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Flat bands in twisted bilayer transition metal dichalcogenides


The crystal structure of a material creates a periodic potential that electrons move through giving rise to its electronic band structure. When two-dimensional materials are stacked, the resulting moiré pattern introduces an additional periodicity so that the twist angle between the layers becomes an extra degree of freedom for the resulting heterostructure. As this angle changes, the electronic band structure is modified leading to the possibility of flat bands with localized states and enhanced electronic correlations1,2,3,4,5,6. In transition metal dichalcogenides, flat bands have been theoretically predicted to occur for long moiré wavelengths over a range of twist angles around 0° and 60° (ref. 4) giving much wider versatility than magic-angle twisted bilayer graphene. Here, we show the existence of a flat band in the electronic structure of 3° and 57.5° twisted bilayer WSe2 samples using scanning tunnelling spectroscopy. Our direct spatial mapping of wavefunctions at the flat-band energy show that the localization of the flat bands is different for 3° and 57.5°, in agreement with first-principles density functional theory calculations4.

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Fig. 1: Stacking configurations of the 3° tWSe2 device.
Fig. 2: dI/dV spectra on the four high-symmetry points for the 3° tWSe2.
Fig. 3: Spatially resolved LDOS at different energies.
Fig. 4: Spatially dependent spectroscopy of the 57.5° tWSe2 device.

Data availability

Data that support the findings of this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.


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We thank E. Yu for a careful reading of the manuscript. The work at the University of Arizona was supported by the National Science Foundation under grants DMR-1708406 and EECS-1607911 and the Army Research Office under grant no. W911NF-18-1-0420. The work at the University of Texas was supported by the National Science Foundation grants EECS-1610008 and DMR-1720595, the Welch Foundation, and Semiconductor Research Corporation. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan and the CREST(JPMJCR15F3), JST. K.U. acknowledges support from the JSPS KAKENHI grant no. 25107004.

Author information

Authors and Affiliations



Z.Z. performed the STM experiments. Y.W. fabricated the samples for STM measurements. K.W. and T.T. provided hexagonal boron nitride crystals, and K.U. provided the WSe2 crystals. E.T. and B.J.L. conceived the experiments. Z.Z. and B.J.L. performed data analysis and wrote the manuscript with input from all co-authors.

Corresponding authors

Correspondence to Emanuel Tutuc or Brian J. LeRoy.

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Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Physics thanks Miguel Ugeda and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Stacking configuration of the 57.5° tWSe2 device.

a, Optical image of the 57.5° device. Blue and gray dashed lines highlight the hBN and bilayer graphene flakes respectively. Red dashed lines mark the tWSe2 region. b, Atomic-resolution STM topography on the 57.5° tWSe2 sample, probed at fixed bias voltage of Vbias = 3 V and current I = 100 pA. c, Illustration of the different stacking configurations: BSe/Se, BW/W and AB. For each configuration, the left panel shows the top view and the right panel shows the side view. The blue and cyan colors denote the W atoms, while pink and yellow denote the Se atoms in the two layers.

Extended Data Fig. 2 Filtering of the topography.

a, Atomic-resolution STM topography on the 3° tWSe2 sample, with a fixed bias voltage Vbias = −2.5 V and set current I = 100 pA. b, Fourier transform of panel a. c, Filtered Fourier transform, black area at the center indicates the components being removed. d, Topography image after the short-pass filter was applied, white dashed lines indicate the distance between nearest-neighbor AA sites in 3 different directions.

Extended Data Fig. 3 Local density of states maps at different energies for the 3° tWSe2 device.

a, Lowest energy band at Q in the conduction band. b, Second band at Q in the conduction band. c, Lowest band at K in the conduction band. d, Highest band at K in the valence band. e, second highest band at K in the valence band. None of these images show the hexagonal network as seen at the flat band energy, indicating that the wavefunction of the flat band is distinctively different from the ordinary wavefunctions that arise from the moiré pattern.

Extended Data Fig. 4 dI/dV spectra on the 4 high symmetry points for the 57.5° tWSe2.

a and c Constant height mode dI/dV vs. bias voltage for the valence band and conduction band respectively, acquired at I = 100 pA. b and d, Constant current mode dI/dV vs. bias voltage for the valence band and conduction band respectively, acquired at I = 50 pA.

Source data

Extended Data Fig. 5 Line cut dI/dV spectra for the 3° tWSe2 device.

a, Illustration of the line along where the dI/dV spectra was taken. b, Constant current dI/dV spectra line cut, acquired at I = 10 pA. The sharp peak around −1.1 V due to the presence of the flat band shows only a slight spatial variation within the BW/Se-Br-BSe/W region. In contrast, this sharp peak is almost completely missing on the AA sites, indicating that the flat band is localized on the BW/Se-Br-BSe/W region and away from the AA sites.

Supplementary information

Supplementary Information

Supplementary Figs. 1–7 and discussion sections 1–7.

Source data

Source Data Fig. 2

Spectroscopy Source Data for the 3° sample.

Source Data Extended Data Fig. 4

Spectroscopy Source Data for the 57.5° sample.

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Zhang, Z., Wang, Y., Watanabe, K. et al. Flat bands in twisted bilayer transition metal dichalcogenides. Nat. Phys. 16, 1093–1096 (2020).

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