Atoms to topological electronic materials: a bedtime story for beginners
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REVIEW PAPER
Atoms to topological electronic materials: a bedtime story for beginners A K Pariari* Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064, India Received: 09 July 2019 / Accepted: 16 September 2020
Abstract: In this review, we discuss the theoretical foundation and experimental discovery of different topological electronic states in solids. At first, we briefly discuss the conventional electronic states, which have been realized in band theory of solid. Next, the simplest non-trivial insulating phase (integer quantum Hall state) and the concept of topological order in condensed matter electronic system are introduced. In the following sections, we discuss quantum spin Hall (QSH) state in two dimensions (2D) and review the theoretical and experimental developments from 2D QSH state to 3D topological insulators. Subsequently, we give a brief overview on theoretical and experimental understanding on recently discovered topological Dirac semimetals, Weyl semimetals, three-, six- , and eightfold degenerate semimetals, and nodal line semimetals. Topological crystalline insulator, which cannot be considered as a descendent of QSH or integer quantum Hall insulator, is discussed in the following section. Finally, we discuss the presence of magnetism in some topological materials and its consequence on electronic band structure. Graphic abstract
Keywords: Topological materials; Topological insulators; Topological semimetals
1. Band theory and conventional electronic phases In the case of a single isolated atom, there are various discrete energy levels, known as atomic orbitals. When two atoms join together to form a molecule, their atomic
*Corresponding author, E-mail: [email protected]
orbitals overlap, and each atomic orbital splits into two molecular orbitals of different energies. In a solid, a large number of atoms are arranged systematically in space lattice and each atom is influenced by neighboring atoms. As a consequence, each atomic orbital splits into large number of discrete molecular orbitals, each with a different energy. The energy of adjacent levels is so close that they can be considered as a continuum, forming an energy band. Figure 1 is a schematic diagram, representing the above
Ó 2020 IACS
A K Pariari Fig. 1 A schematic diagram to show the discrete energy levels of an isolated atom and energy band of crystalline solid. Reproduced from Ref. [1]
discussion. The completely occupied lower band is called the valence band, and the top most partially filled or completely empty band is known as conduction band. For the conduction of electrical energy in a material, there must be partially filled band. In case of a metal, as shown in Fig. 2, the valence and conduction bands overlap with each other in such a way so that the conduction band is partially filled and participates in charge conduction. A semimetal, where the valence and conduction bands just touch at a point without introducing any well-defined Fermi surface, is also a conductor of charge. For an insul
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