Topological phases, topological flat bands, and topological excitations in a one-dimensional dimerized lattice with spin-orbit coupling

Yan, Zhongbo; Wan, Shaolong

doi:10.1209/0295-5075/107/47007

Cited by 26 publications

(26 citation statements)

References 48 publications

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“…with ε ≡ E/t. It is known that the SSH model is topological if the inter-site tunnelling is larger than the intra-site tunnelling [32,78,[83][84][85][86]. This has been confirmed by a direct measurement of the Zak phase [17] and an observation of the topological state [68] in cold atoms.…”

Section: Su-schrieffer-heeger Modelmentioning

confidence: 82%

Exact edge, bulk, and bound states of finite topological systems

2018

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Finite topologically non-trivial systems are characterised, among many other unique properties, by the presence of bound states at their physical edges. These topological edge modes can be distinguished from usual Shockley waves energetically, as their energies remain finite and in-gap even when the boundaries of the system represent an effectively infinite and sharp energetic barrier. Theoretically, the existence of topological edge modes can be shown by means of the bulkedge correspondence and topological invariants. On a clean one-dimensional lattice and reducible two-dimensional models, in either the commensurate or semi-infinite case, the edge modes can be essentially obtained analytically, as shown in [Phys. Rev. Lett. 71, 3697 (1993)] and [Phys. Rev. A 89, 023619 (2014)]. In this work, we put forward a method for obtaining the spectrum and wave functions of topological edge modes for arbitrary finite lattices, including the incommensurate case. A small number of parameters are easily determined numerically, with the form of the eigenstates remaining fully analytical. We also obtain the bulk modes in the finite system analytically and their associated eigenenergies, which lie within the infinite-size limit continuum. Our method is general and can be easily applied to obtain the properties of non-topological models and/or extended to include impurities. As an example, we consider a relevant case of an impurity located next to one edge of a one-dimensional system, equivalent to a softened boundary in a separable two-dimensional model. We show that a localised impurity can have a drastic effect on the original topological edge modes of the system. Using the periodic Harper and Hofstadter models to illustrate our method, we find that, on increasing the impurity strength, edge states can enter or exit the continuum, and a trivial Shockley state bound to the impurity may appear. The fate of the topological edge modes in the presence of impurities can be addressed by quenching the impurity strength. We find that at certain critical impurity strengths, the transition probability for a particle initially prepared in an edge mode to decay into the bulk exhibits discontinuities that mark the entry and exit points of edge modes from and into the bulk spectrum.

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Section: Su-schrieffer-heeger Modelmentioning

confidence: 82%

Exact edge, bulk, and bound states of finite topological systems

2018

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“…The spin-1/2 SSH chain with spin-orbit interaction [53][54][55][56] is similar to the hourglass CSSH ladder in a certain regime, except for the distribution of magnetic fluxes. The hourglass-CSSH ladder with φ = 0, in its trivial phase, also has the same geometry as certain Cu 2 Te 2 O 5 X 2 compounds with X=Cl, Br [57]; and has been analyzed as a chain of interacting spins [57,58].…”

Section: The Cssh Ladder Modelsmentioning

confidence: 90%

Tunable zero modes and quantum interferences in flat-band topological insulators

Zurita

Creffield

Platero

2021

Quantum

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We investigate the interplay between Aharonov-Bohm (AB) caging and topological protection in a family of quasi-one-dimensional topological insulators, which we term CSSH ladders. Hybrids of the Creutz ladder and the SSH chain, they present a regime with completely flat bands, and a rich topological phase diagram, with several kinds of protected zero modes. These are reminiscent of the Creutz ladder edge states in some cases, and of the SSH chain edge states in others. Furthermore, their high degree of tunability, and the fact that they remain topologically protected even in small systems in the rungless case, due to AB caging, make them suitable for quantum information purposes. One of the ladders can belong to the BDI, AIII and D symmetry classes depending on its parameters, the latter being unusual in a non-superconducting model. Two of the models can also harbor topological end modes which do not follow the usual bulk-boundary correspondence, and are instead related to a Chern number. Finally, we propose some experimental setups to implement the CSSH ladders with current technology, focusing on the photonic lattice case.

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“…Another model has been studied recently, in which Δ Δ δ = ± (1 ) [21]. There is also a study on the spinful SSH model with spin-orbital interaction without superconducting coupling [22].…”

Section: Hamiltonianmentioning

confidence: 99%

A NOT operation on Majorana qubits with mobilizable solitons in an extended Su–Schrieffer–Heeger model

Xiong

Tong

2015

New J. Phys.

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Coupling Majorana qubits with other qubits is absolutely essential for storing, manipulating and transferring information for topological quantum computing. We theoretically propose a manner to couple Majorana qubits with solitons, another kind of topological impurity, which was first studied in the spinless Su-Schrieffer-Heeger model. We present a NOT operation on the Majorana qubit by moving the soliton through a heterostructure adiabatically. Based on these two topological impurities, the operation is robust against local disorder. Furthermore, we find that the soliton may carry nonuniversal fractional electric charge instead of fractional charge1 2, because of the breaking of gauge invariance induced by superconducting proximity.

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Topological phases, topological flat bands, and topological excitations in a one-dimensional dimerized lattice with spin-orbit coupling

Cited by 26 publications

References 48 publications

Exact edge, bulk, and bound states of finite topological systems

Exact edge, bulk, and bound states of finite topological systems

Tunable zero modes and quantum interferences in flat-band topological insulators

A NOT operation on Majorana qubits with mobilizable solitons in an extended Su–Schrieffer–Heeger model

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