity of the fermionic Hamiltonian. 54 We arXiv:1902.06995v2 [cond-mat.mes-hall] 13 Jun 2019…”

Section: Introductionmentioning

confidence: 99%

Topology and localization of a periodically driven Kitaev model

et al. 2019

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“…This model is equivalent to a pair of coupled first-order anomalous Floquet TSCs [22] with oppositely propagating Floquet chiral Majorana edge modes. The Hamiltonian has a PH symmetry P = Γ 4 K and C 2 = Γ 45 , which corresponds to n = 2 and γ = 1 (J 1 = 0, J 2 = 1).…”

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confidence: 99%

Superconductors with anomalous Floquet higher-order topology

Vu,

Zhang,

Yang

et al. 2021

Preprint

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We develop a general theory for two-dimensional (2D) anomalous Floquet higher-order topological superconductors (AFHOTSC), which are dynamical Majorana-carrying phases of matter with no static counterpart. Despite the triviality of its bulk Floquet bands, an AFHOTSC generically features the simultaneous presence of corner-localized Majorana modes at both zero and π/T quasienergies, a phenomenon beyond the scope of any static topological band theory. We show that the key to AFHOTSC is its unavoidable singular behavior in the phase spectrum of the bulk timeevolution operator. By mapping such evolution-phase singularities to the stroboscopic boundary signatures, we classify all 2D AFHOTSCs that are protected by a rotation group symmetry in symmetry class D. We further extract a higher-order topological index for unambiguously predicting the presence of Floquet corner Majorana modes, which we confirm numerically. Our theory serves as a milestone towards a dynamical topological theory for Floquet superconducting systems.

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“…In future work, it would be interesting to explore similarly enriched two-dimensional (2D) phases. Driven spinless 2D p + ip superconductors also support doubled-periodicity Floquet Majorana modes [35][36][37] and Here m z 10 represents an Ising spin at the center of the chain, c0 is an auxiliary zero-energy static fermion that enables probing the Floquet Majorana mode periodicity, and c1 is the fermion at the left end of the quantumdot chain. For initialization we use random Ising configurations and random fermionic states that entangle c0 with the rest of the system.…”

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confidence: 99%

Time-Crystalline Topological Superconductors

2020

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Time crystals form when arbitrary physical states of a periodically driven system spontaneously break discrete time-translation symmetry. We introduce one-dimensional time-crystalline topological superconductors, for which time-translation symmetry breaking and topological physics intertwine-yielding anomalous Floquet Majorana modes that are not possible in free-fermion systems. Such a phase exhibits a bulk magnetization that returns to its original form after two drive periods, together with Majorana end modes that recover their initial form only after four drive periods. We propose experimental implementations and detection schemes for this new state. arXiv:1907.12570v1 [cond-mat.mes-hall]

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Floquet Topological Superfluid and Majorana Zero Modes in Two-Dimensional Periodically Driven Fermi Systems

Cited by 13 publications

References 62 publications

Topology and localization of a periodically driven Kitaev model

Topology and localization of a periodically driven Kitaev model

Superconductors with anomalous Floquet higher-order topology

Time-Crystalline Topological Superconductors

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