Observation of $\mathrm{\ensuremath{\Gamma}}$-Valley Moir\'e Bands and Emergent Hexagonal Lattice in Twisted Transition Metal Dichalcogenides

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Observation of $Γ$ -Valley Moiré Bands and Emergent Hexagonal Lattice in Twisted Transition Metal Dichalcogenides

Ding Pei, Binbin Wang, Zishu Zhou, Zhihai He, Liheng An, Shanmei He, Cheng Chen, Yiwei Li, Liyang Wei, Aiji Liang, Jose Avila, Pavel Dudin, Viktor Kandyba, Alessio Giampietri, Mattia Cattelan, Alexei Barinov, Zhongkai Liu, Jianpeng Liu, Hongming Weng, Ning Wang, Jiamin Xue, and Yulin Chen

Phys. Rev. X 12, 021065 – Published 24 June 2022

Abstract

Twisted van der Waals heterostructures have recently been proposed as a condensed-matter platform for realizing controllable quantum models due to the low-energy moiré bands with specific charge distributions moiré superlattices. Here, combining angle-resolved photoemission spectroscopy with submicron spatial resolution ( $μ$ -ARPES) and scanning tunneling microscopy (STM), we performed a systematic investigation on the electronic structure of 5.1° twisted bilayer ${WSe}_{2}$ that hosts correlated insulating and zero-resistance states. Interestingly, contrary to one’s expectation, moiré bands were observed only at $Γ$ valley but not $K$ valley in $μ$ -ARPES measurements, and correspondingly, our STM measurements clearly identified the real-space honeycomb- and kagome-shaped charge distributions at the moiré length scale associated with the $Γ$ -valley moiré bands. These results not only reveal the unusual valley-dependent moiré-modified electronic structure in twisted transition metal dichalcogenides, but also highlight the $Γ$ -valley moiré bands as a promising platform for exploring strongly correlated physics in emergent honeycomb and kagome lattices at different energy scales.

Received 8 December 2021
Revised 23 March 2022
Accepted 23 May 2022

DOI:https://doi.org/10.1103/PhysRevX.12.021065

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)

Electronic structure

Transition metal dichalcogenides

Angle-resolved photoemission spectroscopy Scanning tunneling microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ding Pei ^1,2,9,*, Binbin Wang ^1,7,*, Zishu Zhou ^3,*, Zhihai He^4,8,*, Liheng An³, Shanmei He², Cheng Chen², Yiwei Li¹, Liyang Wei ¹, Aiji Liang¹, Jose Avila ⁵, Pavel Dudin ⁵, Viktor Kandyba⁶, Alessio Giampietri⁶, Mattia Cattelan⁶, Alexei Barinov⁶, Zhongkai Liu^1,9, Jianpeng Liu^1,9, Hongming Weng ^8,7,4, Ning Wang^3,†, Jiamin Xue ^1,‡, and Yulin Chen^2,1,9,§

¹School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
²Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
³Department of Physics, the Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
⁴Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
⁵Synchrotron SOLEIL, L’Orme des Merisiers, Saint Aubin-BP 48, 91192 Gif sur Yvette Cedex, France
⁶Elettra-Sincrotrone Trieste, Trieste, Basovizza 34149, Italy
⁷School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
⁸Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
⁹ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai 200031, China

^*These authors contributed equally to this work.
^†phwang@ust.hk
^‡xuejm@shanghaitech.edu.cn
^§yulin.chen@physics.ox.ac.uk

Popular Summary

A central feature in twisted 2D materials is the moiré superlattice—a periodic interference pattern caused by the mismatch between atomic layers. This leads to the emergence of moiré bands—the energy-momentum dispersion of electrons traveling in the superlattice—which can strongly modify original properties of the constituent layers in twisted 2D materials. For example, moiré bands can introduce zero resistance into twisted transition metal dichalcogenides (TMDs), although the single layer of a TMD is a large-gap semiconductor. In this work, we directly visualize moiré bands in twisted TMDs.

In momentum space, moiré bands with near-zero momentum (around $Γ$ valley) appear as replica bands (to the original bands of constituent layers) with a momentum shift. In position space, these moiré bands show honeycomb- and kagome-shaped charge distributions at nanometer scale. These discoveries identify $Γ$ -valley moiré bands in twisted TMDs as a versatile platform to simulate multiple quantum models.

Curiously, we find no sign of moiré bands with large momentum (around $K$ valley), which is believed as the major contributor to zero-resistance states. This unexpected result calls for further experiments and a revisit of current theoretical understanding of twisted TMDs.

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Vol. 12, Iss. 2 — April - June 2022

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Figure 1
Device design and experiment layout. (a) Schematic illustration of the device design and the experiment layout. From bottom to top, the red, light blue, and purple sheets stand for ${SiO}_{2} / Si$ , $h − BN$ , and graphite substrates, respectively, and the atomic model stands for a bilayer ${WSe}_{2}$ with a twist angle ( $θ$ ). For ARPES measurements, photoelectrons are collected by a hemisphere analyzer; for STM measurements, tunneling electrons are tuned by the current ( $I$ ) and voltage ( $V$ ) sources and collected by the STM tip. (b) Optical image of 5.1° TB ${WSe}_{2}$ device. Dashed lines of red and black mark boundaries of top and bottom layer ${WSe}_{2}$ , respectively. ${SiO}_{2} / Si$ , $h − BN$ , and graphite substrates appear in the same colors as shown in the illustration. The included angle of upper boundaries of top and bottom layers is the twist angle, $θ \approx 5.1 °$ . (c) STM topography, acquired at fixed bias voltage $V_{bias} = - 1.39 V$ and current $I = 90 pA$ , showing the moiré pattern with a periodicity of $λ \approx 3.7 nm$ . The inset presents the atomic structure of TB ${WSe}_{2}$ .
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Figure 2
ARPES measurement on TB ${WSe}_{2}$ . (a) Scanning photoemission microscopy (SPEM) of TB ${WSe}_{2}$ device. The SPEM image is generated from real-space mapping of the valence band spectra. Dashed lines of red, black, and green mark boundaries of top, bottom layer ${WSe}_{2}$ , and Au contact, respectively. The blue square marks the photon beam position during ARPES measurements. (b) Equal energy contour at binding energy $E_{B} = 1.2 eV$ measured at 100 eV, overlapped with BZs of the top (red) and bottom (black) layer ${WSe}_{2}$ . The subscripts $t$ and $b$ of $K$ valleys stand for the top and bottom layer, respectively. The bare $Γ$ -valley pocket (of main band $Γ_{1}$ ) is indicated by the black arrow. moiré bands (MBs) are indicated by the orange arrow. (c) Band dispersion across $K_{t}$ point measured at 100 eV. (d) Band dispersion across $K_{t}$ point measured at 74 eV. (e) Band dispersion across $Γ$ points measured at 100 eV. (f) Band dispersion along $k_{y}$ at $k_{x} = - 0.3 Å^{- 1}$ (around $Γ$ valley) measured at 100 eV. In (c)–(f), the inset red hexagons are the BZs of top layer ${WSe}_{2}$ , showing the sample orientation, and red arrows present the directions of dispersions with respect to BZs. In (e) and (f), $Γ_{1}$ and $Γ_{2}$ stand for two main bands of bilayer ${WSe}_{2}$ , MBs are indicated by orange arrows, $δ k$ is the momentum spacing between MBs and $Γ_{1}$ .
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Figure 3
STM measurement on TB ${WSe}_{2}$ . (a) Definition of high-symmetry sites in TB ${WSe}_{2}$ superlattice. Here, AA (indicated by the red point) means eclipsed stacking sites with W atoms over W atoms, BR (indicated by the green point) means the bridge that connects neighboring AA sites, and B (indicated by the blue point) stands for Bernal stacking, including two inversed configurations with W atom over Se atom ( $B_{W / Se}$ ) or Se atom over W atom ( $B_{Se / W}$ ). The white arrow indicates the direction of $d I / d V$ spectra shown in (b). (b) Left: $d I / d V$ spectra measured in constant height mode (CHSTS) along AA-B-BR-B-AA direction. The positions of AA, B, BR sites are indicated by arrows of corresponding colors. Right: representative $d I / d V$ curves on AA (red), B (blue), and BR (green) sites. The peak positions in AA ( $V_{4}$ ), B ( $V_{2}$ ), and BR $(V_{1}, V_{3})$ curves are marked by dashed lines of corresponding colors. (c) $d I / d V$ curves measured in constant current mode (CCSTS) on AA, B, and BR sites. Black arrows indicate $d I / d V$ signal contributed by $Γ$ and $K$ valleys, respectively. (d)–(g) LDOS maps (in CH mode) corresponding to the peak positions in the AA ( $V_{4}$ ), B ( $V_{2}$ ), and BR $(V_{1}, V_{3})$ curves, respectively. During the LDOS mapping, the tip height was adjusted at $V_{bias} = - 1.6 V$ with $I = 170 pA$ .
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Figure 4
Calculation on TB ${WSe}_{2}$ . (a) Original BZs of a bilayer ${WSe}_{2}$ with a twist angle $θ = 5.1 °$ and resulting mini BZ of TB ${WSe}_{2}$ superlattices. The BZs of top layer, bottom layer ${WSe}_{2}$ , and the mini BZ of TB ${WSe}_{2}$ are illustrated in red, black, and purple, respectively. High-symmetry points are labeled on BZs; the subscripts $t$ and $b$ stand for the top and bottom layer, respectively. (b) Left: first-principles-calculated moiré bands (MBs) of 5.1° TB ${WSe}_{2}$ presented in the mini BZ. The top three $Γ$ -valley MBs are highlighted in red. Right: calculated charge distributions at energies $e_{1}$ and $e_{2}$ (indicated by red arrows in the left-hand part), showing honeycomb ( $e_{1}$ ) and kagome patterns ( $e_{2}$ ). (c) A simplified example illustrating the band unfolding in 1D (more discussion of 2D case can be found in SM [24]). Blue and red lines show the unfolded and folded bands. (d) Left: tight-binding-calculated MBs of 5.1° TB ${WSe}_{2}$ presented in the mini BZ. The top three $Γ$ -valley MBs are highlighted in red. Right: the unfolded MBs around $Γ$ valley (along $K − Γ − M$ direction in the original BZ). The equivalent positions of $e_{1}$ and $e_{2}$ are indicated by red arrows and dashed lines.
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Physical Review X

Observation of Γ-Valley Moiré Bands and Emergent Hexagonal Lattice in Twisted Transition Metal Dichalcogenides

Ding Pei, Binbin Wang, Zishu Zhou, Zhihai He, Liheng An, Shanmei He, Cheng Chen, Yiwei Li, Liyang Wei, Aiji Liang, Jose Avila, Pavel Dudin, Viktor Kandyba, Alessio Giampietri, Mattia Cattelan, Alexei Barinov, Zhongkai Liu, Jianpeng Liu, Hongming Weng, Ning Wang, Jiamin Xue, and Yulin Chen

Phys. Rev. X 12, 021065 – Published 24 June 2022

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Observation of $Γ$ -Valley Moiré Bands and Emergent Hexagonal Lattice in Twisted Transition Metal Dichalcogenides