Confinement-Induced Chiral Edge Channel Interaction in Quantum Anomalous Hall Insulators

Ling-Jie Zhou, Ruobing Mei, Yi-Fan Zhao, Ruoxi Zhang, Deyi Zhuo, Zi-Jie Yan, Wei Yuan, Morteza Kayyalha, Moses H. W. Chan, Chao-Xing Liu, and Cui-Zu Chang

Phys. Rev. Lett. 130, 086201 – Published 21 February 2023

Abstract

In quantum anomalous Hall (QAH) insulators, the interior is insulating but electrons can travel with zero resistance along one-dimensional (1D) conducting paths known as chiral edge channels (CECs). These CECs have been predicted to be confined to the 1D edges and exponentially decay in the two-dimensional (2D) bulk. In this Letter, we present the results of a systematic study of QAH devices fashioned in a Hall bar geometry of different widths under gate voltages. At the charge neutral point, the QAH effect persists in a Hall bar device with a width of only $\sim 72 nm$ , implying the intrinsic decaying length of CECs is less than $\sim 36 nm$ . In the electron-doped regime, we find that the Hall resistance deviates quickly from the quantized value when the sample width is less than $1 μ m$ . Our theoretical calculations suggest that the wave function of CEC first decays exponentially and then shows a long tail due to disorder-induced bulk states. Therefore, the deviation from the quantized Hall resistance in narrow QAH samples originates from the interaction between two opposite CECs mediated by disorder-induced bulk states in QAH insulators, consistent with our experimental observations.

Received 17 July 2022
Revised 20 January 2023
Accepted 23 January 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.086201

Physics Subject Headings (PhySH)

Confinement Edge states Quantum anomalous Hall effect Quantum transport Topological insulators

Dilute magnetic topological insulators Topological materials

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ling-Jie Zhou ^1,*, Ruobing Mei^1,*, Yi-Fan Zhao^1,*, Ruoxi Zhang ¹, Deyi Zhuo¹, Zi-Jie Yan ¹, Wei Yuan ¹, Morteza Kayyalha^1,2, Moses H. W. Chan¹, Chao-Xing Liu^1,†, and Cui-Zu Chang ^1,‡

¹Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA
²Department of Electrical Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, USA

^*These authors contributed equally to this work.
^†Corresponding author. cxl56@psu.edu
^‡Corresponding author. cxc955@psu.edu

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 130, Iss. 8 — 24 February 2023

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
The QAH state in a device with $w \sim 72 nm$ . (a) Schematic of CECs. (b) The scanning electron microscope image. (c) $μ_{0} H$ dependence of $ρ_{x x}$ (red) and $ρ_{y x}$ (blue) measured at $V_{g} = V_{g}^{0}$ and $T = 25 mK$ . $ρ_{y x}$ greater than $h / e^{2}$ at certain magnetic fields might be related to the large contact resistance. (d) ( $V_{g} − V_{g}^{0}$ ) dependence of $ρ_{x x} (0)$ (red) and $ρ_{y x} (0)$ (blue) measured at $μ_{0} H = 0 T$ and $T = 25 mK$ .
Reuse & Permissions
Figure 2
The QAH state in devices with $300 nm \leq w \leq 10 μ m$ . (a)–(f) $μ_{0} H$ dependence of $ρ_{x x}$ (red) and $ρ_{y x}$ (blue) of the QAH devices with $w = 300 nm$ (a), $w = 500 nm$ (b), $w = 1 μ m$ (c), $w = 2 μ m$ (d), $w = 5 μ m$ (e), and $w = 10 μ m$ (f). All measurements are taken at $V_{g} = V_{g}^{0}$ and $T = 25 mK$ . The values of $V_{g}^{0}$ are $+ 4$ , $+ 6$ , $+ 8$ , $+ 8$ , $+ 11$ , and $+ 12 V$ for the $w = 300 nm$ , 500 nm, $1 μ m$ , $2 μ m$ , $5 μ m$ , and $10 μ m$ devices, respectively.
Reuse & Permissions
Figure 3
Evolution of the QAH state in devices with $300 nm \leq w \leq 10 μ m$ . (a)–(f) ( $V_{g} − V_{g}^{0}$ ) dependence of $ρ_{x x} (0)$ (red) and $ρ_{y x} (0)$ (blue) of the QAH devices with $w = 300 nm$ (a), $w = 500 nm$ (b), $w = 1 μ m$ (c), $w = 2 μ m$ (d), $w = 5 μ m$ (e), and $w = 10 μ m$ (f). All measurements are taken at $μ_{0} H = 0 T$ and $T = 25 mK$ after magnetic training. The values of $ρ_{y x} (0)$ and $ρ_{x x} (0)$ are extracted from the data point at $μ_{0} H = 0 T$ .
Reuse & Permissions
Figure 4
Confinement-induced CEC interaction at $V_{g} = V_{g}^{0}$ . (a),(b) $w$ dependence of $ρ_{y x} (0)$ [blue (a)] and $ρ_{x x} (0)$ [red (b)]. The square, circle, and triangle points are from the devices fabricated by electron-beam lithography, photolithography, and mechanical scratching, respectively. (c) The longitudinal electric field $E_{x}$ as a function of the dc excitation current $I_{dc}$ for the QAH devices with $w \leq 10 μ m$ . (d) The characteristic current $I_{0}$ as a function of $w$ .
Reuse & Permissions
Figure 5
Theoretical calculations of confinement-induced CEC interaction. (a)–(d) DOS of CEC as a function of the depth $y$ at $μ = 0 meV$ and disorder strength $V_{0} = 0 eV$ (a), $μ = 0 meV$ and $V_{0} = 0.0 5 eV$ (b), $μ = 4 meV$ and $V_{0} = 0 eV$ (c), and $μ = 4 meV$ and $V_{0} = 0.0 5 eV$ (d). Inset in (c): enlarged vertical axis range to show the nonzero residual DOS caused by bulk states. (e) Schematic of CEC interaction induced by the disorder-induced bulk states. (f) The schematic band structure of the QAH sample. The two CECs (red) do not directly couple with each other, but the bulk states (green) and disorder can mediate the CEC interaction and lead to a slow deviation from the well-quantized QAH effect. (g) The localization length $ξ$ as a function of $μ$ at $V_{0} = 1$ , 5, 10, and 15 meV, respectively.
Reuse & Permissions

Physical Review Letters