Valley-Coherent Quantum Anomalous Hall State in AB-Stacked ${\mathrm{MoTe}}_{2}/{\mathrm{W}\mathrm{S}\mathrm{e}}_{2}$ Bilayers

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Valley-Coherent Quantum Anomalous Hall State in AB-Stacked ${MoTe}_{2} / {W S e}_{2}$ Bilayers

Zui Tao, Bowen Shen, Shengwei Jiang, Tingxin Li, Lizhong Li, Liguo Ma, Wenjin Zhao, Jenny Hu, Kateryna Pistunova, Kenji Watanabe, Takashi Taniguchi, Tony F. Heinz, Kin Fai Mak, and Jie Shan

Phys. Rev. X 14, 011004 – Published 10 January 2024

See Viewpoint: Another Twist in the Understanding of Moiré Materials

Abstract

Moiré materials provide fertile ground for the correlated and topological quantum phenomena. Among them, the quantum anomalous Hall (QAH) effect, in which the Hall resistance is quantized even under zero magnetic field, is a direct manifestation of the intrinsic topological properties of a material and an appealing attribute for low-power electronics applications. The QAH effect has been observed in both graphene and transition metal dichalcogenide (TMD) moiré materials. It is thought to arise from the interaction-driven valley polarization of the narrow moiré bands. Here, we show that the newly discovered QAH state in AB-stacked ${MoTe}_{2} / {W S e}_{2}$ moiré bilayers is not valley polarized but valley coherent. The layer- and helicity-resolved optical spectroscopy measurement reveals that the QAH ground state possesses spontaneous spin (valley) polarization aligned (antialigned) in two TMD layers. In addition, saturation of the out-of-plane spin polarization in both layers occurs only under high magnetic fields, supporting a canted spin texture. Our results call for a new mechanism for the QAH effect and highlight the potential of TMD moiré materials with strong electronic correlations and spin-orbit interactions for exotic topological states.

Received 11 June 2023
Revised 18 September 2023
Accepted 8 December 2023

DOI:https://doi.org/10.1103/PhysRevX.14.011004

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Excitons Magnetic order Magnetism Magneto-optics Topological materials Topological phases of matter Transport phenomena Valley degrees of freedom

2-dimensional systems Transition metal dichalcogenides

Condensed Matter, Materials & Applied Physics

Viewpoint

Another Twist in the Understanding of Moiré Materials

Published 18 March 2024

The unexpected observation of an aligned spin polarization in certain twisted semiconductor bilayers calls for improved models of these systems.

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Authors & Affiliations

Zui Tao^1,‡, Bowen Shen^1,‡, Shengwei Jiang^2,‡, Tingxin Li^1,‡, Lizhong Li¹, Liguo Ma¹, Wenjin Zhao ³, Jenny Hu⁴, Kateryna Pistunova⁴, Kenji Watanabe⁵, Takashi Taniguchi⁵, Tony F. Heinz^4,6, Kin Fai Mak ^1,2,3,*, and Jie Shan^1,2,3,†

¹School of Applied and Engineering Physics, Cornell University, Ithaca, New York, USA
²Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York, USA
³Kavli Institute at Cornell for Nanoscale Science, Ithaca, New York, USA
⁴Departments of Physics and Applied Physics, Stanford University, Stanford, California, USA
⁵National Institute for Materials Science, 1-1 Namiki, 305-0044 Tsukuba, Japan
⁶SLAC National Accelerator Laboratory, Menlo Park, California, USA

^*Corresponding author: kinfai.mak@cornell.edu
^†Corresponding author: jie.shan@cornell.edu
^‡These authors contributed equally to this work.

Popular Summary

Stacking two atomic layers slightly askew to one another provides fertile ground for exploring correlated and topological quantum phenomena. One such phenomenon observed in these “moiré materials” is the quantum anomalous Hall (QAH) effect, in which the resistance transverse to an electrical current is quantized even under zero magnetic field. In transition metal dichalcogenide (TMD) moiré semiconductors, electrons can be labeled by their “valley degree of freedom,” which denotes which of the two valleys in momentum space the electrons reside in. Here, we report that in one such semiconductor the electrons are in a quantum superposition of the two valleys, or “valley coherent,” contrary to what has been thought up to now.

Specifically, we performed optical spectroscopy measurements on the newly discovered QAH state of the moiré heterobilayer ${MoTe}_{2} / {W S e}_{2}$ . These measurements are layer resolved (they can differentiate between the ${MoTe}_{2}$ and ${W S e}_{2}$ layers) as well as handedness resolved (they can distinguish which valley the electrons are in). This resolution reveals that the QAH ground state possesses spontaneous valley coherence.

Our results call for a new mechanism for the QAH effect and highlight the potential of TMD moiré semiconductors with strong electronic correlations and spin-orbit interactions for exotic topological states.

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Vol. 14, Iss. 1 — January - March 2024

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Figure 1
AB-stacked ${MoTe}_{2} / {W S e}_{2}$ moiré bilayers. (a) moiré pattern (left) formed in 60°-aligned (or antiparallel) ${MoTe}_{2}$ and ${WSe}_{2}$ bilayers (right). $M M$ , $M X$ , and $X X$ ( $M = Mo, W$ ; $X = Se, Te$ ) are the high-symmetry stacking sites. The Wannier orbital of the two layers occupies the $M M$ and $X X$ sites, forming a honeycomb lattice. An out-of-plane electric field ( $E$ ) from ${MoTe}_{2}$ to ${WSe}_{2}$ induces the QAH effect. (b) Schematics of the topmost valence bands at the $K$ and $K^{'}$ valley from two layers. Arrows denote the out-of-plane spin alignment. In each layer, spin and valley are locked. In each valley, two bands have opposite spins. (c) Optical selection rules in monolayer TMDs. Attractive polaron, a bound state of the electron-hole excitation in the $K$ ( $K^{'}$ ) valley and hole excitations in the $K^{'}$ ( $K$ ) valley, couples exclusively to the $σ^{+}$ ( $σ^{-}$ ) excitation. When the holes occupy $K$ valley only, the $σ^{-}$ excitation dominates. The dashed line denotes the Fermi level. (d),(e) Two possible QAH ground states: valley polarized (d) and valley coherent (or spin polarized) (e), in which the spin polarization is antialigned and aligned in two layers, respectively.
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Figure 2
QAH effect and topological quantum phase transition at 1.6 K. (a) Hysteretic magnetic field dependence of $R_{x x}$ , $R_{x y}$ (left) and MCD in ${WSe}_{2}$ (right) with fixed $E \approx 0.6 93 V / nm$ and doping density of one hole per moiré unit cell. Quantized $R_{x y}$ at the value of $h / e^{2}$ (dashed lines) and vanishing $R_{x x}$ at zero magnetic field support the QAH effect. (b) Helicity-resolved reflectance contrast (RC) spectrum of the device in the charge neutral state (top) and the QAH state under zero magnetic field (middle). The two helicities are degenerate in the charge neutral state. The MCD spectrum (bottom) is extracted from the data in the QAH state. The low- and high-energy spectra are dominated by ${MoTe}_{2}$ and ${WSe}_{2}$ , respectively. $X^{0}$ , AP, RP denote the neutral exciton, attractive and repulsive polarons, respectively. (c) Electric-field dependence of $R_{x y}$ , $R_{x x}$ (top), absolute MCD in two layers (middle), and RC spectrum of ${WSe}_{2}$ (bottom), all under zero magnetic field. Vertical dashed line denotes the critical field $E_{c} \approx 0.6 87 V / nm$ for the topological transition from a Mott insulator to a QAH insulator. It also marks the onset of charge transfer from ${MoTe}_{2}$ to ${WSe}_{2}$ .
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Figure 3
Spontaneous spin alignment in the bilayer. (a) Magnetic-field dependence of the right-handed ( $σ^{-}$ , top) and left-handed ( $σ^{+}$ , bottom) reflectance contrast spectrum of ${MoTe}_{2}$ (left) and ${WSe}_{2}$ (right) of the bilayer in the QAH state at 1.6 K. The electric field is fixed at $0.693 V / nm$ . The two helicity-resolved spectra were measured together at each magnetic field while it was scanned from $- 8$ to 8 T. The doping density was adjusted at each field following the Streda relation to stay in the QAH state. The two layers have nearly identical magnetic-field dependence. (b) Magnetic-field dependent MCD spectra for ${MoTe}_{2}$ (left) and ${WSe}_{2}$ (right) extracted from the data in (a). The white dashed lines denote the maximum (absolute) value of the MCD in each layer.
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Figure 4
Signature of a canted spin texture. (a) Magnetic-field dependence of normalized MCD in each layer in the range of $\pm 8$ and $\pm 0.1 T$ (inset) at 1.6 K. The MCD is averaged over a narrow spectral range of 0.9 meV centered at the maximum of the attractive polaron feature [dashed lines in Fig. 3]. It is normalized by the value at 8 T in each layer. The MCD shows an abrupt change near zero field and saturates slowly with increasing field. In contrast, $R_{x y}$ (right-hand axis) is quantized at the value of $h / e^{2}$ (dashed lines) near zero magnetic field and does not depend on field. (b) Same as (a) at varying temperatures. All curves are normalized by MCD at 8 T and 1.6 K in each layer. The curves are vertically displaced for clarity. (c) Temperature dependence of the spontaneous MCD for ${MoTe}_{2}$ and ${WSe}_{2}$ (top). Both saturate below 2 K and vanish above 5–6 K. Bottom: temperature dependence of the spin (or magnetic) susceptibility in ${WSe}_{2}$ (symbols) above the magnetic ordering temperature. It is well described by the Curie-Weiss law, $χ^{- 1} \propto T - θ$ , with a Curie-Weiss temperature $θ \approx 5 K$ (red line).
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Physical Review X

Valley-Coherent Quantum Anomalous Hall State in AB-Stacked MoTe2/WSe2 Bilayers

Zui Tao, Bowen Shen, Shengwei Jiang, Tingxin Li, Lizhong Li, Liguo Ma, Wenjin Zhao, Jenny Hu, Kateryna Pistunova, Kenji Watanabe, Takashi Taniguchi, Tony F. Heinz, Kin Fai Mak, and Jie Shan

Phys. Rev. X 14, 011004 – Published 10 January 2024

See Viewpoint: Another Twist in the Understanding of Moiré Materials

Abstract

Physics Subject Headings (PhySH)

Viewpoint

Another Twist in the Understanding of Moiré Materials

Published 18 March 2024

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Valley-Coherent Quantum Anomalous Hall State in AB-Stacked ${MoTe}_{2} / {W S e}_{2}$ Bilayers