Rashba自旋轨道耦合下square-octagon晶格的拓扑相变

本文研究了各向同性square-octagon晶格在内禀自旋轨道耦合、Rashba自旋轨道耦合和交换场作用下的拓扑相变,同时引入陈数和自旋陈数对系统进行拓扑分类.系统在自旋轨道耦合和交换场的影响下会出现许多拓扑非平庸态,包括时间反演对称破缺的量子自旋霍尔态和量子反常霍尔态.特别的是,在时间反演对称破缺的量子自旋霍尔效应中,无能隙螺旋边缘态依然能够完好存在.调节交换场或者填充因子的大小会导致系统发生从时间反演对称破缺的量子自旋霍尔态到自旋过滤的量子反常霍尔态的拓扑相变.边缘态能谱和自旋谱的性质与陈数和自旋陈数的拓扑刻画完全一致.这些研究成果为自旋量子操控提供了一个有趣的途径.     

一维超冷原子动量光晶格中的手征对称性破缺拓扑相

对称性在理解物质的拓扑态方面具有关键作用.过去人们认为手征对称性保证了一维晶格的量子化Zak相位及其对应的非平庸拓扑相.本文展现了在一维手征对称性破缺的情况下,晶格系统仍具有量子化Zak相位和非平庸拓扑相.具体而言,在超冷原子动量晶格系统中有效地模拟了一个链长为26、手征对称性破缺的Zigzag模型,其中相等的次近邻耦合强度能够在保留空间反演对称性的同时破坏手征对称性.通过测量原子的时间平均波包位移来获得系统的拓扑不变量,并得到了其对应的量子化的Zak相位.此外,还观测到系统随着最近邻耦合强度比例的变化会从非平庸拓扑相转变为平庸拓扑相.本文不仅为对称性及拓扑相的相关研究提供了一个完全可控的平台,还可以通过控制格点间耦合强度和原子间相互作用,探索例如Tasaki, Aharonov-Bohm caging模型中的平带拓扑以及引入相互作用研究的非线性拓扑现象.     

具有大磁晶各向异性能的单层BaPb的室温量子反常霍尔效应

具有巨大应用潜力的二维材料在纳米技术领域引起了人们极大的研究兴趣.基于第一性原理计算,本文预测了二维六角晶格BaPb体系具有室温量子反常霍尔效应.体系磁基态是铁磁半金属态,并且自旋极化的Pb-p轨道导致体系的时间反演对称性破缺.具有非零Chern数(C=1)的单层BaPb中非平庸拓扑性来源于全自旋极化的p_(x,y)轨道形成的二次型非狄拉克能带.不同于之前报道的p_z轨道形成的狄拉克拓扑态很容易被衬底破坏,p_(x,y)轨道形成的σ键非常稳定.当考虑自旋-轨道耦合作用时,二次型的非狄拉克点打开了接近177.39 meV的非平庸带隙.通过反常霍尔电导、陈数、贝里曲率和边缘态的计算,证实了 BaPb非平庸的拓扑性.此外,体系还表现出每个单元52.01 meV的大磁晶各向异性能.     

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.     

一维二元复式晶格的拓扑不变量与边缘态

在紧束缚近似下,系统地求解了一维二元复式晶格中电子的能量本征值问题,并且根据推广的布洛赫定理得到了有限晶格边缘态的解析表达式.边缘态可以普遍地存在于一维二元复式晶格中,并不仅仅局限于Su-Schrieffer-Heeger拓扑晶格.由于空间反演对称性破缺,Rice-Mele晶格是拓扑平庸的,但其边缘态对系统的非对角无序也是鲁棒的,缠绕数可以作为有限一维二元复式晶格存在边缘态的普遍判据.     

一维自旋轨道模型中自旋-轨道能隙产生机理分析

讨论考虑洪特耦合的两带赫伯德模型得到的一维自旋轨道模型中自旋-轨道能隙的产生.运用SU(4)赝费米子表象下的平均场理论,计算求得价键序参数、准粒子激发谱能隙和自旋、轨道密度-密度关联函数随系统耦合参数变化的结果.随洪特耦合相互作用由零开始增强,系统激发谱能隙逐渐打开,并且系统在参数取值为J₁/J₂=1/3处由具有阻错的无序状态相变到自旋铁磁有序和轨道反铁磁有序的状态.     

声子晶体中的多重拓扑相

研究了圆环型波导依照蜂窝结构排列的声子晶体系统中的拓扑相变.利用晶格结构的点群对称性实现赝自旋,并在圆环中引入旋转气流来打破时间反演对称性.通过紧束缚近似模型计算的解析结果表明,没有引入气流时,调节几何参数,系统存在普通绝缘体和量子自旋霍尔效应绝缘体两个相;引入气流后,可以实现新的时间反演对称性破缺的量子自旋霍尔效应相,而增大气流强度,则可以实现量子反常霍尔效应相.这三个拓扑相可以通过自旋陈数来分类.通过有限元软件模拟了多个系统中边界态的传播,发现不同于量子自旋霍尔效应相,量子反常霍尔相系统的表面只支持一种自旋的边界态,并且它无需时间反演对称性保护.     

阻挫对准一维非对称子格反铁磁链自旋波激发的影响

子格对称性破缺使得s=1/2准一维海森伯自旋链具有三支自旋波激发谱(其中一支属于声学模，两支属于光学模). 计算表明：阻挫导致两支光学模能隙简并解除；阻挫引起声学模自旋波激发谱软化，但并不导致光学模激发谱软化；阻挫导致两支光学模激发谱中的一支明显下移，这意味着阻挫使光学模激发变得重要且容易实现；阻挫引起的自旋偏离对于属于不同子格的自旋是不同的；阻挫对于系统基态磁性长程序的削弱随着阻挫增强变得越来越明显. 通过与严格对角化方法和DMRG方法的数值结果比较，还分析了自旋波近似的合理性和不足之处. 关键词： 准一维反铁磁自旋系统 自旋波激发 光学模 能隙简并     

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。     

二维拓扑材料的新进展——纯平锡烯中存在大的拓扑能隙

近年来,得益于拓扑物理理论和二维材料制备的迅速发展,以量子自旋霍尔绝缘体为代表的二维拓扑材料的研究受到热切关注^[1,2]。早在2005年前后,理论表明在二维材料体系如石墨烯^[3]和HgTe量子阱体系^[4]中由于自旋轨道耦合作用而存在拓扑量子自旋霍尔效应。然而石墨烯中的碳是轻元素,自旋轨道作用非常微弱,所以其拓扑能隙太小。HgTe由于由重元素组成,自旋轨道耦合作用较强,其拓扑量子自旋霍尔态在2007年的实验中得到验证^[5],但仍需在很低的温度下才能得以实现。人们期望能在更高温度乃至室温下工作的具有更大拓扑能隙的量子自旋霍尔体系的发现。     

An elementary rigorous proof of bulk-boundary correspondence in the generalized Su-Schrieffer-Heeger model

We generalize the Su-Schrieffer-Heeger (SSH) model with the inclusion of arbitrary long-range hopping amplitudes, providing a simple framework to investigate arbitrary adiabatic deformations that preserve the chiral symmetry upon the bulk energy bands with any arbitrary winding numbers. Using only elementary techniques of solving linear difference equations and applying Cauchy's integral formula, we obtain a mathematically rigorous and physically transparent proof of the bulk-boundary correspondence for the generalized SSH model. The multiplicity of robust zero-energy edge modes is shown to be identical to the winding number. On the other hand, nonzero-energy edge modes, if any, are shown to be unstable under adiabatic deformations and not related to the topological invariant. Furthermore, under deformations of small spatial disorder, the zero-energy edge modes remain robust.     

超构材料中的光学拓扑态

拓扑态是当前凝聚态物理中的研究热点,是一种由于整体拓扑效应所导致的全新电子态。近年来,大量理论和实验工作表明,由于拓扑态本质上是一种单粒子波动行为,因此可以在光学体系中找到类比,于是开启了光学拓扑态这一新兴研究方向。光子晶体、光学耦合腔阵列等体系成为重要的拓扑态模拟平台。文章主要以一维Dirac方程体系和二维p波超导体系为例,介绍超构材料(Metamaterials)中的光学拓扑态特性,包括能带翻转、边界态、畴壁、涡旋零能态等典型拓扑行为。     

Topological Phonon Modes in a Two-Dimensional Wigner Crystal

We investigate the spin-orbit coupling effect in a two-dimensional(2D)Wigner crystal.It is shown that sufficiently strong spin-orbit coupling and an appropriate sign of g-factor could transform the Wigner crystal to a topological phonon system.We demonstrate the existence of chiral phonon edge modes in finite size samples,as well as the robustness of the modes in the topological phase.We explore the possibility of realizing the topological phonon system in 2D Wigner crystals confined in semiconductor quantum wells/heterostructure.It is found that the spin-orbit coupling is too weak for driving a topological phase transition in these systems.It is argued that one may look for topological phonon systems in correlated Wigner crystals with emergent effective spin-orbit coupling.     

Topological superfluid in a two-dimensional polarized Fermi gas with spin-orbit coupling and adiabatic rotation

We study the properties of superfluid in a two-dimensional(2 D) polarized Fermi gas with spin–orbit coupling and adiabatic rotation which are trapped in a harmonic potential. Due to the competition between polarization, spin–orbit coupling, and adiabatic rotation, the Fermi gas exhibits many intriguing phenomena. By using the Bardeen–Cooper–Schrieffer(BCS) mean-field method with local density approximation, we investigate the dependence of order parameter solution on the spin–orbit coupling strength and the rotation velocity. The energy spectra with different rotation velocities are studied in detail. Besides, the conditions for the zero-energy Majorana fermions in topological superfluid phase to be observed are obtained. By investigating distributions of number density, we find that the rotation has opposite effect on the distribution of number density with different spins, which leads to the enhancement of the polarization of Fermi gas. Here,we focus on the region of BCS pairing and ignore the Fulde–Ferrell–Larkin–Ovchinnikov state.     

Topological origin of zero-energy edge states in particle-hole symmetric systems

A criterion to determine the existence of zero-energy edge states is discussed for a class of particle-hole symmetric Hamiltonians. A "loop" in a parameter space is assigned for each one-dimensional bulk Hamiltonian, and its topological properties, combined with the chiral symmetry, play an essential role. It provides a unified framework to discuss zero-energy edge modes for several systems such as fully gapped superconductors, two-dimensional d-wave superconductors, and graphite ribbons. A variance of the Peierls instability caused by the presence of edges is also discussed.     

Majorana zero modes induced by skyrmion lattice

One-dimensional s-wave superconductor with spin-orbit coupling is a platform for the realization of Majorana zero modes. The spin-exchange with the magnetic skyrmion lattice can induce spin-orbit coupling in a s-wave superconductor system and the effects are different from the constant spin-orbit coupling. The strength of the effective spin-orbit coupling as well as the rich topoloigcal phase diagram are directly connected to the radius of the skyrmion lattice R. We obtain the rich topological phase diagram of this system with different skyrmion lattice radii by numerically evaluating the spectrum of the system under the periodic boundary condition, and we also find the Majorana zero modes under the open boundary condition to verify the bulk-edge correspondence.     

Topological and Nontopological Edge States Induced by Qubit-Assisted Coupling Potentials

In the usual Su–Schrieffer–Heeger (SSH) chain, the topology of the energy spectrum is divided into two categories in different parameter regions. Here, the topological and nontopological edge states induced by qubit-assisted coupling potentials in circuit quantum electrodynamics (QED) lattice modeled as a SSH chain are studied. It is found that, when the coupling potential added on only one end of the system raises to a certain extent, the strong coupling potential will induce a new topologically nontrivial phase accompanied by the appearance of a nontopological edge state, and the novel phase transition leads to the inversion of odd–even effect directly. Furthermore, the topological phase transitions when two unbalanced coupling potentials are injected into both ends of the circuit QED lattice are studied, and it is found that the system exhibits three distinguishing phases with multiple flips of energy bands. These phases are significantly different from the previous phase induced via unilateral coupling potential due to the existence of a pair of nontopological edge states. The scheme provides a feasible and visible method to induce different topological and nontopological edge states through controlling the qubit-assisted coupling potentials in circuit QED lattice both in experiment and theory.     

Distinguishing the Topological Zero Mode and Tamm Mode in a Microwave Waveguide Array

The Su–Schrieffer–Heeger (SSH) model has been the subject of extensive experimental research in the context of topological photonics. Ideally, the on‐site potential and hopping strength are sufficiently accurate for implementation in photonic coupled waveguide arrays. Here, two localized edge modes, the topological zero mode and trivial Tamm mode, are proposed and demonstrated in the modified SSH model using a microwave photonic waveguide array. The system used is composed of an array of evanescently coupled ultrathin corrugated metallic “H‐bar” waveguides. Furthermore, the differences between the zero mode and Tamm mode are clearly demonstrated by microwave near‐field experiments on the coupling behavior along the propagation direction for 40 cm at the excitation frequency of 17 GHz. These findings should deepen the understanding of localized edge mode confinement mechanisms, both in coupled waveguide array systems and other topological or quantum systems.     

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.     

Quantum transport signatures of non-trivial topological edge states in a ring-shaped Su–Schrieffer–Heeger double-chain system

In the ring-shaped Su–Schrieffer–Heeger(SSH)double-chain,the quantum interference between the two different electron tunneling paths of the upper and lower chains has an important influence on the electron transport properties of non-trivial topological edge states.Here,we have studied the electron transport signatures of non-trivial topological edge states in a ring-shaped SSH double-chain system based on the wave-guide theory and transfer-matrix method.In the ringshaped SSH double-chain with the upper chain being different from the lower one,it is demonstrated that the electron transmission probability displays the four and two resonance peaks associated with the non-trivial topological edge states in the weak and strong coupling regimes,respectively.Whereas in the case of the upper chain being the same as the lower one,the two transmission resonance peaks associated with the non-trivial topological edge states in the weak coupling regime are only found,and that in the strong coupling regime disappear that originated from the destructive interference between the two different electron tunneling paths of the upper and lower chains.Consequently,the variation of the number of transmission resonance peaks associated with the non-trivial topological edge states in the weak and strong coupling regimes suggests that an alternative scheme for detecting non-trivial topological edge states in the ring-shaped SSH doublechain system.