Intrinsic Nonlinear Hall Effect and Gate-Switchable Berry Curvature Sliding in Twisted Bilayer Graphene

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Intrinsic Nonlinear Hall Effect and Gate-Switchable Berry Curvature Sliding in Twisted Bilayer Graphene

Meizhen Huang, Zefei Wu, Xu Zhang, Xuemeng Feng, Zishu Zhou, Shi Wang, Yong Chen, Chun Cheng, Kai Sun, Zi Yang Meng, and Ning Wang

Phys. Rev. Lett. 131, 066301 – Published 11 August 2023

Abstract

Though the observation of the quantum anomalous Hall effect and nonlocal transport response reveals nontrivial band topology governed by the Berry curvature in twisted bilayer graphene, some recent works reported nonlinear Hall signals in graphene superlattices that are caused by the extrinsic disorder scattering rather than the intrinsic Berry curvature dipole moment. In this Letter, we report a Berry curvature dipole induced intrinsic nonlinear Hall effect in high-quality twisted bilayer graphene devices. We also find that the application of the displacement field substantially changes the direction and amplitude of the nonlinear Hall voltages, as a result of a field-induced sliding of the Berry curvature hotspots. Our Letter not only proves that the Berry curvature dipole could play a dominant role in generating the intrinsic nonlinear Hall signal in graphene superlattices with low disorder densities, but also demonstrates twisted bilayer graphene to be a sensitive and fine-tunable platform for second harmonic generation and rectification.

Received 23 December 2022
Revised 14 April 2023
Accepted 26 June 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.066301

Physics Subject Headings (PhySH)

Hall effect Transport phenomena Twistronics

Twisted bilayer graphene

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Meizhen Huang^1,*, Zefei Wu^1,*,†,§, Xu Zhang ^2,*, Xuemeng Feng¹, Zishu Zhou ¹, Shi Wang¹, Yong Chen^1,3, Chun Cheng³, Kai Sun⁴, Zi Yang Meng ^2,‡, and Ning Wang ^1,∥

¹Department of Physics and Center for Quantum Materials, The Hong Kong University of Science and Technology, Hong Kong, China
²Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Hong Kong, China
³Department of Materials Science and Engineering, Southern University of Science and Technology, Shenzhen, China
⁴Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA

^*These authors contributed equally to this work.
^†Corresponding author. zefei.wu@manchester.ac.uk
^‡Corresponding author. zymeng@hku.hk
^∥Corresponding author. phwang@ust.hk
^§Present address: Department of Physics and Astronomy and National Graphene Institute, University of Manchester, Manchester M13 9PL, United Kingdom.

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Vol. 131, Iss. 6 — 11 August 2023

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Images

Figure 1
Basic characterization of the TBG device. (a) Schematic structure of the 1.30° TBG device. The carrier density $n$ and the displacement field $D$ are controlled by the top and bottom gates with gate voltage $V_{tg}$ and $V_{bg}$ , respectively. (b) The four-probe measurement scheme. Here, we measure the longitudinal voltage $V_{xx}$ and Hall voltage $V_{xy}$ in the presence of an ac longitudinal current $I^{ω}$ . (c) The longitudinal resistance $R_{xx} = V_{xx} / I^{ω}$ (upper panel) and the carrier density measured via the Hall effect $n_{H}$ (middle panel) as functions of $υ$ and $V_{bg}$ ( $V_{tg} = 0 V$ ). The vertical dashed lines denote the CNP and fully filled moiré bands. Bottom panel: The second harmonic Hall voltage $V_{⊥}^{2 ω}$ as a function of filling factor $υ$ measured at $I^{ω} = 100 nA$ and $T = 1.5 K$ .
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Figure 2
Electric field tunable nonlinear Hall effect. (a) Filling and displacement field mapping of $V_{⊥}^{2 ω}$ measured at $T = 1.5 K$ . Dashed lines marked with $p$ and $n$ indicate $υ = - 1.5$ and $υ = + 1$ , respectively. Dash dotted lines marked with 1, 2, and 3 indicate three different fields: $D = + 0.4, 0, - 0.4 V / nm$ . Their intersection points are named as shown in the figure. (b) $V_{⊥}^{2 ω}$ versus $D$ measured at $υ = - 1.5$ at $I^{ω} = 100 nA$ . (c) $V_{⊥}^{2 ω}$ versus $I^{ω}$ at various displacement fields at $υ = - 1.5$ . Dots are the experimental data and the solid lines are parabolic fittings. (d),(e) Same as (b) and (c) for $υ = + 1$ .
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Figure 3
Sliding of the Berry curvature hotspot. (a) $Λ$ as a function of $υ$ and $D$ calculated by using the Bistritzer-MacDonald model with a strain strength of 0.3%. (b) Calculated band structure of the moiré bands near charge neutrality with $D = + 0.4$ , 0, and $- 0.4 V / nm$ . The color represents the value of $Ω$ . The parallelogram marks the reciprocal lattice (high symmetry points are labeled in Supplemental Material, Fig. 9). (c) The distribution of the product of the Berry curvature $Ω$ and the slope of the band distribution $(\partial E / \partial k)$ within the reciprocal lattice at the energies marked by the dashed parallelograms in (b) at six representative points in (a). The zero-temperature dipole moment can be calculated by integrating $Ω (\partial E / \partial k)$ at the Fermi level in the first moiré Brillouin zone.
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Figure 4
Phase diagram of the NHE. The color marks the difference between the Berry curvature dipole and the effective dipole of the scattering mechanism $Δ_{Dipole - scattering}$ . The dashed line represents the position where the Berry curvature dipole and the scattering contribute equally to the nonlinear Hall signal. The red (blue) area represents the dipole (scattering) dominated area. The strain strength is the total uniaxial strain used in theoretical calculation. The effective disorder is from screened Coulomb potential scatterer.
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