Tunable Sample-Wide Electronic Kagome Lattice in Low-Angle Twisted Bilayer Graphene

Qi Zheng, Chen-Yue Hao, Xiao-Feng Zhou, Ya-Xin Zhao, Jia-Qi He, and Lin He

Phys. Rev. Lett. 129, 076803 – Published 11 August 2022

Abstract

Overlaying two graphene layers with a small twist angle $θ$ can create a moiré superlattice to realize exotic phenomena that are entirely absent in a graphene monolayer. A representative example is the predicted formation of localized pseudo-Landau levels (PLLs) with kagome lattice in tiny-angle twisted bilayer graphene (TBG) with $θ < 0.3 °$ when the graphene layers are subjected to different electrostatic potentials. However, this was shown only for the model of rigidly rotated TBG, which is not realized in reality due to an interfacial structural reconstruction. It is believed that the interfacial structural reconstruction strongly inhibits the formation of the PLLs. Here, we systematically study electronic properties of the TBG with $0.075 ° \leq θ < 1.2 °$ and demonstrate, unexpectedly, that the PLLs are quite robust for all the studied TBG. The structural reconstruction suppresses the formation of the emergent kagome lattice in the tiny-angle TBG. However, for the TBG around the magic angle, the sample-wide electronic kagome lattices with tunable lattice constants are directly imaged by using a scanning tunneling microscope. Our observations open a new direction to explore exotic correlated phases in moiré systems.

Received 4 April 2022
Accepted 20 July 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.076803

Physics Subject Headings (PhySH)

Graphene Kagome lattice Twisted bilayer graphene

Scanning tunneling microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Qi Zheng ^*, Chen-Yue Hao^*, Xiao-Feng Zhou, Ya-Xin Zhao, Jia-Qi He, and Lin He ^†

Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing 100875, People’s Republic of China

^*These authors contributed equally to this work.
^†Corresponding author. helin@bnu.edu.cn

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 129, Iss. 7 — 12 August 2022

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Kagome lattice embedded in TBG. (a) Schematic diagram of destructive interference in the kagome lattice. The blue dotted lines frame the region of an elementary cell, which consists of three lattice points (marked by dark green, green, and brown). The red, yellow, and purple arrows represent electron wave vectors in three different directions. The destructive interference of wave vectors at the brown lattice points results in the strongly localization of electrons in the black dotted circle. (b) Structural model of a TGB with rotation angle $θ$ . The $A A$ , $A B / B A$ , and DW stacking sites are marked by red, yellow, and purple circles, respectively. The DW sites exhibit the kagome lattice.
Reuse & Permissions
Figure 2
STM and STS measurements of tiny-angle TBG on $h$ -BN. (a) STM image of a 0.176° TBG measured by using the W tip. STM image ( $V_{bias} = 500 mV$ , $I = 200 pA$ ). Schematic bands along with the Fermi level (the dashed line) are plotted. (b) Representative STS spectra recorded in different stacking regions in (a). The charge neutrality point (CNP) of the TBG is $E_{N} = - 10 meV$ . (c),(d) Energy-fixed $d I / d V$ maps at $E = 60$ and $- 10 meV$ ( $I = 150 pA$ ). (e) STM image of a 0.12° TBG measured by using the Au-coated W tip. Schematic bands along with the Fermi level (the dashed line) and the CNP of the TBG (the solid purple line) are plotted. The large work function difference between gold and graphene generates an interlayer electric field on the graphene below the tip. STM image ( $V_{bias} = 500 mV$ , $I = 150 pA$ ). (f) Representative STS spectra recorded in different stacking regions in (e). The blue rectangle denotes the band gap in $A B$ -stacking sites. (g),(h) Energy-fixed $d I / d V$ maps at $E = - 40$ and 130 meV.
Reuse & Permissions
Figure 3
Electronic kagome lattice of the PLL states at the DWs in the low-angle TBG by using the Au-coated W tip. (a) $d I / d V$ spectra taken at $A A$ -stacked regions of TBG with different rotation angles. At $θ \sim 1.0 7 °$ , only a single peak is observed in the flat band (FB) energy region, whereas there are two peaks at $θ \sim 0.9 8 °$ and 0.88°. (b) $d I / d V$ spectra taken at the DW regions of the TBG with different rotation angles. DW states can be observed in all the studied TBG. (c) STM images of the low-angle TBG with different rotation angles ( $V_{bias} = 500 mV$ and $I = 100 pA$ ). The bright regions in the red circles represent $A A$ -stacking sites, and the purple circles represent the DW regions. (d) Energy-fixed $d I / d V$ maps at $V_{bias} = 380 mV$ in the TBG. Electronic kagome lattices can be clearly imaged in all three TBG.
Reuse & Permissions
Figure 4
Evolution of the DW states and the flat bands in $A A$ regions as a function of the twist angle. (a) The measured energies of the PLL (blue dots) at the DW regions as a function of the rotation angles. The dashed curves are the theoretical results extracted from Fig. 2 in Ref. [11] with the fixed interlayer electric field $U = 0.0 5 eV$ (green), $U = 0.1 eV$ (red), $U = 0.1 5 eV$ (black), and $U = 0.2 eV$ (purple). (b) The measured FWHM of the flat bands at the $A A$ -stacked regions as a function of the rotation angles. The red dashed curve is the calculated bandwidth of the low-energy flat bands in the TBG. The FWHM of the DW states in the spectra was used to estimate the error bar in (a). The error bar in (b) is the fitted standard deviation.
Reuse & Permissions

Physical Review Letters