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Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene

Abstract

Bilayer graphene can be modified by rotating (twisting) one layer with respect to the other. The interlayer twist gives rise to a moiré superlattice that affects the electronic motion and alters the band structure1,2,3,4. Near a ‘magic angle’ of twist2,4, where the emergence of a flat band causes the charge carriers to slow down3, correlated electronic phases including Mott-like insulators and superconductors were recently discovered5,6,7,8 by using electronic transport. These measurements revealed an intriguing similarity between magic-angle twisted bilayer graphene and high-temperature superconductors, which spurred intensive research into the underlying physical mechanism9,10,11,12,13,14. Essential clues to this puzzle, such as the symmetry and spatial distribution of the spectral function, can be accessed through scanning tunnelling spectroscopy. Here we use scanning tunnelling microscopy and spectroscopy to visualize the local density of states and charge distribution in magic-angle twisted bilayer graphene. Doping the sample to partially fill the flat band, we observe a pseudogap phase accompanied by a global stripe charge order that breaks the rotational symmetry of the moiré superlattice. Both the pseudogap and the stripe charge order disappear when the band is either empty or full. The close resemblance to similar observations in high-temperature superconductors15,16,17,18,19,20,21 provides new evidence of a deeper link underlying the phenomenology of these systems.

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Fig. 1: STM/STS near the magic angle.
Fig. 2: Doping dependence of dI/dV spectra.
Fig. 3: Spatial charge modulation in the correlated phase.
Fig. 4: Global stripe charge order.

Data availability

The data that support the findings of this study are available from the corresponding authors on reasonable request.

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Acknowledgements

We acknowledge support from NSF-DMR 1708158 (Y.J.), DOE-FG02-99ER45742 (E.Y.A. and J.M.), National Key R&D Program of China (grant number 2018YFA0305800; J.M.), NSF-DMR 1709229 (K.H.). We thank R. Fernandes and Z. Bi for stimulating discussions.

Author information

Affiliations

Authors

Contributions

Y.J. and J.M. performed STM experiments. Y.J., J.M. and E.Y.A. performed data analysis and wrote the paper with input from all authors. K.H. provided calculations. X.L. fabricated the devices. K.W. and T.T. provided hexagonal boron nitride. E.Y.A. supervised the project.

Corresponding authors

Correspondence to Jinhai Mao or Eva Y. Andrei.

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Competing interests

The authors declare no competing interests.

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

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

Extended data figures and tables

Extended Data Fig. 1 Atomic-resolution STM of AB and BA regions in TBG near the magic angle.

a, Large-area STM topography, 8.9 nm × 8.9 nm, taken at Vb = −200 mV, I = 30 pA. b, c, Magnified views of the green and blue boxed areas, respectively, in a. A schematic drawing of the graphene lattice is superposed on the STM topography to highlight the sublattice polarization due to the AB (BA) stacking.

Extended Data Fig. 2 dI/dV spectra and evolution of VHS with doping away from the magic angle in TBG.

a, Back-gate (Vg) dependence of dI/dV spectra for TBG at θ ≈ 1.2°. Assignments of peaks to VHS 1 and VHS 2 are indicated. b, Zoomed-in image of the boxed area in a. c, Evolution of the dI/dV spectra with back-gate (Vg) for a TBG at θ ≈ 1.7°.

Extended Data Fig. 3 Estimate of the filling fraction from the area under the LDOS peak.

a, dI/dV curve for ν ≈ −0.3 (Vg = −10 V in Fig. 2, sample 1). The dashed line represents the background subtraction. b, dI/dV spectrum after background subtraction. Coloured areas are used to estimate the filling fraction as described in the text. ALB and AUB are the areas under the lower and upper bands, respectively.

Extended Data Fig. 4 Charge polarization within moiré cells of TBG at ±1/4 filling.

a, b, dI/dV curves and maps at +1/4 filling (a) and −1/4 filling (b), taken at Vb = −200 mV, I = 50 pA. The left two panels show the dI/dV curves at +1/4 filling (upper panel) and −1/4 filling (lower panel), the centre panels show the dI/dV maps at the LB energy in dI/dV curves (−30 mV for +1/4 filling and −17 mV for −1/4 filling), and the right panels show the dI/dV maps at the UB energy (11 mV for +1/4 filling and 33 mV for −1/4 filling).

Extended Data Fig. 5 Absence of broken symmetry in the full flat band in sample 1.

STM topography (a) and dI/dV map (b) of the same area discussed in the main text, measured at the energy corresponding to the centre of the flat band (dashed line in inset) in the highly n-doped regime (Vg = +55 V) corresponding to the fully filled flat band (taken at Vb = 200 mV, I = 15 pA). Inset, dI/dV spectra in AA/AB (Vg = +55 V).

Extended Data Fig. 6 Absence of broken symmetry at non-magic twist angles.

a, STM topography of TBG away from the magic angle (θ = 1.5°), centred on the AA region (shown by the dotted circle; data taken at Vb = −150 mV, I = 20 pA). Inset, dI/dV spectra in the AA/BA regime (Vb = −150 mV, I = 50 pA). b, dI/dV map of the same area as shown in a, at the energy of the left VHS (−29 mV), which is labelled by the dashed line in the inset in a (Vb = −150 mV, I = 50 pA).

Extended Data Fig. 7 Relative orientation of the negative charge lobes and the charge stripe direction.

a, Charge order extracted from a large area in sample 1, showing stripe charge orientation along a crystallographic axis of the moiré lattice (same as Fig. 4c; see Fig. 4c legend for details). b, The relative orientation angle between the charge quadrupole lobes (green lines) and the charge stripes (red lines), 16° ± 2°, is roughly constant within this region.

Extended Data Fig. 8 Different charge-order orientations.

a, dI/dV maps at the energy of the LB (left panel) and the UB (right panel) for the same sample (sample 1) as that discussed in the main text, but in a different region in which the charge stripe is along a different direction. b, Charge modulation map obtained by subtracting the two intensity maps shown in a. The black arrow shows the direction of the electron lobe, and the green arrow marks the direction of the global charge stripe, which coincides with a crystallographic axis of the moiré pattern (see inset). Inset, large STM image of the moiré pattern. The scale bar is 10 nm. c, For comparison we show Fig. 3c, illustrating that the orientation (labelled by the black arrow) has changed compared to that in b. Inset, large STM image of the moiré pattern in c. The scale bar is 10 nm.

Extended Data Fig. 9 Charge modulation in magic-angle TBG (sample 2).

a, STM topography in a 10 nm × 10 nm area centred on the AA region (red circle; taken at Vb = −100 mV, I = 40 pA). b, dI/dV map over the same area as a for the LB (left panel) and the UB (right panel) at Vg = 0 V (Vb = −100 mV, I = 40 pA). c, Map of net charge obtained by the method described in the main text. Red corresponds to electron doping and blue to hole doping. The four dashed lobes mark the sectors with alternating electron (e) and hole (h) doping. d, Spatial dependence of dI/dV curves along the coloured arrows in a and c shows the shift of spectral weight between the LB and the UB with position. e, Position dependence of filling fraction from d along the path indicated by the arrow in c. The filling fraction was obtained from the relative area under the LB peak, as discussed in the text. f, Large-scale dI/dV map (40 nm × 40 nm) of net charge, obtained by the method described in the text and in Fig. 3c.

Extended Data Fig. 10 Energy shift in the LB and UB peak positions.

In the left panel (which is the same as Fig. 3d), the distance spanned, about 5 nm, is too small to distinguish the energy shift in the two bands (dashed lines). In the right panel, the data is extended out to r = 6.8 nm, where an energy shift in both LB and UB can be seen. See Methods for details.

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Jiang, Y., Lai, X., Watanabe, K. et al. Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene. Nature 573, 91–95 (2019). https://doi.org/10.1038/s41586-019-1460-4

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