Valley polarization dependence of nonreciprocal transport in a chiral semiconductor

Kenta Sudo, Yuki Yanagi, Takeshi Takahashi, Kim-Khuong Huynh, Katsumi Tanigaki, Kaya Kobayashi, Michi-To Suzuki, and Motoi Kimata

Phys. Rev. B 108, 125137 – Published 22 September 2023

Abstract

We report that the strong spin-valley coupling in chiral tellurium can modify the electronic structures, and how it dominates the nonreciprocal transport. The observed nonreciprocal magnetoresistance shows anomalous suppression in high magnetic fields. This behavior contradicts the linearity of nonreciprocal signals to the fields observed in other materials. We find that the magnetic field-induced fully valley polarized states in tellurium trigger the deviation from the linearity. Our results establish the essential role of the valley degree of freedom for the cross-correlation phenomena in chiral materials, in addition to the previously discussed spin-charge coupling.

Received 21 October 2022
Revised 24 July 2023
Accepted 18 August 2023

DOI:https://doi.org/10.1103/PhysRevB.108.125137

Physics Subject Headings (PhySH)

Electrical conductivity Magnetoelectric effect Spin-orbit coupling Valleytronics

Elemental semiconductors

First-principles calculations Resistivity measurements

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Kenta Sudo¹, Yuki Yanagi², Takeshi Takahashi³, Kim-Khuong Huynh⁴, Katsumi Tanigaki ⁵, Kaya Kobayashi ^3,6, Michi-To Suzuki^1,7, and Motoi Kimata ^1,*

¹Institute for Materials Research, Tohoku University, Sendai, Miyagi, Japan
²Liberal Arts and Sciences, Toyama Prefectural University, Imizu, Toyama 939-0398, Japan
³Department of Physics, Okayama University, Okayama, Japan
⁴AIMR, Tohoku University, 1-1-2 Katahira, Aoba, Sendai 980-8577, Miyagi, Japan
⁵BAQIS, Bld. 3, No.10 Xibeiwang East Rd., Haidian District, Beijing 100193, China
⁶Research Institute for Interdisciplinary Science, Okayama University, Okayama, Japan
⁷Center for Spintronics Research Network, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan

^*motoi.kimata.b4@tohoku.ac.jp

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Issue

Vol. 108, Iss. 12 — 15 September 2023

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Images

Figure 1
(a) Schematic of the crystal structure of elemental Te. (b) Solid line is schematic semiempirical valence band structure near the $H$ point [22]. Dashed lines exhibit energy levels with various $E_{F}$ from the top of the valence band. Corresponding values of $n$ are also shown in the right axis. (c) Angular dependence of $ρ_{c}$ (right axis) and $ρ_{c}^{NR}$ (left axis) for $B = 4$ T and $T = 20$ K. In such low-field and high-temperature conditions, Zeeman energy for spin-polarized valley is smaller than the thermal broadening of Fermi level. (d) Main panel: Magnetic field dependence of $ρ_{c}^{NR}$ at different temperatures. Inset: Temperature dependence of $γ^{'}$ extracted from the low-field slope of $ρ_{c}^{NR}$ .
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Figure 2
Main panel: Magnetic field dependence of $\tilde{γ}$ for distinct samples. Inset: $n$ dependence of $| γ^{'} |$ for three samples obtained from low-field linear region of $\tilde{γ}$ , that is, $\tilde{γ} = γ^{'} B$ .
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Figure 3
(a),(b) Spin texture of the top of the valence bands for right-handed and left-handed Te crystals in the $k_{x} − k_{z}$ plane, respectively. The sign of spin texture is inverted depends on the crystal chirality. The direction of spin is indicated by orange arrows. Solid red lines show FS cross section with various $E_{F}$ . (c) Main panel: Magnetic field evolution of spin-polarized band in Te for $B | | c$ obtained from the first-principles calculations. Inset: Spin texture for $B = 8.6$ T near the $H$ point obtained from the first-principles calculations (orange arrows). The spin texture is mostly not affected by the external magnetic field in such field range. Ellipsoidal solid line is FS for $E_{F} = - 0.2$ meV. Only the single FS is observed at high magnetic valley polarized state. The Zeeman effect only for spin moment is considered in this calculation.
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Figure 4
(a),(b) Schematic illustrations of field evolution of spin-polarized band for $c$ -axis magnetic field. Panels (a) and (b) represent the case for right-handed and left-handed crystals, respectively. Red arrows in (a) and blue arrows in (b) represent outward and inward spin textures for right- and left-handed crystals, respectively. When $n$ is sufficiently small, the spin-polarized FS split into two distinct valleys as shown in the left figure. As the field increases, one of two valleys disappear when the Zeeman energy of spin-polarized valley exceeds $E_{F}$ . Since the crystal chirality is opposite for (a) and (b), the excited valleys by magnetic field are also opposite. (c) Calculated field dependence of $\sum v_{F}^{z}$ . $E_{F}$ is set to −0.4 meV, which corresponds to $n$ of sample 1 ( $n \approx 4 \times 10^{15} c m^{- 3}$ ). (d) Experimentally obtained $B_{\inf}$ vs $n$ for distinct samples (symbols). The solid line is obtained from the simulation based on the model calculation. In this model calculation, the Zeeman effect is considered for effective magnetic moment including spin and orbital moments.
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Figure 5
Main panel: Magnetic field evolution of angular dependence of $ρ_{c}^{NR}$ at 2 K. For $ρ_{c}^{NR}$ , nonmonotonous angular dependence was observed at high fields above 3 T. Inset: Simulated angular dependence of $\sum v_{F}^{z}$ for magnetic field strength of 1, 3, 6, and 14 T. The value of $E_{F}$ is set to −0.4 meV corresponding to $n$ of sample 1.
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