Dirac Fermions in Solids: From High-Tc Cuprates and Graphene to Topological Insulators and Weyl Semimetals

Vafek, Oskar; Vishwanath, Ashvin

doi:10.1146/annurev-conmatphys-031113-133841

Cited by 614Topological Materials and PhenomenaPhysics of Superconductivity and MagnetismAdvanced Condensed Matter Physics

Dirac Fermions in Solids: From High-Tc Cuprates and Graphene to Topological Insulators and Weyl Semimetals

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Vafek, Oskar, Vishwanath, Ashvin·2014·Annual Review of Condensed Matter Physics

DOI 10.1146/annurev-conmatphys-031113-133841

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Abstract

Understanding Dirac-like fermions has become an imperative in modern condensed matter sciences: All across the research frontier, from graphene to high T c superconductors to the topological insulators and beyond, various electronic systems exhibit properties that can be well described by the Dirac equation. Such physics is no longer the exclusive domain of quantum field theories and other esoteric mathematical musings; instead, physics of real condensed matter systems is governed by such equations, and important materials science and practical implications hinge on our understanding of Dirac particles in two and three dimensions. Although the physics that gives rise to the massless Dirac fermions in each of the above-mentioned materials is different, the low-energy properties are governed by the same Dirac kinematics. The aim of this article is to review a selected cross-section of this vast field by highlighting the generalities and contrasting the specifics of several physical systems.

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The (100) surface states of the tetragonal photonic crystal reveal the Z2 topology of the Dirac points.
“According to the bulk-edge correspondence principle, [2][3][4] the (100) surface states of the tetragonal PhC can reveal the Z 2 topology of the DPs.”
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Authors: Vafek, O., & Vishwanath, A.
Affiliations: Florida State University (US)
University of California, Berkeley (US)
ORCID: Vafek, Oskar
Vishwanath, Ashvin
Venue: Annual Review of Condensed Matter Physics
Publisher: Annual Reviews
Published: 2014-03-01
Volume: 5
Issue: 1
Pages: 83-112
ISSN: 1947-5454 (ISSN-L)
1947-5462
DOI: 10.1146/annurev-conmatphys-031113-133841
OpenAlex: W2165553044
Cited by: 614
References: 12
Citations by year: 2026: 24 · 2025: 33 · 2024: 27 · 2023: 44 · 2022: 32 · 2021: 51 · 2020: 82 · 2019: 53 · 2018: 52 · 2017: 72 · 2016: 83 · 2015: 39 · 2014: 17 · 2013: 3
FWCI: 7.11
Type: journal article
Language: en
Open access: green
arxiv.org
Locations: Annual Review of Condensed Matter Physics (publishedVersion)
arXiv (Cornell University) (submittedVersion)
arXiv (Cornell University)
Topics: Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Physics of Superconductivity and Magnetism
Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
Keywords: Dirac fermions, massless Dirac fermions, cuprate superconductors, graphene, topological insulators, Weyl semimetals, Dirac equation, two-dimensional Dirac materials

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Dirac Fermions in Solids: From High-Tc Cuprates and Graphene to Topological Insulators and Weyl Semimetals

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