Apr 2012, Volume 7 Issue 2

Cover illustration

  • Linearly dispersive surface state of topological insulator Bi2Te3 measured by angle resolved photoemission spectroscopy, forming a single Dirac fermion. The crystal structure of Bi2Te3 is illustrated below. Topological insulators represent a new state of quantum matter with a bulk insulting gap and odd number of relativistic Dirac fermions on the surface. In the simplest case, the surface state consists of a single Dirac cone, with [Detail] ...

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    Shoucheng Zhang, Zhong Fang, Qi-Kun Xue
    Ke He
    Kevin Walker, Zhenghan Wang

    Levin-Wen models are microscopic spin models for topological phases of matter in (2+ 1)-dimension. We introduce a generalization of such models to (3+ 1)-dimension based on unitary braided fusion categories, also known as unitary premodular categories. We discuss the ground state degeneracy on 3-manifolds and statistics of excitations which include both points and defect loops. Potential connections with recently proposed fractional topological insulators and projective ribbon permutation statistics are described.

    Zhi-yong Wang, Peng Wei, Jing Shi

    Bi2Se3 has been predicted to be a three-dimensional (3D) topological insulator (TI) with Dirac fermions residing on the two-dimensional (2D) surface. Unique transport properties such as high carrier mobility due to the suppressed backscattering are expected for the Dirac fermions. In order to eliminate the contribution of the bulk carriers, therefore, to place the Fermi level in the band gap of Bi2Se3, we first introduce various amounts of Ca dopants into the crystal to realize the bulk insulating state. Then by avoiding uncontrolled heating and electron beam irradiation in the nanofabrication process, we maintain the insulating state in thin devices. By sweeping the gate voltage, we have observed a conductivity minimum that is expected for the Dirac fermions in the band gap of 3D TIs.

    Yong-qing Li, Ke-hui Wu, Jun-ren Shi, Xin-cheng Xie

    We review experimental advances in the study of the electron transport in three-dimensional topological insulators with emphasis on experiments that attempted to identify the surface transport. Recent results on transport properties of topological insulator thin films will be discussed in the context of weak antilocalization and electron–electron interactions. Current status of gate-voltage control of the chemical potential in topological insulators will also be described.

    Yulin Chen

    Three-dimensional (3D) topological insulators represent a new state of quantum matter with a bulk gap and odd number of relativistic Dirac fermions on the surface. The unusual surface states of topological insulators rise from the nontrivial topology of their electronic structures as a result of strong spin–orbital coupling. In this review, we will briefly introduce the concept of topological insulators and the experimental method that can directly probe their unique electronic structure: angle resolved photoemission spectroscopy (ARPES). A few examples are then presented to demonstrate the unique band structures of different families of topological insulators and the unusual properties of the topological surface states. Finally, we will briefly discuss the future development of topological quantum materials.

    Jun-liang Zhang, Si-jia Zhang, Hong-ming Weng, Wei Zhang, Liu-xiang Yang, Qing-qing Liu, Pan-pan Kong, Jie Zhu, Shao-min Feng, Xian-cheng Wang, Ri-cheng Yu, Lie-zhao Cao, Shoucheng Zhang, Xi Dai, Zhong Fang, Chang-qing Jin

    By applying pressure on the topological insulator Bi2Te3 single crystal, superconducting phase was found without a crystal structure phase transition. The new superconducting phase is under the pressure range of 3 GPa to 6 GPa. The high pressure Hall effect measurements indicated that the superconductivity caused by bulk hole pockets. The high pressure structure investigations with synchrotron X-ray diffraction indicated that the superconducting phase is of similar structure to that of ambient phase structure with only slight change with lattice parameter and internal atomic position. The topological band structures indicate the superconducting phase under high pressure remained topologically nontrivial. The results suggested that topological superconductivity can be realized in Bi2Te3 due to the proximity effect between superconducting bulk states and Diractype surface states. We also discussed the possibility that the bulk state could be a topological superconductor.

    Ivan Knez, Rui-Rui Du

    We review the recent experimental progress towards observing quantum spin Hall effect in inverted InAs/GaSb quantum wells (QWs). Low temperature transport measurements in the hybridization gap show bulk conductivity of a non-trivial origin, while the length and width dependence of conductance in this regime show strong evidence for the existence of helical edge modes proposed by Liu et al. [Phys. Rev. Lett., 2008, 100: 236601]. Surprisingly, edge modes persist in spite of comparable bulk conduction and show only weak dependence on magnetic field. We elucidate that seeming independence of edge on bulk transport comes due to the disparity in Fermi-wave vectors between the bulk and the edge, leading to a total internal reflection of the edge modes.

    Hui Li (李辉), Hailin Peng (彭海琳), Wenhui Dang (党文辉), Lili Yu (余力立), Zhongfan Liu (刘忠范)

    Nanostructured topological insulator materials such as ultrathin films, nanoplates, nanowires, and nanoribbons are attracting much attention for fundamental research as well as potential applications in low-energy dissipation electronics, spintronics, thermoelectrics, magnetoelectrics, and quantum computing due to their extremely large surface-to-volume ratios and exotic metallic edge/surface states. Layered Bi2Se3 and Bi2Te3 serve as reference topological insulator materials with a large nontrivial bulk gap up to 0.3 eV (equivalent to 3600 K) and simple single-Dirac-cone surface states. In this mini-review, we present an overview of recent advances in nanostructured topological insulator Bi2Se3 and Bi3Te3 from the viewpoints of controlled synthesis and physical properties. We summarize our recent achievements in the vapor-phase synthesis and structural characterization of nanostructured topological insulator Bi2Se3 and Bi2Te3, such as nanoribbons and ultrathin nanoplates.We also demonstrate the evolution of Raman spectra with the number of few-layer topological insulators, as well as the transport measurements that have succeeded in accessing the surface conductance and surface state manipulations in the device of topological insulator nanostructures.

    Werner A. Hofer

    We show by a statistical analysis of high-resolution scanning tunneling microscopy (STM) experiments, that the interpretation of the density of electron charge as a statistical quantity leads to a conflict with the Heisenberg uncertainty principle. Given the precision in these experiments we find that the uncertainty principle would be violated by close to two orders of magnitude, if this interpretation were correct. We are thus forced to conclude that the density of electron charge is a physically real, i.e., in principle precisely measurable quantity.

    Yao-hua Chen, Wei Wu, Guo-cai Liu, Hong-shuai Tao, Wu-ming Liu

    We review our recent theoretical advances in phase transition of cold atoms in optical lattices, such as triangular lattice, honeycomb lattice, and Kagomé lattice. By employing the new developed numerical methods called dynamical cluster approximation and cellular dynamical mean-field theory, the properties in different phases of cold atoms in optical lattices are studied, such as density of states, Fermi surface and double occupancy. On triangular lattice, a reentrant behavior of phase translation line between Fermi liquid state and pseudogap state is found due to the Kondo effect. We find the system undergoes a second order Mott transition from a metallic state into a Mott insulator state on honeycomb lattice and triangular Kagomé lattice. The stability of quantum spin Hall phase towards interaction on honeycomb lattice with spin–orbital coupling is systematically discussed. And we investigate the transition from quantum spin Hall insulator to normal insulator in Kagomé lattice which includes a nearest-neighbor intrinsic spin–orbit coupling and a trimerized Hamiltonian. In addition, we propose the experimental protocols to observe these phase transition of cold atoms in optical lattices.

    Jia-qi Zhong (仲嘉琪), Geng-hua Yu (余庚华), Jin Wang (王谨), Ming-sheng Zhan (詹明生)

    Whether the transitions between 6s5d 3D and 5d6p 3F can be used for laser cooling of barium heavily depends upon the transition probabilities of 5d6p 3F-5d23F. Taking the transition 6s5d 3D32-5d6p 3F4 as a scale, the leakage rate of 5d6p 3F4-5d23F was used to evaluate the transition probabilities. 706 nm laser pulses with different durations were applied to a barium atomic beam for 6s5d3D3-5d 2 3F4 optical pumping, and the remaining percentages in 6s5d 3D3 were measured. After exponential fitting, the transition probability of 5d6p 3F4-5d2 3F3,4 was determined to be 2.1(4)×104 s-1, which is in agreement with theoretical calculations using the scaled Thomas–Fermi–Dirac method.

    Lü-bi Deng (邓履璧)

    In this paper, we have presented and established a new theoretical formulation of photon optics based on photon path and Feynman path integral idea. We have used Feynman path integral approach to discuss Fraunhofer, Fresnel diffraction of single photon and entangled photon pairs by ultrasonic wave and obtained the following results: i) quantum state and probability distribution of single photon and entangled photon pairs by Fraunhofer and Fresnel ultrasonic diffraction, ii) oblique incidence Raman–Nath and Bragg diffraction conditions, iii) total correlation state and its probability distribution. Our calculation results are in agreement with the experiment results. Comparing one-photon and two-photon diffraction effects by ultrasonic waves, we have found that two-photon diffraction by ultrasonic waves is also a sub-wavelength diffraction.

    Shi-jian Gu

    Let a general quantum many-body system at a low temperature adiabatically cross through the vicinity of the system’s quantum critical point. We show that the system’s temperature is significantly suppressed due to both the entropy majorization theorem in quantum information science and the entropy conservation law in reversible adiabatic processes. We take the one-dimensional transverse-field Ising model and the spinless fermion system as concrete examples to show that the inverse temperature might become divergent around the systems’ critical points. Since the temperature is a measurable quantity in experiments, it can be used, via reversible adiabatic processes at low temperatures, to detect quantum phase transitions in the perspectives of quantum information science and quantum statistical mechanics.

    Zhi-wen Wang, Yang Guo

    The transition energies, wavelengths and oscillator strengths for the 1s22s–1s2np (n 9) transitions of Ni25+ ion are calculated. In calculation of the energies, we not only take account of the firstorder corrections from relativistic and mass–polarization effects, but also estimate the higher-order relativistic contribution and QED correction by introducing the effective nuclear charge. The results agree with experimental data available in literature satisfactorily. Grotrian diagram showing these transitions is given.