Constructing Low-Dimensional Quantum Devices Based on the Surface State of Topological Insulators

We propose a new method to construct low-dimensional quantum devices consisting of the magnetic topological insulators. Unlike previous systems based on locally depleting two-dimensional electron gas in semiconductor heterojunctions, magnetization provides a simpler and rewriteable fabrication way. The motion of electrons can be manipulated through the domain wall formed by the boundary between different magnetic domains.Here, three devices designed by local magnetization are presented. For the quantum point contact, conductance exhibits quantized plateaus with the increasing silt width between two magnetic domains. For the quantum dot, conductance shows pronounced peaks as the change of gate voltage. Finally, for the Aharonov–Bohm ring,conductance oscillates periodically with the external magnetic field. Numerical results show that the transport of these local magnetization systems is identical to that of the previous systems based on depleting two-dimensional electron gas, and the only difference is the approach of construction. These findings may pave the way for realization of low-power-consumption devices based on magnetic domain walls.     

Probe Knots and Hopf Insulators with Ultracold Atoms

Knots and links are fascinating and intricate topological objects. Their influence spans from DNA and molecular chemistry to vortices in superfluid helium, defects in liquid crystals and cosmic strings in the early universe. Here we find that knotted structures also exist in a peculiar class of three-dimensional topological insulators—the Hopf insulators. In particular, we demonstrate that the momentum-space spin textures of Hopf insulators are twisted in a nontrivial way, which implies the presence of various knot and link structures. We further illustrate that the knots and nontrivial spin textures can be probed via standard time-of-flight images in cold atoms as preimage contours of spin orientations in stereographic coordinates. The extracted Hopf invariants, knots, and links are validated to be robust to typical experimental imperfections. Our work establishes the existence of knotted structures in Hopf insulators, which may have potential applications in spintronics and quantum information processing.     

Topological Insulators in α-Graphyne

In this paper, we investigate topological phases of α-graphyne with tight-binding method. By calculating the topological invariant Z2 and the edge states, we identify topological insulators. We present the phase diagrams of α-graphyne with different filling fractions as a function of spin-orbit interaction and the nearest-neighbor hopping energy. We find there exist topological insulators in α-graphyne. We analyze and discuss the characteristics of topological phases of α-graphyne.     

Quantum Chains of Hopf Algebras with Quantum Double Cosymmetry

Given a finite dimensional C ^*-Hopf algebra H and its dual Ĥ we construct the infinite crossed product and study its superselection sectors in the framework of algebraic quantum field theory. is the observable algebra of a generalized quantum spin chain with H-order and Ĥ-disorder symmetries, where by a duality transformation the role of order and disorder may also appear interchanged. If is a group algebra then becomes an ordinary G-spin model. We classify all DHR-sectors of – relative to some Haag dual vacuum representation – and prove that their symmetry is described by the Drinfeld double . To achieve this we construct localized coactions and use a certain compressibility property to prove that they are universal amplimorphisms on . In this way the double can be recovered from the observable algebra as a universal cosymmetry. Received: 4 September 1995\,/\,Accepted: 3 December 1996     

Classification of Topological Insulators with Time-Reversal and Inversion Symmetry

In this paper, we find that topological insulators with time-reversal symmetryand inversion symmetry featuring two-dimensional quantum spin Hall (QSH) state can be divided into 16 classes, which are characterized by four Z₂topological variables ζ_k=0,1 at four points with high symmetry in the Brillouin zone. We obtain the corresponding edge states for each one of these sixteen classes of QSHs. In addition, it is predicted that massless fermionic excitations appear at the quantum phase transition between different QSH states. In the end, we also briefly discuss the three-dimensional case.     

Making Axion Dynamical in Non-Centrosymmetric Magnetic Topological Insulators

“Axion”was predicted as a hypothetical elementary particle to resolve the strong conjugation-parity problem in particle physics,^[1]and it is also an attractive candidate for the as-yet-unobserved dark matter in cosmology.^[2]While the detection of axions still remains elusive in particle physics and cosmology,it was recently proposed that the elegant physics of axions,known“axion electrodynamics”,^[3]can emerge in certain condensed matter systems,particularly topological insulator materials,^[4]in which a variety of exotic physical phenomena(e.g.topological magnetoelectric effect)have been theoretically predicted.     

Topological Insulators on the Ruby Lattice with Rashba Spin-Orbit Coupling

We investigate a tight-binding model of the ruby lattice with Rashba spin-orbit coupling. We calculate the band structure of the lattice and evaluate the Z₂ topological indices. According to the Z₂ topological indices and the band structure, we present the phase diagrams of the lattice with different filling fractions. We find that topological insulators occur in some range of parameters at 1/6, 1/3, 1/2, 2/3 and 5/6 filling fractions. We analyze and discuss the characteristics of these topological insulators and their edge states.     

Topological Insulators on the Ruby Lattice with Rashba Spin-Orbit Coupling

We investigate a tight-binding model of the ruby lattice with Rashba spin-orbit coupling. We calculate the band structure of the lattice and evaluate the Z2 topological indices. According to the Z2 topological indices and the band structure, we present the phase diagrams of the lattice with different filling fractions. We find that topological insulators occur in some range of parameters at 1/6, 1/3, 1/2, 2/3 and 5/6 filling fractions. We analyze and discuss the characteristics of these topological insulators and their edge states.     

Realization of Quantum Maxwell's Demon with Solid-State Spins

We report experimental realization of a quantum version of Maxwell's demon using solid state spins where the information acquiring and feedback operations by the demon are achieved through conditional quantum gates.A unique feature of this implementation is that the demon can start in a quantum superposition state or in an entangled state with an ancilla observer. Through quantum state tomography, we measure the entropy in the system, demon, and the ancilla, showing the influence of coherence and entanglement on the result. A quantum implementation of Maxwell's demon adds more controllability to this paradoxical thermal machine and may find applications in quantum thermodynamics involving microscopic systems.     

Formation of the Magnetic Order in Three-Dimensional Topological Insulators for the Quantum Anomalous Hall Effect (Scientific Summary)

JETP Letters - A cycle of measurements of the polarization characteristics of coherent transition radiation and coherent diffraction radiation at the LUCX accelerator has been performed. It has...     

Photo- and Thermoelectric Phenomena in Two-Dimensional Topological Insulators and Semimetals Based on HgTe Quantum Wells (Scientific Summary)

JETP Letters - Experimental studies of photo- and thermoelectric phenomena in two-dimensional topological insulators and semimetals based on HgTe quantum wells have been briefly reviewed.     

Topological Insulators and Topological Superconductors,by B. Andrei Bernevig with Taylor L. Hughes

After introductory remarks the recent discovery of the superfluid phases of ³He is described. This is followed by a discussion of the P, T-diagram below 3 mK. NMR and susceptibility measurements on liquid ³He are then explained. Next, heat capacity and heat flow data are briefly mentioned and experiments involving the zero and fourth sound are described. The viscosity and the density of the normal component of liquid ³He are then discussed. The paper is concluded by a theoretical section.     

金刚石固态量子计算中的高分辨率成像

20世纪90年代中期,随着Shor算法和Grover算法的提出,量子计算领域得到广泛关注.金刚石固态NV色心方案作为量子计算机热门物理实现方案之一,因其在室温下的超长相干时间和可精确操控等独特优势而备受青睐;此外,NV色心还有望通过磁共振成像方式实现单核自旋探测.然而NV色心固态量子计算的一种扩展方式受限于相邻NV色心之间的磁偶极相互作用,要求两个NV色心之间相距只有数十纳米.这一尺度远小于普通远场光学的分辨率,即光学衍射极限,采用传统的共聚焦方法已无法分辨.受激发射损耗(STED)和基态损耗(GSD)等超分辨成像技术能够突破光学衍射极限限制,达到纳米量级的分辨率;同时结合最新的金刚石表面微纳刻蚀技术,可实现NV色心固态量子计算中不同色心的分辨和精确定位.该文从固态金刚石NV色心体系和光学衍射等主要方面对利用STED和GSD高分辨成像技术提高传统共聚焦显微镜对NV色心体系成像分辨率进行简要的介绍,并结合实例介绍一些最新的研究进展.     

凝聚体中的拓扑量子态

探寻拓扑上非平庸的凝聚体物质状态,特别是其电子结构和输运性质,是当前凝聚体物理 学领域非常重要的前沿研究方向。本文讨论的大多数主题都与电子波函数的拓扑性质有关。全文 除简短的引言外,包括拓扑量子现象、各种拓扑相、拓扑性准粒子的异常输运性质、拓扑性集 体激发和耦合激发,以及继续发展的拓扑量子态研究五个章节。这些章节着重反映拓扑量子态研 究的各个侧面,汇总起来方可以凸显凝聚体中拓扑量子态的全貌。     

Topological Knots in Quantum Spin Systems

Knot theory provides a powerful tool for understanding topological matters in biology, chemistry, and physics.Here knot theory is introduced to describe topological phases in a quantum spin system. Exactly solvable models with long-range interactions are investigated, and Majorana modes of the quantum spin system are mapped into different knots and links. The topological properties of ground states of the spin system are visualized and characterized using crossing and linking numbers, which capture the geometric topologies of knots and links. The interactivity of energy bands is highlighted. In gapped phases, eigenstate curves are tangled and braided around each other, forming links. In gapless phases, the tangled eigenstate curves may form knots. Our findings provide an alternative understanding of phases in the quantum spin system, and provide insights into one-dimension topological phases of matter.     

Dynamics of Electronic States and Magnetoabsorption in 3D Topological Insulators in a Quantizing Magnetic Field

Quantum states have been calculated analytically; the dynamics of a wave packet in a magnetic field has been investigated, and the optical absorption coefficient has been calculated for surface states in 3D topological insulators of the Bi₂Te₃ family. We have detected a qualitative effect of the hexagonal warping of the spectrum on the structure of wavefunctions at the Landau levels, its manifestation in the features of the wave packet dynamics in a quantizing magnetic field, as well as in the frequency dependence of the optical absorption coefficient, in which new peaks that are absent in the isotropic model of the spectrum appear depending on the polarization of the incident wave. The effects considered here can be manifested in the optical and transport experiments with topological insulators, which makes it possible to determine the parameters of their band structure.     

Microwave Photoresistance of a Two-Dimensional Topological Insulator in a HgTe Quantum Well

JETP Letters - The microwave photoresistance of a two-dimensional topological insulator in a HgTe quantum well with an inverted spectrum has been experimentally studied under irradiation at...     

Interference Transport in a Two-Dimensional Topological Insulator in a CdHgTe Quantum Well

JETP Letters - Interference transport in mesoscopic samples of a two-dimensional topological insulator in CdHgTe quantum wells is studied for the first time. It is established that quasi-ballistic...