类石墨烯复杂晶胞光子晶体中的确定性界面态

拓扑绝缘体是当前凝聚态物理领域研究的热点问题.利用石墨烯材料的特殊能带特性来实现拓扑输运特性在设计下一代电子和能谷电子器件方面具有较广泛的应用前景.基于光子与电子的类比,利用光子拓扑材料实现了确定性界面态;构建了具有C_(6v)。对称性的类似石墨烯结构的的光子晶体复杂晶格;通过多种方式降低晶格对称性来获得具有C_(3v),C_3,C_(2v)和C_2对称的晶体,从而打破能谷简并实现全光子带隙结构;将体拓扑性质不同的两种光子晶体摆放在一起,在此具有反转体能带性质的界面上,实现了具有单向传输特性的拓扑确定性界面态的传输.利用光子晶体结构的容易加工性,可以简便地调控拓扑界面态控制光的传播,可为未来光拓扑绝缘体的研究提供良好的平台.     

Atomic-Ordering-Induced Quantum Phase Transition between Topological Crystalline Insulator and Z_2 Topological Insulator

Topological phase transition in a single material usually refers to transitions between a trivial band insulator and a topological Dirac phase, and the transition may also occur between different classes of topological Dirac phases.It is a fundamental challenge to realize quantum transition between Z_2 nontrivial topological insulator(TI) and topological crystalline insulator(TCI) in one material because Z_2 TI and TCI have different requirements on the number of band inversions. The Z_2 TIs must have an odd number of band inversions over all the time-reversal invariant momenta, whereas the newly discovered TCIs, as a distinct class of the topological Dirac materials protected by the underlying crystalline symmetry, owns an even number of band inversions. Taking PbSnTe_2 alloy as an example, here we demonstrate that the atomic-ordering is an effective way to tune the symmetry of the alloy so that we can electrically switch between TCI phase and Z_2 TI phase in a single material. Our results suggest that the atomic-ordering provides a new platform towards the realization of reversibly switching between different topological phases to explore novel applications.     

Weyl and Nodal Ring Magnons in Three-Dimensional Honeycomb Lattices

We study the topological properties of magnon excitations in a wide class of three-dimensional(3 D) honeycomb lattices with ferromagnetic ground states. It is found that they host nodal ring magnon excitations. These rings locate on the same plane in the momentum space. The nodal ring degeneracy can be lifted by the DzyaloshinskiiMoriya interactions to form two Weyl points with opposite charges. We explicitly discuss these physics in the simplest 3 D honeycomb lattice and the hyerhoneycomb lattice, and show drumhead and arc surface states in the nodal ring and Weyl phases, respectively, due to the bulk-boundary correspondence.     

Transport features of topological corner states in honeycomb lattice with multihollow structure

Higher-order topological phase in 2-dimensional (2D) systems is characterized by in-gap corner states, which are hard to detect and utilize. We numerically investigate transport properties of topological corner states in 2D honeycomb lattice, where the second-order topological phase is induced by an in-plane Zeeman field in the conventional Kane–Mele model. Through engineering multihollow structures with appropriate boundaries in honeycomb lattice, multiple corner states emerge, which greatly increases the probability to observe them. A typical two-probe setup is built to study the transport features of a diamond-shaped system with multihollow structures. Numerical results reveal the existence of global resonant states in bulk insulator, which corresponds to the resonant tunneling of multiple corner states and occupies the entire scattering region. Furthermore, based on the well separated energy levels of multiple corner states, a single-electron source is constructed.     

Topological states in quasicrystals

With the rapid development of topological states in crystals, the study of topological states has been extended to quasicrystals in recent years. In this review, we summarize the recent progress of topological states in quasicrystals, particularly focusing on one-dimensional (1D) and 2D systems. We first give a brief introduction to quasicrystalline structures. Then, we discuss topological phases in 1D quasicrystals where the topological nature is attributed to the synthetic dimensions associated with the quasiperiodic order of quasicrystals. We further present the generalization of various types of crystalline topological states to 2D quasicrystals, where real-space expressions of corresponding topological invariants are introduced due to the lack of translational symmetry in quasicrystals. Finally, since quasicrystals possess forbidden symmetries in crystals such as five-fold and eight-fold rotation, we provide an overview of unique quasicrystalline symmetry-protected topological states without crystalline counterpart.     

Floquet engineering in topological crystalline insulator

There is a peculiar type of insulator, which is protected by the crystal symmetry known as topological crystalline insulator (TCI). In off-resonant cases, Floquet theory is an another way to study conventional Rabi oscillations. By using Floquet theory, the various type of Dirac fermionic systems and phases can be distinguished. In this article, it is shown that Floquet frequency can be used as a tool to distinguish different phases of TCI. The study of Bloch-Siegert shift has been performed and shown its variation in different phases of TCI. The collapse-revival spectra have also been studied in the perspective of Floquet theory and shown how quantum and classical Floquet oscillations are related to each other. The verification of the Floquet theory is justified by using numerical simulation.     

Topological phases in Bi/Sb planar and buckled honeycomb monolayers

We investigate topological phases in two-dimensional Bi/Sb honeycomb crystals considering planar and buckled structures, both freestanding and deposited on a substrate. We use the multi-orbital tight-binding model and compare results with density functional theory calculations. We distinguish topological phases by calculating topological invariants, analyzing edge states properties of systems in a ribbon geometry and studying their entanglement spectra. We show that coupling to the substrate induces transition to the $Z_2$ topological insulator phase. It is observed that topological crystalline insulator (TCI) phase, found in planar crystals, exhibits an additional pair of edge states in both energy spectrum and entanglement spectrum. Transport calculations for TCI phase suggest robust quantized conductance even in the presence of crystal symmetry-breaking disorder.     

Conductance of disordered graphene sheets: A real space approach

In this work the conducting properties of graphene lattice (buckled as well as planar) having different concentrations of defects are studied with the help of real space block recursion method introduced by Haydock et al. Since the defects are completely random, reciprocal space based methods which need artificial periodicity are not applicable here. Different resonant states appear because of the presence of topological and local defects which are calculated within the framework of Green function. Except random voids, in all other density of states (DOS) spectra there are signatures of Breit–Wigner and Fano resonance at occupied and unoccupied regime respectively. Although Fano resonance states are not prominent for graphene with random voids, however Stone–Wales (SW) type defect can naturally introduce their resonance states. The appearance of localized states depends strongly on the concentration of defects.     

Topological Fulde–Ferrell and Larkin–Ovchinnikov states in spin-orbit-coupled lattice system

The spin-orbit coupled lattice system under Zeeman fields provides an ideal platform to realize exotic pairing states. Notable examples range from the topological superfluid/superconducting (tSC) state, which is gapped in the bulk but metallic at the edge, to the Fulde–Ferrell (FF) state (having a phase-modulated order parameter with a uniform amplitude) and the Larkin–Ovchinnikov (LO) state (having a spatially varying order parameter amplitude). Here, we show that the topological FF state with Chern number (C=−1) (tFF₁) and topological LO state with C= 2 (tLO₂) can be stabilized in Rashba spin-orbit coupled lattice systems in the presence of both in-plane and out-of-plane Zeeman fields. Besides the inhomogeneous tSC states, in the presence of a weak in-plane Zeeman field, two topological BCS phases may emerge with C=−1 (tBCS₁) far from half filling and C= 2 (tBCS₂) near half filling. We show intriguing effects such as different spatial profiles of order parameters for FF and LO states, the topological evolution among inhomogeneous tSC states, and different non-trivial Chern numbers for the tFF₁ and tLO_1,2 states, which are peculiar to the lattice system. Global phase diagrams for various topological phases are presented for both half-filling and doped cases. The edge states as well as local density of states spectra are calculated for tSC states in a 2D strip.     

一维准周期晶格的性质及应用

准周期晶格在冷原子领域被广泛研究,它使得人们可以在一维或者二维系统里研究扩展到安德森局域的转变. 2008年, Inguscio研究组在冷原子系统里制备了一维准周期晶格,并观测到了安德森局域化现象,这极大地推动了准周期系统的理论和实验研究.后来, Bloch研究组在制备的一维和二维准周期晶格中都观测到了多体局域的现象.最近,他们还在准周期晶格中成功观测到迁移率边以及存在迁移率边的系统的多体局域现象.这些冷原子实验推动了多体局域以及迁移率边等方向的研究.准周期晶格已经成为一个平台,它对很多物理现象的影响正在被广泛研究,并可以尝试在冷原子实验中观测到这种影响.本文结合作者的一些相关工作,对一维准周期晶格一些近期的研究进行了简要综述,介绍了一些相关的重要的冷原子实验,讨论了准周期晶格的一些重要性质,以及它对一些物理现象(比如拓扑态)的影响.     

拓扑绝缘体/超导体异质结中的近邻效应

拓扑超导体自身具有对量子退相干天然的免疫性以及可编织性,这使得它在现代量子计算领域中受到了越来越多的重视,并且成为了下一代计算技术中最有希望的候选者之一。由于拓扑超导态在固有拓扑超导体中相当罕见,因此,当前大部分实验上的工作主要集中在由 s 波超导体与拓扑绝缘体之间通过近邻效应所诱导的拓扑超导体上。本论文中,我们回顾了基于拓扑绝缘体/超导体异质结的拓扑超导体的研究进展。在理论上,Fu 和 Kane 提出,通过近邻效应将 s 波超导体的能隙引入到拓扑绝缘体,可以诱导出拓扑超导电性。在实验上,我们也回顾了一些不同体系中的拓扑超导近邻效应的研究进展。文章的第一部分,我们介绍了一些异质结,包括：三维拓扑绝缘体 Bi2Se3和 Bi2Se3 与 s 波超导体NbSe2 以及 d 波超导体 Bi2Sr2CaCu2O8+δ 的异质结,拓扑绝缘体 Sn1−xPbxTe 与 Pb 的异质结,二维拓扑绝缘体 WTe2 与NbSe2 的异质结。此外,还介绍了 TiBiSe2 在 Pb 上的拓扑绝缘近邻效应。另一部分中,我们对基于拓扑绝缘体的约瑟夫森结进行了回顾,包括著名的基于 Fu-Kane 体系的拓扑绝缘体约瑟夫森结,以及基于约瑟夫森结的超导量子干涉器件。     

Stanene: A good platform for topological insulator and topological superconductor

Two dimensional (2D) topological insulators (TIs) and topological superconductors (TSCs) have been intensively studied for recent years due to their great potential for dissipationless electron transportation and fault-tolerant quantum computing, respectively. Here we focus on stanene, the tin analogue of graphene, to give a brief review of their development as a candidate for both 2D TI and TSC. Stanene is proposed to be a TI with a large gap of 0.3 eV, and its topological properties are sensitive to various factors, e.g., the lattice constants, chemical functionalization and layer thickness, which offer various methods for phase tunning. Experimentally, the inverted gap and edge states are observed recently, which are strong evidences for TI. In addition, stanene is also predicted to be a time reversal invariant TSC by breaking inversion symmetry, supporting helical Majorana edge modes. The layer-dependent superconductivity of stanene is recently confirmed by both transport and scanning tunneling microscopy measurements. This review gives a detailed introduction to stanene and its topological properties and some prospects are also discussed.     

Band gap anomaly and topological properties in lead chalcogenides

Band gap anomaly is a well-known issue in lead chalcogenides Pb X(X = S, Se, Te, Po). Combining ab initio calculations and tight-binding(TB) method, we have studied the band evolution in Pb X, and found that the band gap anomaly in Pb Te is mainly related to the high on-site energy of Te 5s orbital and the large s–p hopping originated from the irregular extended distribution of Te 5s electrons. Furthermore, our calculations show that Pb Po is an indirect band gap(6.5 me V) semiconductor with band inversion at L point, which clearly indicates that Pb Po is a topological crystalline insulator(TCI). The calculated mirror Chern number and surface states double confirm this conclusion.     

Simulation and detection of the topological properties of a modulated Rice-Mele model in a one-dimensional circuit-QED lattice

Here, we propose a simple scheme to realize a one-dimensional (1D) modulated Rice-Mele model (RMM) and investigate its topological properties with a 1D circuit quantum electrodynamics (QED) lattice. The system can be mapped into a Chern insulator model by introducing a period parameter. Interestingly and surprisingly, we found that the circuit-QED lattice system always exhibits topologically nontrivial phases if both the nearest-neighbor hopping strength between two resonators and the qubit-assisted on-site potentials are alternately changed in the direction of the lattice. The numerical results show that the topological phases can be obtained by introducing an additional modulation parameter and both the edge state and topological invariant can be unambiguously seen with the existence of decay and disorders, even with few resonators in the lattice.     

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.     

Geometry of crystal structure with defects. II. Non-Euclidean picture

The following point of view is geometrically formulated and its consequences examined: the lattice of a crystalline body with a continuous distribution of dislocations can be locally described as an ideal lattice in non-Euclidean space. The types of distribution of dislocations are described by the classification of three-dimensional real Lie algebras. The influence of point defects and the elastic deformation field on the geometry of the material structure of a crystalline body with dislocations is examined. The case where a crystal with dislocations reacts as a body with internal rotational degrees of freedom is discussed.     

Topological phase in one-dimensional Rashba wire

We study the possible topological phase in a one-dimensional(1D) quantum wire with an oscillating Rashba spin–orbital coupling in real space. It is shown that there are a pair of particle–hole symmetric gaps forming in the bulk energy band and fractional boundary states residing in the gap when the system has an inversion symmetry. These states are topologically nontrivial and can be characterized by a quantized Berry phase ±π or nonzero Chern number through dimensional extension. When the Rashba spin–orbital coupling varies slowly with time, the system can pump out 2 charges in a pumping cycle because of the spin flip effect. This quantized pumping is protected by topology and is robust against moderate disorders as long as the disorder strength does not exceed the opened energy gap.     

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.     

Spontaneous SU(2) symmetry breaking in one-dimensional quantum antiferromagnet

We present a Bethe Ansatz based investigation of a one-dimensional (1D) Heisenberg spin chain in a real 3D crystal lattice. We have shown that due to an influence of the lattice distortion on a crystalline field of ligands of magnetic ions, a Heisenberg antiferromagnetic spin chain is unstable under the appearance of a magnetic anisotropy of the “easy-plane” type. The effects of an external magnetic field and nonzero temperature onto such a phase transition are studied. Received: 19 January 1998 / Revised: 16 March 1998 / Accepted: 17 March 1998