Distinct Quantum Anomalous Hall Ground States Induced by Magnetic Disorders

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Distinct Quantum Anomalous Hall Ground States Induced by Magnetic Disorders

Chang Liu, Yunbo Ou, Yang Feng, Gaoyuan Jiang, Weixiong Wu, Shaorui Li, Zijia Cheng, Ke He, Xucun Ma, Qikun Xue, and Yayu Wang

Phys. Rev. X 10, 041063 – Published 30 December 2020

Abstract

The quantum anomalous Hall (QAH) effect in a magnetic topological insulator (TI) represents a new state of matter originating from the interplay between topology and magnetism. The defining characteristics of the QAH ground state are the quantized Hall resistivity ( $ρ_{yx}$ ) and vanishing longitudinal resistivity ( $ρ_{xx}$ ) in the absence of an external magnetic field. A fundamental question concerning the QAH effect is whether it is merely a zero-magnetic-field quantum Hall (QH) effect or if it can host unique quantum phases and phase transitions that are unavailable elsewhere. The most dramatic departure of the QAH systems from other QH systems lies in the magnetic disorders that induce spatially random magnetization. Because disorder and magnetism play pivotal roles in the phase diagram of two-dimensional electron systems, the high degree of magnetic disorders in QAH systems may create novel phases and quantum critical phenomena. In this work, we perform systematic transport studies of a series of magnetic TIs with varied strength of magnetic disorders. We find that the ground state can be categorized into two distinct classes: the QAH phase and the anomalous Hall (AH) insulator phase, as the zero-magnetic-field counterparts of the QH liquid and Hall insulator phases in the QH systems. In the low-disorder limit of the QAH phase, we observe a universal quantized longitudinal resistance $ρ_{xx} = h / e^{2}$ at the coercive field. In the AH insulator regime, we find that a magnetic field can drive it to the QAH phase through a quantum critical point with scaling behaviors that are distinct from those in the QH phase transition. We propose that the transmission between chiral edge states at domain boundaries, tunable by magnetic disorder and magnetic fields, is the key for determining the QAH ground state.

Received 24 March 2020
Accepted 29 October 2020

DOI:https://doi.org/10.1103/PhysRevX.10.041063

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)

Quantum anomalous Hall effect

Topological insulators

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Chang Liu ^1,2,*, Yunbo Ou^1,*, Yang Feng¹, Gaoyuan Jiang¹, Weixiong Wu¹, Shaorui Li¹, Zijia Cheng ¹, Ke He^1,2,3,†, Xucun Ma^1,3, Qikun Xue^1,2,3, and Yayu Wang ^1,3,‡

¹State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People’s Republic of China
²Beijing Academy of Quantum Information Sciences, Beijing 100193, People’s Republic of China
³Frontier Science Center for Quantum Information, Beijing 100084, People’s Republic of China

^*These authors contributed equally to this work.
^†kehe@tsinghua.edu.cn
^‡yayuwang@tsinghua.edu.cn

Popular Summary

Emerging quantum materials that offer the potential for novel electronics rely in part on the quantum anomalous Hall effect, in which intrinsic current flow produces a small voltage. This leads to exotic behavior such as the flow of electrical current without resistance along the edge of the material. Here, we present systematic measurements of 82 samples exhibiting the quantum anomalous Hall effect and find two distinct ground states that have never been suspected before, thus providing insight into this effect’s fundamental nature.

The quantum anomalous Hall effect is “anomalous” because it arises in the absence of an external magnetic field, unlike its counterpart known simply as the quantum Hall effect. One fundamental question concerning the anomalous effect is whether it is a special case of its counterpart or a unique phase of quantum matter. The most dramatic difference between these two effects is the presence of strong magnetic disorder in the anomalous version.

To investigate this further, we study charge transport in magnetic topological insulators—exotic materials known to host the quantum anomalous Hall effect—with a range of magnetic disorders. We find that the ground state can be categorized into two distinct classes, depending on the strength of magnetic disorder. In the low-disorder limit of the quantum anomalous Hall phase, we observe a quantized longitudinal resistance at the domain flipping regime. Whereas in the high-disorder anomalous Hall insulator regime, we find that a magnetic field can drive it back to the quantum anomalous Hall phase through a quantum critical point.

Our work indicates that the quantum anomalous Hall effect exhibits rich physics unique to itself. These systems, therefore, not only provide a new platform for building exotic phases but also inspire more rigorous theoretical studies regarding quantum phase transitions.

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Vol. 10, Iss. 4 — October - December 2020

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Images

Figure 1
Transport properties of five representative magnetic TIs. Magnetic-field-dependent $ρ_{yx}$ (upper panel) and $ρ_{xx}$ (lower panel) measured at varied $T s$ for (a) #S1, (b) #S2, (c) #S3, (d) #S4, and (e) #S5. All the measurements were performed when $V_{g}$ was tuned to the CNP regime. All five samples show similar Hall traces, although the ${ρ_{yx}}^{0}$ value decreases from $0.96 h / e^{2}$ in sample #S1 to $0.56 h / e^{2}$ in sample #S5. The $ρ_{xx}$ values increase from samples #S1 to #S5, indicating the increase of disorder. (f,g) Extracted $T$ -dependent ${ρ_{xx}}^{0}$ and ${ρ_{xx}}^{H c}$ for the five samples. (h) Evolution of ${ρ_{xx}}^{H c}$ as ${ρ_{xx}}^{0}$ at different $T s$ in the five samples.
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Figure 2
QAH and AH insulator behaviors in more samples. (a,b) Magnetic-field-dependent $ρ_{yx}$ and $ρ_{xx}$ in six QAH samples (#S6 to #S11) and five AH insulator samples (#S12 to #16). All the data were measured at $T = 1.6 K$ . (c) Experimental phase diagram summarized from the transport data of 16 QAH samples. The error bars result from the uncertainty of the geometrical size of the devices. The blue horizontal dashed line marks the universal quantum resistance of ${ρ_{xx}}^{H c}$ in the low-disorder regime of the QAH phase. The vertical black dashed line at ${ρ_{xx}}^{0} \sim 2 h / e^{2}$ marks the phase boundary between the QAH phase and the AH insulator phase.
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Figure 3
Low- $T$ transport properties of two representative QAH samples. (a,b) Magnetic-field-dependent $ρ_{xx}$ and $ρ_{yx}$ of a QAH sample (#S6) and an AH insulator sample (#S13) at low $T s$ with $V_{g}$ tuned to the CNP. (c,d) Extracted $T$ -dependent data of ${ρ_{xx}}^{0}$ (red) and ${ρ_{yx}}^{0}$ (blue) for samples #S6 and #S13, respectively. In both samples, ${ρ_{yx}}^{0}$ approaches the $h / e^{2}$ at low $T$ , but ${ρ_{xx}}^{0}$ exhibits the opposite $T$ dependence.
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Figure 4
Magnetic-field-driven quantum phase transition between the QAH phase and the AH insulator phase. (a) Magnetic-field-dependent $ρ_{xx}$ in the AH insulator sample (#S13) measured at varied $T s$ . (b) $T$ -dependent $ρ_{xx}$ extracted from panel (a) at different magnetic fields. (c) Scaling analysis of $ρ_{xx}$ in the vicinity of the QCP as a function of $(H − H_{T}) / T^{κ}$ . All the curves collapse together for $κ \sim 0.31$ .
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Figure 5
Schematic illustrations of the chiral-edge-state transmission picture. (a) The hopping transmission between two neighboring chiral edge states in an AH insulator sample at zero field. The blue puddles represent the out-of-plane magnetized domains, and the red halos represent the chiral edge states at domain boundaries. The grey region represents the area without out-of-plane magnetic order. The lower panel depicts the spatial distribution of chiral edge states. (b) Ohmic transmission in a QAH sample when neighboring magnetic domains are in close proximity to each other. (c) Transmission between two edge states with opposite chirality in a QAH sample at $H_{C}$ , when the neighboring domains have opposite magnetization. The numbers on the edges denote the chemical potential at different sections of the boundaries.
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