Topological edge states in Rashba-Dresselhaus spin-orbit-coupled atoms in a Zeeman lattice

Abstract

The last decade has witnessed continuously growing interest in the investigation of spin degrees of freedom in various systems in solid-state physics, atomic physics, optics, and acoustics. The dynamics of spin (or quasi-spin) becomes especially intriguing when it interacts with other degrees of freedom. A well-known example of such interaction is the coupling between spinor and translational degrees of freedom, known as spin-orbit coupling. One of the most spectacular manifestations of the spin-orbit coupling is the appearance of in-gap topological edge states at the boundaries or interfaces between periodic structures. Such topological edge states are particularly robust because they are immune to weak disorder and to absence of backscattering by surface defects. Novel prospects for the exploration of the physics of topological edge states and insulators open in systems of neutral atoms placed in periodic potentials, where diverse gauge potentials can be artificially created. Here, we suggest a new platform, where topological edge states emerge due to the interplay between spin-orbit coupling and a Zeeman lattice, characterized by opposite signs for the spinor components. We illustrate strong effect of different components of spin-orbit coupling on the emergence of the topological states. We also obtain nonlinear edge states and study their instabilities in the presence of interatomic interaction in spin-orbit coupled Bose-Einstein condensates.Discrete and continuous lattices exhibit degeneracies in the eigenmode spectrum when the corresponding Hamiltonian is characterized by suitable spatial symmetries and time-reversal invariance [1]. Graphene, as the paradigm of a honeycomb lattice [2], is one of the best-known examples of structures where energy bands touch at Dirac points. If the underlying symmetries are broken, a gap may open at the Dirac points thus leading to a transition to either a conventional or a topological insulator phase, depending on which symmetry is broken [1]. When such a lattice is located in contact with a material having distinct topological properties, topological states with energies falling into the gap and localized at the edge between two materials may appear. An outstanding perturbation that leads to the appearance of topological edge states is spin-orbit coupling (SOC), which in electronic systems gives rise to the quantum spin Hall effect [3,4].Interest in topological edge states is constantly growing [4,5] and to date the concept of topological insulation has been extended to several areas of physics, where SOC can be emulated by coupling the translational and the internal spinor degrees of freedom, the latter often referred as pseudo-spin. Topological insulators have been realized in acoustic [6] and mechanical systems [7], as well as in optical and optoelectronic systems [8], including gyromagnetic photonic crystals [9][10][11], semiconductor quantum wells [12], arrays of coupled resonators [13,14], metamaterial superlattices [15], helical waveguide arrays [16][17][18], system...

Edge states in proximitized graphene ribbons and flakes in a perpendicular magnetic field: emergence of lone pseudohelical pairs and pure spin-current states

“…Zeeman effects in proximitized graphene were investigated earlier, demonstrating the appearance of the quantum anomalous Hall effect [39] and chiral Majorana modes [40]. Magnetic orbital response of helical edge states to magnetic fields was studied in previous works [7,[41][42][43][44][45][46][47]. Rather surprisingly, the quantum spin Hall edge states, which are generated by uniform intrinsic (Kane-Mele) spin-orbit coupling, are not necessarily destroyed by the cyclotron effect [48,49], which can theoretically be used to switch between the quantum spin Hall and quantum Hall regimes by gating.…”

Floquet Edge Multicolor Solitons

“…To this end, we introduce a formal small parameter 0 < µ 1 as well as scaled variables y j = µ j y and z j = µ j z. These variables are considered independent and thus allow for representations of operators (7) in the form…”

“…The phenomenon of topological insulation, first introduced in solid-state physics, has grown into rapidly expanding interdisciplinary research concept, covering many areas of modern physics, where topological insulators and associated unique physical phenomena and applications have been demonstrated (see reviews [1,2]). For instance, topological insulators have been observed experimentally and analyzed theoretically in mechanical systems [3], acoustics [4,5], with cold atoms in optical lattices [6,7], atomic Bose-Einstein condensates [8,9], polaritons in microcavities [10][11][12], and in various photonic systems [13][14][15][16]. The majority of experiments with topological systems, conducted so far, were performed in essentially linear regime, see, for instance, recent overviews on topological effects in photonics [17,18].…”

Floquet Edge Multicolor Solitons

“…The phenomenon of topological insulation, first introduced in solid‐state physics, has grown into rapidly expanding interdisciplinary research concept, covering many areas of modern physics, where topological insulators and associated unique physical phenomena and applications have been demonstrated (see refs. [1, 2]) For instance, topological insulators have been observed experimentally and analyzed theoretically in mechanical systems, [ 3 ] acoustics, [ 4,5 ] with cold atoms in optical lattices, [ 6,7 ] atomic Bose–Einstein condensates, [ 8,9 ] polaritons in microcavities , [ 10–12 ] and in various photonic systems [ 13–16 ] . The majority of experiments with topological systems, conducted so far, were performed in essentially linear regime, see, for instance, recent overviews on topological effects in photonics.…”