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Physics Today

Foundational theories in topological physics garner Nobel Prize

Sung Kee Chang

Published Nov 30, 2016• 5 citations
Publisher

Abstract

The laureates bucked conventional wisdom to redefine the meaning of phases and phase transitions in one- and two-dimensional materials.
DOI
10.1063/pt.3.3381

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Topological Phases in Condensed Matter Physics

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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 TaAs family has stimulated lots of studies on the chiral Weyl fermions, which have not been found in vacuum but observed as quasiparticles in Weyl semimetals. More topological semimetals, such as node-line semimetal and multiple-degenerate nodal point semimetal, have been also proposed. The distinguished property of topological states of matter is its stability in both bulk and boundary states against the perturbation preserving the protecting symmetry. This is expected for potential applications in electronic devices. Therefore, three Laureates of Nobel Prize in physics of 2016 revealed the secrets of exotic matter and opened the door to topological states.