Dirac materials

Abstract

A wide range of materials, like d-wave superconductors, graphene, and topological insulators, share a fundamental similarity: their low-energy fermionic excitations behave as massless Dirac particles rather than fermions obeying the usual Schrödinger Hamiltonian. This emergent behavior of Dirac fermions in condensed matter systems defines the unifying framework for a class of materials we call "Dirac materials". In order to establish this class of materials, we illustrate how Dirac fermions emerge in multiple entirely different condensed matter systems and we discuss how Dirac fermions have been identified experimentally using electron spectroscopy techniques (angle-resolved photoemission spectroscopy and scanning tunneling spectroscopy). As a consequence of their common low-energy excitations, this diverse set of materials shares a significant number of universal properties in the lowenergy (infrared) limit. We review these common properties including nodal points in the excitation spectrum, density of states, specific heat, transport, thermodynamic properties, impurity resonances, and magnetic field responses, as well as discuss many-body interaction effects. We further review how the emergence of Dirac excitations is controlled by specific symmetries of the material, such as time-reversal, gauge, and spin-orbit symmetries, and how by breaking these symmetries a finite Dirac mass is generated. We give examples of how the interaction of Dirac fermions with their distinct real material background leads to rich novel physics with common fingerprints such as the suppression of back scattering and impurity-induced resonant states. PACS

CaTe: a new topological node-line and Dirac semimetal

“…Protected by the crystal symmetry and time reversal symmetry, 3D DSMs can be robust against external perturbations. Several materials have been theoretically predicted to be 3D DSMs 12,[17][18][19][20][21] and some of them have already been confirmed by experiments. [30][31][32][33] If one breaks the time reversal symmetry 8,22,23,34 or the inversion symmetry, [35][36][37][38] the 3D DSM will evolve into WSM.…”

“…[8][9][10][11][12] These systems could demonstrate many fascinating phenomena, such as Weyl fermion quantum transport and various Hall effects, [13][14][15][16] consequently become the rising stars of the field. Up to now, three kinds of topological semimetals have been discovered, i.e., 3D Dirac semimetal (DSM), 12,[17][18][19][20][21] Weyl semimetal (WSM), 8,9,22,23 and node-line semimetal (NLS). [24][25][26][27][28][29] The 3D DSM has four-fold degeneracy point, which can be viewed as the kiss of two Weyl fermions with opposite chiralities in the Brillouin zone (BZ).…”

One-dimensional Coulomb problem in Dirac materials

“…The rise of Dirac materials [20], condensed matter systems with quasiparticles welldescribed by the Dirac equation, has led to revisits of Dirac-Kepler problems with Dirac-like matrix Hamiltonians. One example is the two-dimensional (2D) relativistic solution and its application to graphene [21], which has charge carriers described by a massless DiracWeyl equation.…”

Generation of coherent radiation by magnetization reversal in graphene

“…When considering electronic properties of graphene, magnetic effects are usually disregarded, since they occur on much smaller energy scales than other energies [2][3][4][5][6][7][8][9][10]. For instance, the Zeeman energy gµ B B, in the external field of B = 1 T, is only 4.3 × 10 −5 eV (0.5 K).…”

“…Magnetic effects become more pronounced in the presence of disorder that can come about in many different forms, such as adatoms, vacancies, admixtures on the top of graphene or in the substrate, and also extended defects, such as cracks and edges [2,3,5,[7][8][9][10][11]. Adatoms can possess magnetic moments, interacting with electronic spins as in the Kondo problem [12].…”