Abstract
We expand the phase diagram of two-dimensional, nonsymmorphic crystals at integer fillings that do not guarantee gaplessness. In addition to the trivial, gapped phase that is expected, we find that band inversion leads to a class of topological, gapless phases. These topological phases are exemplified by the monolayers of () if spin-orbit coupling is neglected. We characterize the Dirac band touching of these topological metals by the Wilson loop of the non-Abelian Berry gauge field. Furthermore, we develop a criterion for the proximity of these topological metals to 2D and 3D topological insulators when spin-orbit coupling is included; our criterion is based on nonsymmorphic symmetry eigenvalues, and may be used to identify topological materials without inversion symmetry. An additional feature of the Dirac cone in monolayer is that it tilts over in a Lifshitz transition to produce electron and hole pockets—a type-II Dirac cone. These pockets, together with the pseudospin structure of the Dirac electrons, suggest a unified, topological explanation for the recently reported, nonsaturating magnetoresistance in , as well as its circular dichroism in photoemission. We complement our analysis and first-principles band structure calculations with an ab-initio-derived tight-binding model for the monolayer.
- Received 14 May 2016
DOI:https://doi.org/10.1103/PhysRevX.6.041069
Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Topological metals have robust properties that are immune to environmental disturbances and structural deformations of the crystal. One such robust property is that the electrons in topological metals behave like relativistic electrons in free space, as first studied by Paul Dirac. Both types of electrons have in common an energy-momentum dispersion that resembles a cone, i.e., a “Dirac cone.” Here, we propose a new class of topological metals.
In this class of metals, the velocity of the electrons may strongly depend on the direction of motion, and it can even reverse its sign in certain directions where the Dirac cone tilts over. These “type-II” Dirac cones occur in and monolayers, as well as in a wide class of metals having the same symmetry; a generalization of our theory even applies to photons in a periodic medium. Additionally, we introduce an efficient method to identify these metals from first-principles band-structure calculations.
Our findings synthesize symmetry and topology to extend our understanding of the possible phases of light and matter.
