A Primer on Weyl Semimetals: Down the Discovery of Topological Phases

Main Article Content

Satyaki Kar
Arun M. Jayannavar


Recently discovered Weyl semimetals (WSM) have found special place in topological condensed matter studies for they represent first example of massless Weyl fermions found in electronic condensed matter systems. A WSM shows gapless bulk energy spectra with Dirac-like point degeneracies, famously called Weyl nodes, which carry with themselves well defined chiralities and topologically protected chiral charges. One finds the Berry curvature of the Bloch bands to become singular, like in a magnetic monopole, at these Weyl nodes. Moreover, these systems feature topological surface states in the form of open Fermi arcs. In this review, we undergo a concise journey from graphene based Dirac physics to Weyl semimetals: the underlying Hamiltonians, their basic features and their unique response to external electric and magnetic fields in order to provide a basic walk-through of how the Weyl physics unfolded with time starting from the discovery of Graphene.

Dirac equation, Weyl fermion, Magnetic monopole, Fermi arc, Chiral anomaly.

Article Details

How to Cite
Kar, S., & Jayannavar, A. M. (2021). A Primer on Weyl Semimetals: Down the Discovery of Topological Phases. Asian Journal of Research and Reviews in Physics, 4(1), 34-45. https://doi.org/10.9734/ajr2p/2021/v4i130136
Minireview Article


Armitage NP, et al: Rev. Mod. Phys. 2018;90:015001.

Rao S. arXiv: 2016;1603.02821.

Yan B, Felser C. Ann. Rev. Cond. Mat. Phys. 2017;8:337.

Hasan MZ, et: al: Phys. Scr. 2015;014001.

Zou J, He Z, Xu G. NJP Comp. Mat. 2019;5:96.

Shen SQ. Topological Weyl and Dirac semimetals. Springer Publication; 2017.

Joshi AW. Matrices and tensors in physics. New Age International; 1995.

Bevan TDC, et al: Nature. 1997;386:689.

Novoselov KS, et:al: Science. 2004;306(5696):666-669.

Neto AHC, et al: Rev. Mod. Phys. 2009;81:109.

Sharma SD, et al: Rev. Mod. Phys. 2011;83:407.

Beenakker CWJ. Rev. Mod. Phys. 2008;80:1337.

Hasan MZ, Kane CL. Rev. Mod. Phys. 2010;82:3045.

Kittel C. Introduction to solid state physics. Wiley Publication. 8th Edition; 2004.

Di Xiao, et al: Rev. Mod. Phys. 2010;82:1959.

Kane CL, Mele EJ. Phys. Rev. Lett. 2005;95:146802.

Saha A, Jayannavar AM. Resonance. 2017;22(8):787-800.

Cayssol J, et al: Phys. Stat. Solidi RRL. 2013;7(1-2):101-108.

Kar S, Basu B. Phys. Rev. B. 2018;98:245119.

Ozawa T, et al: Rev. Mod. Phys. 2019;91:015006.

Okugawa R, Murakami S. Phys. Rev. B. 2014;89:235315.

Murakami S. New Jour. Phys. 2007;9:356.

McCormick TM, Kimchi I, Trivedi N. Phys. Rev. B. 2014;89:235315.

Zyuzin AA, et al: Phys. Rev. B. 2012;85:165110.

Soluyanov AA, et: al: Nature. 2015;527:495.

Burkov AA. J. Phys. Cond. Mat. 2015;27:113201.

Li P, et: al: Nat. Comm. 2017;8:2150.

Yang SA. SPIN. 2016;06:1640003:1-19.

Burkov AA. Nat. Mat. 2016;15:1145.

Das. Lectures on Quantum Field Theory. World Scientific Publication; 2007.

McDonald KT. Electrodynamics is 1 and 2 spatial dimensions. Available:http://www.physics.princeton.edu/- mcdonald/examples/2dem.pdf

Kim P, et al: Phys. Rev. Lett. 2017;119:266401.