Weyl semimetal in the rare-earth hexaboride family supporting a pseudonodal surface and a giant anomalous Hall effect

Ruiqi Zhang, Cheng-Yi Huang, Jamin Kidd, Robert S. Markiewicz, Hsin Lin, Arun Bansil, Bahadur Singh, and Jianwei Sun

Phys. Rev. B 105, 165140 – Published 21 April 2022

Abstract

Rare-earth hexaborides offer a rich tapestry for exploring the interplay of topological orders, magnetism, and electron-correlation effects associated with protected quantum phenomena. Here, using first-principles modeling, we identify in cerium hexaboride ( $Ce B_{6}$ ) a topological state that harbors a pseudonodal surface (PNS) along with double-Weyl fermions. An analysis of the electronic states in the vicinity of the Fermi level reveals the presence of $M_{z}$ -mirror-symmetry-protected band crossings that involve itinerant ( $d$ ) and localized ( $f$ ) states of Ce. These band crossings are found to remain nearly gapless as one goes away from the mirror plane, driving the formation of PNS states. We also demonstrate the presence of coexisting double-Weyl fermions with chiral charges of $\pm 2$ on the $C_{4 z}$ rotational axis. By analyzing the Berry curvature field associated with the topological states, we predict that $Ce B_{6}$ supports a giant anomalous Hall conductivity of $- 1840 Ω^{- 1} {cm}^{- 1}$ in the slightly electron-doped regime, which would be larger than the values reported to date in magnetic Weyl semimetals. Our study thus indicates that $Ce B_{6}$ , which combines ferromagnetic order with topological physics in a heavy-fermion matrix, would provide a promising playground for investigating topological magnetic states with giant anomalous Hall responses.

Received 10 August 2021
Revised 23 February 2022
Accepted 5 April 2022

DOI:https://doi.org/10.1103/PhysRevB.105.165140

Physics Subject Headings (PhySH)

Electronic structure Symmetry protected topological states Topological phases of matter

Density functional theory

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ruiqi Zhang ^1,*, Cheng-Yi Huang^2,*, Jamin Kidd¹, Robert S. Markiewicz², Hsin Lin³, Arun Bansil², Bahadur Singh^4,†, and Jianwei Sun^1,‡

¹Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
²Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA
³Institute of Physics, Academia Sinica, Taipei 11529, Taiwan
⁴Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Mumbai 400005, India

^*These authors contributed equally to this work.
^†bahadur.singh@tifr.res.in
^‡jsun@tulane.edu

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Vol. 105, Iss. 16 — 15 April 2022

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Images

Figure 1
Topological state, crystal structure, and band structure of $Ce B_{6}$ . (a)–(c) Coexisting PNS and double-Weyl fermions. The nodal crossings that form the nodal surface are protected on the $M_{z} = 0$ mirror plane marked with shaded gray. These nodal crossings interact weakly away from the $M_{z}$ mirror plane, remaining nearly degenerate to form a PNS. (c) A pair of double-Weyl fermions with chiral charge $C_{w} = \pm 2$ on the $C_{4 z}$ rotational axis with double Fermi arc surface states. Crystal structure of (d) nonmagnetic and (e) ferromagnetic $Ce B_{6}$ . Blue and green balls represent Ce and B atoms, respectively. (f) Primitive bulk Brillouin zone (BZ) of $Ce B_{6}$ with relevant high-symmetry points. The projected plane represents the associated (001) surface BZ and the dashed lines locate the projection of bulk high-symmetry points on the (001) surface. First-principles band structure of (g) nonmagnetic and (h) ferromagnetic $Ce B_{6}$ . (i) Spin-resolved electronic structure of ferromagnetic $Ce B_{6}$ with spin-orbit coupling (SOC). Color scale gives the spin polarization of the states.
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Figure 2
Pseudonodal surface in $Ce B_{6}$ . $M_{z}$ mirror-eigenvalue-resolved band structures of $Ce B_{6}$ (including SOC) at (a) $k_{z} = 0$ and (b) $k_{z} = π / c$ planes. Red and blue curves identify bands with $+ i$ and $- i M_{z}$ mirror eigenvalues. These bands form protected crossings on the mirror planes. (c),(d) Nodal band crossings on (c) $k_{z} = 0$ and (d) $k_{z} = π / a$ planes. Numbers 1, 2, 3, and 4 on graphs identify inner and outer regions of the nodal lines (see text for details). (e),(f) Distribution of nodal band crossings in the bulk BZ. The band crossings form (e) a closed nodal surface surrounding the $k_{z} = 0$ plane and (f) an open nodal surface around $k_{z} = π / a$ plane. Color scales represent the $k_{z}$ value of the nodal band crossings.
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Figure 3
Weyl nodes and Berry curvature field in $Ce B_{6}$ . (a) $k − space$ location of the Weyl nodes in 3D bulk Brillouin zone. Pink (yellow) balls represent the Weyl points of chiral charge $+ 1$ ( $- 1$ ), while green (blue) balls represent the Weyl points of chiral charge $+ 2$ ( $- 2$ ). (b) $C_{4 z}$ rotational eigenvalue resolved band structure of $Ce B_{6}$ on the $k_{z}$ axis. $e^{i (3 π / 4)}, e^{i (π / 4)}, e^{- i (π / 4)}$ , and $e^{- i (3 π / 4)}$ denote $C_{4 z}$ eigenvalue of the bands. Black (green) dots denote the chiral charge $C_{w} = 2 (1)$ of the Weyl nodes. (c) The distribution of Berry curvature on $k_{x} = 0$ plane. Pink and blue dots denote the Weyl points with positive and negative chiral charge, respectively. (d) Closeup of the area highlighted in (c). Color bar denotes the magnitude of Berry curvature on a logarithmic scale and arrows represent the Berry curvature field.
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Figure 4
Calculated anomalous Hall conductivity of bulk and thin film of $Ce B_{6}$ . (a) Energy dependence of anomalous Hall $σ_{x y}$ on the (001) plane of $Ce B_{6}$ . (b) Berry curvature [ $Ω_{x y}^{z} (k)$ ] distribution in the 3D $k_{x} − k_{y} − k_{z}$ space. (c) The accumulated Berry curvature along the $k_{z}$ direction. (d) 2D anomalous Hall conductance $G_{x y}$ as a function of $Ce B_{6}$ layers (L).
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