Dirac materials

AbstractA 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 low-energy (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:: 73.20.-r Electron states at surfaces and interfaces73.25.+i Surface conductivity and carrier phenomena73.50.-h Electronic transport phenomena in thin films74.20.-z Theories and models of superconducting state73.22.Pr Electronic structure of graphene75.76.+j Spin transport effects71.55.-i Impurity and defect levelsKeywords: Dirac materialsd-wave superconductorsgraphenetopological insulatorschiralityback scatteringimpurity resonance AcknowledgementsWe are grateful to D. Arovas, D. Abergel, R. Biswas, A.H. Castro Neto, H. Dahal, V. Fal'ko, M. Fogelström, J. Fransson, M. Graf, Z. Huang, P. Hoffmann, M.I. Katsnelson, A.I. Lichtenstein, J. Linder, F. Lombardi, H. Manoharan, J. Moore, N. Nagaosa, K. Scharnberg, Z.X. Shen, Y. Tanaka, O. Tjernberg, A. Yazdani, S.C. Zhang, J.X. Zhu for discussions. This work has been supported by US DOE BES E304, LDRD, University of California UCOP-09-027, the German Research Foundation (DFG) via SFB 668 and SPP 1459, Dirac Materials ERC-DM-321031, and the Swedish Research Council (VR). TOW thanks KITP Santa Barbara for hospitality during a visit where parts of this work were written.For figures with copyright from the American Physical Society: Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.