Topological phase transition in anisotropic square-octagon lattice with spin–orbit coupling and exchange field

We investigate the topological phase transitions in an anisotropic square-octagon lattice in the presence of spin–orbit coupling and exchange field. On the basis of the Chern number and spin Chern number, we find a number of topologically distinct phases with tuning the exchange field, including time-reversal-symmetry-broken quantum spin Hall phases, quantum anomalous Hall phases and a topologically trivial phase. Particularly, we observe a coexistent state of both the quantum spin Hall effect and quantum anomalous Hall effect. Besides, by adjusting the exchange filed, we find the phase transition from time-reversal-symmetry-broken quantum spin Hall phase to spin-imbalanced and spin-polarized quantum anomalous Hall phases, providing an opportunity for quantum spin manipulation. The bulk band gap closes when topological phase transitions occur between different topological phases. Furthermore, the energy and spin spectra of the edge states corresponding to different topological phases are consistent with the topological characterization based on the Chern and spin Chern numbers.     

Li(Na)AuS体系拓扑绝缘体材料的能带结构

在拓扑领域中发现可以通过大数据搜索拓扑绝缘体,使得此领域对材料的探索转变为对材料性质的研究.半Heusler合金体系是非平庸拓扑绝缘体材料的重要载体.通过全势线性缀加平面波方法计算Li(Na)AuS体系拓扑绝缘体材料的能带结构.采用各种关联泛函计算LiAuS的平衡晶格常数,发现得到的能带图均为具有反带结构的拓扑绝缘体,...     

Spin-filtered edge states in graphene

Spin–orbit coupling changes graphene, in principle, into a two-dimensional topological insulator, also known as quantum spin Hall insulator. One of the expected consequences is the existence of spin-filtered edge states that carry dissipationless spin currents and undergo no backscattering in the presence of non-magnetic disorder, leading to quantization of conductance. Whereas, due to the small size of spin–orbit coupling in graphene, the experimental observation of these remarkable predictions is unlikely, the theoretical understanding of these spin-filtered states is shedding light on the electronic properties of edge states in other two-dimensional quantum spin Hall insulators. Here we review the effect of a variety of perturbations, like curvature, disorder, edge reconstruction, edge crystallographic orientation, and Coulomb interactions on the electronic properties of these spin filtered states.     

Persistence of Spin Edge Currents in Disordered Quantum Spin Hall Systems

For a disordered two-dimensional model of a topological insulator (such as a Kane-Mele model with disordered potential) with small coupling of spin invariance and time-reversal symmetry breaking terms (such as a Rashba spin-orbit coupling and a Zeeman term), it is proved that the spin edge currents persist provided there is a spectral gap and the spin Chern numbers are well-defined and non-trivial. These are sufficient conditions for being in the quantum spin Hall phase. The result materializes the general philosophy that topological insulators are topologically non-trivial bulk systems with persistent edge or surface currents.     

The nondissipative spin Hall current in a nonuniform Rashba effect system

The spin Hall current in a two-dimensional electron system with nonuniform Rashba spin–orbit interaction (SOI) is investigated by means of the lattice Green's function method. Large electric and spin Hall currents are produced by this nonuniform Rashba SOI, while the electric Hall current vanishes in the uniform Rashba SOI system. A nondissipative spin Hall current is also produced, without any longitudinal voltage bias, any external magnetic field and any special class of band insulators.     

缀饰格子中时间反演对称破缺的量子自旋霍尔效应

<正>研究了缀饰格子中的量子自旋霍尔效应,模型中同时考虑了Rashba自旋轨道耦合和交换场的作用.缀饰格子具有简立方对称性,以零能平带和单狄拉克锥结构为主要特点.在缀饰格子中,不论是实现量子自旋霍尔效应还是量子反常霍尔效应,都需要一个不为零的内禀自旋轨道耦合作用来打开一个完全的体能隙,这与石墨烯等六角格子模型有着很大的不同.在交换场破坏了时间反演对称性的情况下,以自旋陈数为标志的量子自旋霍尔效应仍然能够存在,边缘态和极化率的相关结果也证明了这一结论.结果表明自旋陈数比z2拓扑数在表征量子自旋霍尔效应方面有着更广泛的适用范围,相应的结论为利用磁场控制量子自旋霍尔效应提出了一个理论模型和依据.     

A computational investigation of topological insulator Bi2Se3 film

Topological insulators have a bulk band gap like an ordinary insulator and conducting states on their edge or surface which are formed by spin–orbit coupling and protected by time-reversal symmetry. We report theoretical analyses of the electronic properties of three-dimensional topological insulator Bi₂Se₃ film on different energies. We choose five different energies (–123, –75, 0, 180, 350 meV) around the Dirac cone (–113 meV). When energy is close to the Dirac cone, the properties of wave function match the topological insulator’s hallmark perfectly. When energy is far way from the Dirac cone, the hallmark of topological insulator is broken and the helical states disappear. The electronic properties of helical states are dug out from the calculation results. The spin-momentum locking of the helical states are confirmed. A 3-fold symmetry of the helical states in Brillouin zone is also revealed. The penetration depth of the helical states is two quintuple layers which can be identified from layer projection. The charge contribution on each quintuple layer depends on the energy, and has completely different behavior along K and M direction in Brillouin zone. From orbital projection, we can find that the maximum charge contribution of the helical states is p_z orbit and the charge contribution on p_yand p_x orbits have 2-fold symmetry.     

二维有机拓扑绝缘体的研究进展

新材料的发现促进了科学与技术的进步.拓扑绝缘体是近期材料领域新的研究热点,相关研究的进一步深入,不仅加深了人们对材料物理性质的理解,也为其在自旋电子学和量子计算机等领域的潜在应用提供了有价值的参考.近年来,理论工作预测了一系列由金属和有机物构筑的二维有机拓扑绝缘体,本文主要介绍六角对称的金属有机晶格与Kagome金属有机晶格两类典型的二维有机拓扑绝缘体的研究进展,其中重点介绍了理论预测的氰基配位二维本征有机拓扑绝缘体.除了理论计算方面的工作,还简要介绍了关于二维有机拓扑绝缘体材料合成方面的实验工作.二维有机拓扑绝缘体的理论与实验研究不仅拓展了拓扑绝缘体的研究体系,还为寻找新的拓扑绝缘体材料提供了思路.     

Modification of the Hybridization Gap by Twisted Stacking of Quintuple Layers in a Three-Dimensional Topological Insulator Thin Film

Twisting the stacking of layered materials leads to rich new physics. A three-dimensional topological insulator film hosts two-dimensional gapless Dirac electrons on top and bottom surfaces, which, when the film is below some critical thickness, will hybridize and open a gap in the surface state structure. The hybridization gap can be tuned by various parameters such as film thickness and inversion symmetry, according to the literature. The three-dimensional strong topological insulator Bi(Sb)Se(Te) family has layered structures composed of quintuple layers(QLs) stacked together by van der Waals interaction. Here we successfully grow twistedly stacked Sb_2Te_3 QLs and investigate the effect of twist angels on the hybridization gaps below the thickness limit. It is found that the hybridization gap can be tuned for films of three QLs, which may lead to quantum spin Hall states.Signatures of gap-closing are found in 3-QL films. The successful in situ application of this approach opens a new route to search for exotic physics in topological insulators.     

Intrinsic spin–orbit interaction in carbon nanotubes and curved nanoribbons

We present a theoretical study of spin–orbit interaction effects on single wall carbon nanotubes and curved graphene nanoribbons by means of a realistic multiorbital tight-binding model, which takes into account the full symmetry of the honeycomb lattice. Several effects relevant to spin–orbit interaction, namely, the importance of chirality, curvature, and a family-dependent anisotropic conduction and valence band splitting are identified. We show that chiral nanotubes and nanoribbons exhibit spin-split states. Curvature-induced orbital hybridization is crucial to understand the experimentally observed anisotropic spin–orbit splittings in carbon nanotubes. In fact, spin–orbit interaction is important in curved graphene nanoribbons, since the induced spin-splitting on the edge states gives rise to spin-filtered states.     

超冷原子中拓扑超流的发展现状

拓扑超流态是一种奇异物质态,它的内部受能隙保护,而在其系统边缘却可以容纳无能隙的Majorana 费米子。由于该粒子满足非阿贝尔统计,并且受拓扑保护具有良好的稳定性,用它 们携带量子化的信息,可以用于拓扑量子计算的研究。近年来,理论工作预测了各类系统中可能 存在的拓扑超流态。我们首先介绍了在各类光晶格模型中的拓扑超流, 光晶格的超冷原子具有良 好的可控性与普适性,是实现拓扑超流的理想模型系统。接下来我们介绍了自旋轨道耦合调控下 的拓扑超流,自旋轨道耦合效应是诱导拓扑相的重要条件,并且人们已经在实验上合成了人工自 旋轨道耦合,这为实验上观测拓扑超流取得了突破性的进展。随着近年来实验技术的提高,曾经 难以在实验中观测的,被人们所忽略的拓扑Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) 超流相也 成为了人们研究的热点,因此我们接下来介绍了拓扑的FFLO 超流。此外,我们还介绍了拓扑超 流其他方面的进展,包括孤子引诱的拓扑超流、三组分的拓扑超流、大陈数的拓扑超流以及拓扑 超流临界温度的提高。在实验中,如何检测与实现拓扑超流,是其研究的目的及意义所在,因 此我们在文章的最后介绍了拓扑超流的识别与实现。     

Quantum spin Hall effect in graphene

We study the effects of spin orbit interactions on the low energy electronic structure of a single plane of graphene. We find that in an experimentally accessible low temperature regime the symmetry allowed spin orbit potential converts graphene from an ideal two-dimensional semimetallic state to a quantum spin Hall insulator. This novel electronic state of matter is gapped in the bulk and supports the transport of spin and charge in gapless edge states that propagate at the sample boundaries. The edge states are nonchiral, but they are insensitive to disorder because their directionality is correlated with spin. The spin and charge conductances in these edge states are calculated and the effects of temperature, chemical potential, Rashba coupling, disorder, and symmetry breaking fields are discussed.     

Z2 topological order and the quantum spin Hall effect

The quantum spin Hall (QSH) phase is a time reversal invariant electronic state with a bulk electronic band gap that supports the transport of charge and spin in gapless edge states. We show that this phase is associated with a novel Z2 topological invariant, which distinguishes it from an ordinary insulator. The Z2 classification, which is defined for time reversal invariant Hamiltonians, is analogous to the Chern number classification of the quantum Hall effect. We establish the Z2 order of the QSH phase in the two band model of graphene and propose a generalization of the formalism applicable to multiband and interacting systems.     

圆环结构磁光光子晶体中的拓扑相变

二维圆环结构的三角晶格磁光光子晶体中可以呈现多重拓扑相.在不同的几何参数和磁场下,这些拓扑相包括正常光子带隙相、量子自旋霍尔相和反常量子霍尔相.与文献[1]类似,该结果展现了二维光子晶体丰富的拓扑相变现象.     

Chemical memory erasure; a photochemical model

In this paper we propose an exactly solvable model of a topological insulator defined on a spin- \(\tfrac{1}{2}\) square decorated lattice. Itinerant fermions defined in the framework of the Haldane model interact via the Kitaev interaction with spin- \(\tfrac{1}{2}\) Kitaev sublattice. The presented model, whose ground state is a non-trivial topological phase, is solved exactly. We have found out that various phase transitions without gap closing at the topological phase transition point outline the separate states with different topological numbers. We provide a detailed analysis of the model’s ground-state phase diagram and demonstrate how quantum phase transitions between topological states arise. We have found that the states with both the same and different topological numbers are all separated by the quantum phase transition without gap closing. The transition between topological phases is accompanied by a rearrangement of the spin subsystem’s spectrum from band to flat-band states.     

Spin-charge separated solitons in a topological band insulator

In this Letter we construct a simple, controllable, two-dimensional model based on a topological band insulator. It has many attractive properties. (1) We obtain spin-charge separated solitons that are associated with dynamic pi fluxes. (2) These solitons obey Bose statistics and their condensation triggers a phase transition from a spin Hall insulator to an easy-plane ferromagnet. (3) It suggests an alternative way to classify the Z2 topological band insulator without resorting to the sample boundary.     

拓扑绝缘体Bi_2Se_3中层堆垛效应的第一性原理研究

运用第一性原理方法,研究了拓扑绝缘体Bi_2Se_3块体和薄膜中的层堆垛对其结构、电子态、拓扑态和自旋劈裂的影响.发现不同的堆垛会引起Bi_2Se_3层间的相互作用,改变系统的中心对称性.块体的ABC和AAA堆垛都具有中心对称性和相似的能带结构.ABA堆垛破坏了体系的中心对称性,能带发生很大改变,并且产生了很大的能带自旋劈裂.用能带反转的方法判定体系的拓扑相,在不同堆垛的Bi_2Se_3块体中,考虑自旋轨道耦合时都发生了能带反转,因而具有不同堆垛的Bi2Se3仍是拓扑绝缘体.进一步研究了Bi_2Se_3薄膜中的堆垛效应,发现非中心对称的ABA堆垛在Bi_2Se_3薄膜中引起明显的自旋劈裂,并且提出和验证了用应变调控自旋劈裂的方法.     

Time-reversal-symmetry-broken quantum spin Hall effect

The quantum spin Hall (QSH) state of matter is usually considered to be protected by time-reversal (TR) symmetry. We investigate the fate of the QSH effect in the presence of the Rashba spin-orbit coupling and an exchange field, which break both inversion and TR symmetries. It is found that the QSH state characterized by nonzero spin Chern numbers C(±) = ±1 persists when the TR symmetry is broken. A topological phase transition from the TR-symmetry-broken QSH phase to a quantum anomalous Hall phase occurs at a critical exchange field, where the bulk band gap just closes. It is also shown that the transition from the TR-symmetry-broken QSH phase to an ordinary insulator state cannot happen without closing the band gap.