拓扑相和拓扑相变:浅谈固体中的拓扑物态  

Topological phase and topological phase transition: A brief introduction to topological states of matter in solids

作　　者：翁红明[1,2] 

机构地区：[1]中国科学院物理研究所,北京凝聚态物理国家实验室,北京100190 [2]量子物质科学协同创新中心,北京100190

出　　处：《科学通报》2016年第36期3907-3916,共10页Chinese Science Bulletin

摘　　要：通过对2016年诺贝尔物理学奖的解读,介绍了凝聚态物质中以整数量子霍尔态,Z2拓扑绝缘体和拓扑半金属等为代表的拓扑物态.它们的发现和发展过程,以及随之建立起来的能带拓扑理论和对称性保护拓扑物态理论等标志着人们认识物质世界的又一重大进展.The Nobel Prize in physics of year 2016 has been awarded to David J. Thouless, F. Duncan M. Haldane and J. Michael Kosterlitz for their theoretical discoveries of topological phase transitions and topological phase of matter. This paper starts with a brief introduction to their groundbreaking works made in 1970s–1980s, including the KT phase transition due to topological defects, vortex and antivortex pairs, in two-dimensional superfluid or superconductor, the TKNN number identifying the integer quantum Hall state, as well as the Haldane model to realize quantum Hall effect without external magnetic field in crystal lattice. Their insightful findings have revealed a new quantum state of matter, which cannot be described by local order parameter within Landau symmetry-breaking theory but by some global topological invariant of electronic states. In topology, a branch of mathematics, topological invariant describes the preserved properties of an object under continuous deformations. The combination of topology with the state of matter is a breakthrough in condensed matter physics. The band topology theory based on Berry phase is introduced in order to understand the origin of topology of the electronic states in solids. But only in last ten years, their pioneering works have been rediscovered and greatly extended. Around 2005, the time-reversal symmetry protected topological state identified by Z2 number has been discovered theoretically and soon it is realized in material called as Z2 topological insulator. Quickly, the concept of symmetry protected topological states has been generalized from time-reversal symmetry to all the space group symmetries, from electronic states to those in photonic crystal, phonon spectrum and cold atoms, and even from the insulators to metals. The first experimentally realized topological metal is Dirac semimetal, a three-dimensional version of graphene, with massless Dirac equation describing the low energy excitation around Fermi level. The discovery of Weyl semimetal in TaA s fam

关 键 词：TOPOLOGICAL INSULATOR TOPOLOGICAL SEMIMETAL TOPOLOGICAL quantum state TOPOLOGICAL PHASE transition BERRY PHASE 

分 类 号：O469[理学—凝聚态物理]