Chemical Principles of Topological Semimetals

Abstract

PrefaceThe recent rapid development in the field of topological materials raises expectations that these materials might allow solving a large variety of current challenges in condensed matter science, ranging from applications in quantum computing, to infra-red sensors or heterogenous catalysis. 1-8 In addition, exciting predictions of completely new physical phenomena that could arise in topological materials drive the interest in these compounds. 9,10 For example, charge carriers might behave completely different from what we expect from the current laws of physics if they travel through topologically non-trivial systems. 11,12 This happens because charge carriers in topological materials can be different from the normal type of fermions we know, which in turn affects the transport properties of the material. It has also been proposed that we could even find "new fermions", i.e. fermions that are different from the types we currently know in condensed matter systems as well as in particle physics. 10 Such proposals connect the fields of high energy or particle physics, whose goal it is to understand the universe and all the particles it is composed of, with condensed matter physics, 1 arXiv:1804.10649v1 [cond-mat.mtrl-sci] 27 Apr 2018where the same type, or even additional types, of particles can be found as so-called quasiparticles, meaning that the charge carriers behave in a similar way as it would be expected from a certain particle existing in free space.The field of topology in condensed matter physics evolved from the idea that there can be insulators whose band structure is fundamentally different (i.e. has a different topology) from that of the common insulators we know. If two insulators with different topologies are brought into contact, electrons that have no mass and cannot be back scattered are supposed to appear at the interface. These edge states also appear if a topological insulator (TI) is in contact with air, a trivial insulator. 2D TIs have conducting edge states whereas 3D TIs, which were discovered later, have conducting surface states. TIs have already been reviewed multiple times, [13][14][15][16] which is why we focus here on the newer kind of topological materials, namely topological semimetals (TSMs). Nevertheless, we will refer to TIs and their properties where relevant in the context of topological materials and to contrast them with TSMs.The term "topological semimetal" is widely used and basically includes all semimetals that exhibit some non-trivial band topology. We will describe in more detail later in this review what non-trivial topology actually means. Since TSMs are semimetals they are characterized by a gap-less band structure, i.e. they differ from normal metals by being charge balanced, meaning the amount of electrons and holes contributing to their conductivity is exactly the same. Or, phrased differently, the hole and electron pockets composing the Fermi surface are of the same size.

Topological Semimetals in Square-Net Materials

“…as Weyl fermions (18,19). For an in-depth description of TSMs and the chemical principles behind them, we like to refer readers to a recent review article (20). The electronic structure of a TSM consists of two linearly dispersed bands that cross each other at the so-called Dirac (or Weyl) point, which is ideally located at the Fermi level.…”

Charge Density Waves and Magnetism in Topological Semimetal Candidates GdSbxTe2−x−δ

“…Topological semimetals (TSMs) have attracted significant attention for their potential in applications in novel electronics . Many TSMs host exceptional electronic properties, ranging from high carrier mobility, large magnetoresistance, to more exotic electron–hole tunneling, chiral magnetotransport phenomena, or bulk half‐integer quantum Hall behavior .…”

“…Topological semimetals (TSMs) have attracted significant attention for their potential in applications in novel electronics. [1,2] Many TSMs host exceptional electronic properties, ranging from high carrier mobility, [3][4][5] large magnetoresistance, [3][4][5] to more exotic electron-hole tunneling, [6] chiral magnetotransport phenomena, [7,8] or bulk half-integer quantum Hall behavior. [9] TSMs can also exhibit fascinating optical properties, such as frequency-independent optical conductivity in 2D systems, [10,11] or linear frequency-dependent optical conductivity in 3D systems.…”

Gapless Dirac surface states in the antiferromagnetic topological insulator MnBi2Te4

“…The discovery of different types of exotic topological states that can be experimentally realized in semimetals has ignited intensive studies [1][2][3][4][5][6][7]. Besides their unprecedented importance for fundamental science, they also offer intriguing possibilities for device design revolutionizing computation capabilities, as well as laser technology [8].…”