been observed ( 3 , 4 ). Large area topography
of a sample region with angle mismatchdq~
0.25° is shown in Fig. 3A and fig. S8A. Over-
laid on the topography of Fig. 3A is a map of
the local twist angle, giving a spatially aver-
aged value ofq¼ 1 :55°. The MLR segregates
the system into domains of uniform moiré
plaquettes arranged in a honeycomb lattice with
qx~ 1.5°, separated by quasi–one-dimensional
moiré solitons. Populating the nodes of this
soliton network is a hexagonal lattice of point-
like faults in the local twist angle correspond-
ing to topological moiré defects that we term
“twistons.”Zoomed-in topographs of these
three types of region of the MLR are shown in
Fig. 3, B to D. Of the three sites, only the moirésolitons showed considerable breaking ofC 3
rotational symmetry, which is consistent with
a distinctly large value of local heterostrain
ex≳ 0 : 5 %on these structures ( 24 ).
The large variation inqxandexon theL
scale has a dramatic effect on the local elec-
tronic structure of TTG.qxserves as a con-
venient parameter to quantitatively classifySCIENCEscience.org 8 APRIL 2022•VOL 376 ISSUE 6589 197
EFEnergy (meV)K' K Γ M K'0100-100Energy (meV)K' K Γ M K'0100-1001.8 ̊
1.45 ̊1.8 ̊
1.45 ̊Energy (meV)- 80 0 08
T
P-3-2-1012320 1015 5
n = -0.3x10^12 cm-2n = -3.7x10^12 cm-2n = 3.4x10^12 cm-2IIRSCPlaquette TwistonIIRSC-80 -40 0 40 80
Energy (meV)-1-2-3-42
3
4x10^120
n (cm^1-2)-80 -40 0 40 80
Energy (meV)0-1-2-3231ABD GHIJ0.5 3
LDOS LDOS0.6 2.2
Lo LDOS Hi(meV)(meV)SolitonLDOS0.4 1.1-80 -40 0 40 80
Energy (meV)CFig. 4. Correlated gaps and flat-band resonance.(AtoC) Gate-dependent
LDOS spectroscopy on the plaquette, twiston, and moiré soliton regions. Yellow
arrows in (A) and (C) indicate full filling of the moiré superlattice. Green arrows
in (B) and (C) indicate correlated gaps that are confined to the twiston and soliton
regions. (DandE) Continuum model calculations showing (left) the band
structure and (right) density of states for twist angles of 1.45° (red) and 1.8°
(blue) at two different fillings. The zero of energy corresponds to the position
of the chemical potential. Flat band resonance (D) for these angles occurs when the
moiré plaquette (1.45°) superlattice is filled tonP= 2.4. (F) Doping-dependent
LDOS spectroscopy on the twiston (blue) and plaquette (red) regions showing
flat-band resonance atjjne 2 :5. Curves are offset vertically for clarity and
are plotted on the same vertical scale. The vertical dashed line indicates the Fermi
level. (G) Extracted values of flat-band energy splitting between twiston and
plaquette sites,dc/n[see (E)], as a function of doping. Minima correspond to flat-
band resonances and the resulting reduction in real-space electronic disorder.
(HtoJ) Fermi-level LDOS maps at (I) charge neutrality and at the (H) electron-
and (J) hole-doped flat-band resonances. Scale bars, 25 nm.Vset= 300 mV,
Iset= 120 pA, andVmod= 2 mV.RESEARCH | REPORTS