Experimental evidence for orbital magnetic moments generated by moir\'e-scale current loops in twisted bilayer graphene

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Experimental evidence for orbital magnetic moments generated by moiré-scale current loops in twisted bilayer graphene

Si-Yu Li, Yu Zhang, Ya-Ning Ren, Jianpeng Liu, Xi Dai, and Lin He

Phys. Rev. B 102, 121406(R) – Published 18 September 2020

Abstract

Electron-electron $(e − e)$ interactions in the twisted bilayer graphene (TBG) near the magic angle ∼1.1° can lift the valley degeneracy, allowing for the realization of orbital magnetism and topological phases. However, direct measurement of the orbital-based magnetism in the TBG is still lacking up to now. Here we report evidence for orbital magnetic moment generated by the moiré-scale current loops in a TBG with a twist angle $θ \sim 1 . 68^{\circ}$ . The valley degeneracy of the 1.68° TBG is removed by $e − e$ interactions when its low-energy Van Hove singularity (VHS) is nearly half filled. A large and linear response of the valley splitting to magnetic fields is observed, which we interpret as arising from the coupling to the large orbital magnetic moment induced by chiral current loops circulating in the moiré pattern. According to our experiment, the orbital magnetic moment is about $10.7 μ_{B}$ per moiré supercell. Our result paves the way to explore magnetism that is purely orbital in a slightly twisted graphene system.

Received 31 May 2020
Revised 1 September 2020
Accepted 2 September 2020

DOI:https://doi.org/10.1103/PhysRevB.102.121406

Physics Subject Headings (PhySH)

Graphene

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Si-Yu Li^1,2, Yu Zhang², Ya-Ning Ren², Jianpeng Liu^3,4,*, Xi Dai⁴, and Lin He ^2,†

¹Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, College of Materials Science and Engineering, Hunan University, Changsha 410082, People's Republic of China
²Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China
³School of Physical Science and Technology, ShanghaiTech University, Shanghai 200031, China
⁴Department of Physics, Hong Kong University of Science and Technology, Kowloon, Hong Kong, China

^*Corresponding author: liujp@shanghaitech.edu.cn
^†Corresponding author: helin@bnu.edu.cn

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Vol. 102, Iss. 12 — 15 September 2020

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Figure 1
(a) A STM image ( $V_{sample} = 500 mV$ and $I = 0.3 nA$ ) of multilayer graphene on Rh, which exhibits two series of moiré patterns with different periods. The large-period scale ( $L_{1}$ , $L_{2}$ , $L_{3}$ ) and the short-period scale D are indicated in the STM image. The inset shows a fast Fourier transform image of the moiré patterns. (b)–(d) Atomic-resolved STM images taken from different regions of the large-period moiré pattern. (e) Schematic structure of the topmost twisted trilayer graphene. (f) dI/dV spectra taken from the large-period moiré pattern, with the setpoint conditions $V_{sample} = 700 mV$ and $I = 0.4 n A$ when taking the STS measurement. The position of Fermi level is marked. The low-energy VHSs in the AA-stacked region are completely empty. There is NDC between the VHSs and the remote bands.
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Figure 2
(a) and (b) High-resolution dI/dV spectra taken from the AA-stacked region of the 1.68° TBG with different doping. In panel (a), all the VHSs are unfilled and have fourfold spin and valley degeneracy. In panel (b), the left two VHSs are half filled and split into four peaks because the valley degeneracy is lifted (the setpoint conditions of the STS measurement: $V_{sample} = 600 mV$ and $I = 0.5 nA$ ). The valley splitting $Δ E$ is defined in panel (b). (c) and (d) The calculated band structures and corresponding DOS of the K valley in the 1.68° TBG supported by Bernal-stacked bilayer graphene. The twist angle between the second layer and the third layer is 8.4°. (e) and (f) The band structures and corresponding DOS of the 1.68° TBG with including the staggered sublattice potential.
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Figure 3
(a) and (b) dI/dV spectra taken from the AA-stacked regions of the 1.68° TBG with different dopings as a function of magnetic fields. The positions of Fermi level are marked. The setpoint conditions of the STS measurement: $V_{sample} = 600 mV$ , $I = 0.5 nA$ for panel (a), and $V_{sample} = 500 mV$ , $I = 0.5 nA$ for panel (b). (c) Summarizing the splitting of the half-filled VHS in panel (b) as a function of magnetic fields. The blue dashed line marks the linear fitting between the valley splitting and the magnetic fields. The data in panel (c) are the average results by measuring several different dI/dV spectra in each magnetic field. The error bars reflect the standard error of the data.
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Figure 4
(a) The real-space distribution of the current density (black arrows) and the current-induced magnetic field (color coding) within the moiré supercell of the 1.68° TBG. (b) The evolution of the valley-resolved DOS of the 1.68° TBG with including the staggered sublattice potential under different vertical magnetic fields. Coulomb interactions have been included, and are treated within Hartree-Fock approximations at −1/2 filling of the VHS. (c) Linear fitting of the correlated gaps vs the magnetic fields. The slope determines the effective $g$ factor from the orbital magnetic moment.
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Physical Review B

covering condensed matter and materials physics

Experimental evidence for orbital magnetic moments generated by moiré-scale current loops in twisted bilayer graphene

Si-Yu Li, Yu Zhang, Ya-Ning Ren, Jianpeng Liu, Xi Dai, and Lin He

Phys. Rev. B 102, 121406(R) – Published 18 September 2020

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Physical Review B

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Experimental evidence for orbital magnetic moments generated by moiré-scale current loops in twisted bilayer graphene

Si-Yu Li, Yu Zhang, Ya-Ning Ren, Jianpeng Liu, Xi Dai, and Lin He

Phys. Rev. B 102, 121406(R) – Published 18 September 2020

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