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Semi-Dirac Fermions in a Topological Metal

Yinming Shao1,2,*, Seongphill Moon3,4, A. N. Rudenko5, Jie Wang6,7,8, Jonah Herzog-Arbeitman9, Mykhaylo Ozerov4, David Graf4, Zhiyuan Sun7, Raquel Queiroz1 et al.

Seng Huat Lee2, Yanglin Zhu2, Zhiqiang Mao2, M. I. Katsnelson5, B. Andrei Bernevig9,10,11, Dmitry Smirnov4, Andrew J. Millis1,12, and D. N. Basov1,†

  • *Contact author: ymshao@psu.edu
  • †Contact author: db3056@columbia.edu
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Phys. Rev. X 14, 041057 – Published 5 December, 2024

DOI: https://doi.org/10.1103/PhysRevX.14.041057

Abstract

Topological semimetals with massless Dirac and Weyl fermions represent the forefront of quantum materials research. In two dimensions, a peculiar class of fermions that are massless in one direction and massive in the perpendicular direction was predicted 16 years ago. These highly exotic quasiparticles—the semi-Dirac fermions—ignited intense theoretical and experimental interest but remain undetected. Using magneto-optical spectroscopy, we demonstrate the defining feature of semi-Dirac fermions—B2/3 scaling of Landau levels—in a prototypical nodal-line metal ZrSiS. In topological metals, including ZrSiS, nodal lines extend the band degeneracies from isolated points to lines, loops, or even chains in the momentum space. With ab initio calculations and theoretical modeling, we pinpoint the observed semi-Dirac spectrum to the crossing points of nodal lines in ZrSiS. Crossing nodal lines exhibit a continuum absorption spectrum but with singularities that scale as B2/3 at the crossing. Our work sheds light on the hidden quasiparticles emerging from the intricate topology of crossing nodal lines and highlights the potential to explore quantum geometry with linear optical responses.

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Popular Summary

Among the emerging quasiparticles, semi-Dirac fermions stand out. In 2D systems, these exotic quasiparticles are thought to have mass in one direction yet be massless in the perpendicular direction. These peculiar fermions have so far evaded detection in solid materials. Here, we present experimental evidence of the defining feature of semi-Dirac fermions in samples of the metal ZrSiS.

In a typical metal, the presence of an external magnetic field induces cyclotron motion of electrons, and the ensuing cyclotron energy scales linearly with the strength of the magnetic field. In graphene, the presence of massless Dirac fermions leads to a cyclotron energy that scales with the square root of the field. Semi-Dirac fermions are predicted to have a different response: Their cyclotron energy scales with the two-thirds power of the field. Initial proposals to realize semi-Dirac fermions require stretching graphene until its two Dirac points—features in the energy band structure that signify the presence of Dirac fermions—merge in momentum space. However, monolayer graphene breaks down before reaching the desired strain level.

In ZrSiS, the continuous extension of Dirac points in momentum space, known as a nodal line, presents exciting opportunities to realize semi-Dirac fermions. Through high-precision magnetoinfrared spectroscopy, we observe compelling evidence of the two-thirds power-law behavior of the cyclotron energy with magnetic field. Combining these findings with calculations and modeling, we identify semi-Dirac fermions at special crossings of nodal lines in ZrSiS. Those crossings facilitate the merging of Dirac points without the need for the unrealistic large strain required in graphene.

Our work sheds light on the hidden quasiparticles emerging from the intricate topology and geometry of crossing nodal lines.

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Phys. Rev. X 14, 041057– Published 5 December, 2024
  • Received 19 April 2024
  • Revised 16 July 2024
  • Accepted 23 October 2024
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