Magnetic states and Kondo screening in Weyl semimetals with chiral anomaly

Lin Li, Jin-Hua Sun, Zhen-Hua Wang, Dong-Hui Xu, Hong-Gang Luo, and Wei-Qiang Chen

Phys. Rev. B 98, 075110 – Published 7 August 2018

Abstract

We theoretically study the localized magnetic states and the Kondo screening of a magnetic impurity in the bulk of Weyl semimetals (SMs). The linear dispersion near the Weyl nodes and the anomalous broadening of the impurity level lead to a nonvanishing magnetic moment in a wide region of parameters. The magnetic susceptibility is significantly enhanced by increasing the chirality imbalance for the chemical potential fixed at the Weyl nodes. The Kondo effect takes place whenever the chemical potential is tuned away from the nodes. The low-temperature susceptibility is determined by both the Kondo screening and the broadening of the magnetic impurity level. In the presence of chiral anomaly, the Kondo screening displays opposite behaviors for the chemical potential situated below and above the Weyl nodes. The magnetic susceptibility can be tuned by the charge imbalance of the nodes, which provides a scheme to study the chiral anomaly in Weyl SMs.

Received 15 March 2018
Revised 13 July 2018

DOI:https://doi.org/10.1103/PhysRevB.98.075110

Physics Subject Headings (PhySH)

Kondo effect Magnetic susceptibility Topological phases of matter

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Lin Li^1,2, Jin-Hua Sun³, Zhen-Hua Wang^2,4, Dong-Hui Xu⁵, Hong-Gang Luo^4,6,*, and Wei-Qiang Chen^2,†

¹College of Physics and Electronic Engineering, and Center for Computational Sciences, Sichuan Normal University, Chengdu, 610068, China
²Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
³Department of Physics, Ningbo University, Ningbo 315211, China
⁴Beijing Computational Science Research Center, Beijing 100084, China
⁵Department of Physics, Hubei University, Wuhan 430062, China
⁶Center of Interdisciplinary Studies and Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou 730000, China

^*luohg@lzu.edu.cn
^†chen.wq@sustc.edu.cn

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Vol. 98, Iss. 7 — 15 August 2018

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Images

Figure 1
The Kondo screening of a magnetic impurity in the bulk of Weyl SMs, where a spin-down (-up) electron on the impurity level $ɛ_{d}$ is replaced by a spin-up (-down) electron through the empty or double occupation virtual states. The chiral anomaly introduces the charge imbalance between the Weyl nodes with opposite chirality ( $h = \pm$ ), and the chemical potentials $μ_{\pm} = μ_{0} \pm δ μ / 2$ . $μ_{0}$ is the chemical potential in the absence of chiral anomaly, and $δ μ$ denotes the charge imbalance.
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Figure 2
The phase boundary between the magnetic and nonmagnetic regions of a magnetic impurity coupled with two Weyl nodes. The chemical potential $μ_{0}$ is tuned above (a) and below (b) the nodes with $μ_{0} = \pm 0.05, \pm 0.1, \pm 0.2$ , and other parameters are $E_{z} = 0$ , $Q_{z} = 0.1$ , $U = 2$ , and the temperature $T = 0$ .
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Figure 3
The influence of the chiral anomaly on the phase boundary between the magnetic and nonmagnetic states of a magnetic impurity in Weyl SMs. (a) and (b) The chemical potential situates above and below the Weyl nodes with $μ_{0} = \pm 0.1$ and $δ μ = 0.0, 0.02, 0.04$ . Other parameters are the same with that in Fig. 2.
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Figure 4
The susceptibility of a magnetic impurity in Weyl SMs with the chemical potential $μ_{0} = 0$ . (a) The enhancement of magnetic susceptibility by increasing the coupling amplitudes $Γ_{0} = 1.0, 1.5, 1.75$ in the absence of chirality imbalance $δ μ = 0$ . The inset is the local density of states (LDOS) of the magnetic impurity. (b) The variation of magnetic susceptibility in the presence of chiral anomaly with $μ_{\pm} = \pm δ μ / 2$ , and the coupling amplitude $Γ_{0} = 1.5$ . The inset is the temperature dependent LDOS for the chiral imbalance $δ μ = 0.08$ . Other parameters are the impurity level $ɛ_{d} = - 0.3$ , $Q_{z} = 0.1$ , and the Coulomb repulsion $U = 2.0$ .
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Figure 5
The magnetic susceptibility of an impurity in Weyl SMs with finite DOSs at the Fermi level. (a) The chirality imbalance $δ μ$ dependent susceptibility for the chemical potential above the Weyl nodes with $μ_{0} = 0.3$ , the coupling amplitude $Γ_{0} = 0.5$ , the impurity level $ɛ_{d} = 0.2$ , and the Coulomb repulsion $U = 2.0$ . (b) The susceptibility varying with the chirality imbalance $δ μ$ for the chemical potential posited below the Weyl nodes, and the parameters are $μ_{0} = - 0.2$ , $Γ_{0} = 0.4$ , $ɛ_{d} = - 0.3$ , $Q_{z} = 0.1$ , and $U = 2.0$ . The insets in (a) and (b) are the LDOS of the magnetic impurity with $δ μ = 0.0, 0.04, 0.08$ .
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Figure 6
(a) The schematic diagram of the Zeeman splitting induced coherent internode spin-flipping scattering (SFS) processes in the Weyl SMs with chiral anomaly. (b) The Zeeman splitting of the Kondo resonance in the local DOS with the parameters $μ_{0} = 0.3$ , $ɛ_{d} = 0.2$ , $Γ_{0} = 0.5$ , $Q_{z} = 0.1$ , $U = 2$ , $T = 0$ , and $δ μ = 0.02$ . The Zeeman interaction is arranged from $E z = 0$ to $E z = 0.01$ . (c) The Zeeman splitting of Kondo resonance for the chemical potentials situated below the Weyl nodes with $μ_{0} = - 0.2$ , the impurity level $ɛ_{d} = - 0.3$ , and the coupling amplitude $Γ_{0} = 0.4$ . Other parameters are the same with that in (b). (e) and (f) The temperature dependent susceptibilities correspond to the chemical potential situated above and below the Weyl nodes in (b) and (c), respectively.
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