Science - USA (2022-04-08)

broadening of 4 meV is sufficient to repro-
duce the widths quantitatively (Fig. 2E and
fig. S14A).
TuningVgaway from zero produces system-
atic changes in the intensities, separation, and
widths of the VHSs. We examined the effect
ofDon the single-particle band structure and
found that although it does account for the

shift in relative intensity of the VHSs, values of

Dwithin the experimentally accessible range

fail to produce notable changes in either the

predicted separation or widths of the VHSs

(fig. S14B). The inability of single-particle cal-

culations to reproduce the measured quasi-

particle spectrum, combined with the strong

doping dependence of the latter, provides

clear evidence for a pronounced band renor-

malization in TTG near the magic angle

caused by strong quasiparticle interactions.

To isolate and better visualize this reconfig-

uration of the band structure, we plotted in

Fig. 2F gate-dependent STS, with each curve

shifted so that the flat bands remain centered

on zero energy ( 18 ). The position of the chem-

ical potential at each doping is indicated in

Fig. 2F with the red dashed line. Unlike

MATBG, in which superconductivity occurs in

the vicinity of multiple integer filling factors of

the moiré bands ( 21 ), observations of super-

conductivity in TTG have been strictly limited

to within the vicinity ofjj¼n 2, with optimal

doping occurring in a roughly particle-hole

symmetric fashion for 2<jjn<3( 3 , 4 ). In

MATBG, superconductivity occurs when the

chemical potential is embedded in the moiré

flat bands, leading to a large density of states

at the Fermi level. The enhancement of the

densityofstatesrelativetopristinegraphene

or graphite has been hypothesized to support

conventional electron-phonon–mediated super-

conductivity ( 22 , 23 ). In TTG, however, our

measurements (Fig. 2F) show that large den-

sities of states occur at multiple fillings

betweenn=–4 andn= 4, even though super-

conductivity has not been observed in all of

these regions in transport measurements. It is

thus clear that it is not the density of states

alone that controls the superconducting dome

observed in transport.

One aspect of the LDOS spectrum studied

inFig.2isthatitbreaksparticle-holesym-

metry in a way that is not expected on the

basis of noninteracting calculations. This is

apparent in that the CB remains considerably

broader than the VB for all measured dopings

(Fig. 2C). One implication of this particle-hole

asymmetry is that the chemical potential crosses

the VHSs at different filling factors for electron

as compared with hole doping, which is re-

produced by our Hartree-Fock calculations

(fig. S16). For hole doping, the chemical po-

tential crosses the VHS in the vicinity of the

parent state atn~–2.5, whereas for electron

doping, the chemical potential has already

crossed the VHS byn~ 1. The enhancement

of the Fermi level density of states for the

hole-doped parent state may contribute to the

comparative robustness of the hole-doped super-

conducting dome ( 3 , 4 ). However, the particle-

hole asymmetry of the tunneling spectrum

stands in contrast to the approximate particle-

hole symmetry of the superconducting phase

diagram measured in transport. This apparent

discrepancy suggests that additional factors

may be relevant in determining the bounda-

ries of the superconducting phase.

Having analyzed the electronic structure at

the sub-Llength scale, we next turned to a

detailed study of the MLR at twist angles near

those for which robust superconductivity has

196 8 APRIL 2022•VOL 376 ISSUE 6589 science.orgSCIENCE

Moiré Soliton(S)

0.5%

1.6°

Twiston (T)

0.2%

1.8°

Λ

λ

1.5 ̊

1.7 ̊

1.9 ̊

P

T

S

P

S

T

1.4 ̊

2.0 ̊

Energy (meV)

-200 - 100 0 100 002

A B

C

D

E

Energy (meV)

-200 -100 0 100 200

Measured LDOS Calculated LDOS

1.45 ̊, 0%

1.6 ̊, 0.55%

1.8 ̊, 0%

F

0.1%

0.5%

0.2%

1.35 1.45 1.55 1.65

Local Twist Angle ( ̊)

Counts^50

100

150

H

1.4 ̊

1.5 ̊

1.6 ̊

G

Relaxation Model

S T

P

PST

Plaquette (P)

0.1%

1.5°

Fig. 3. Moiré lattice reconstruction.(A) STM topography colored in proportion to the local twist angle.
Scale bar, 50 nm. (Inset) FFT of 320-nm^2 topograph centered on this field of view, showing two sets of moiré
wave vectors. (BtoD) Zoomed-in topography of the circled regions in (A), illustrating the local structure
of the MLR. Numbers indicate local twist-angle and heterostrain values extracted from dashed moiré lattice
vectors. Scale bars, 10 nm. (E) Experimental AAA site LDOS spectra extracted from conductance maps
taken over the field of view of (A), displaying the change in electronic structure over different regions of
the MLR. Curves are offset vertically for clarity and are plotted on the same vertical scale. Percentages
denote characteristic heterostrain values for each MLR region. (F) Continuum model (SP2) TTG densities of
states for three sets of structural parameters (q,e). Calculations at finite heterostrain preserve mirror
symmetry by applying a uniaxial strain to the middle layer only. (G) Local twist angle as determined with
nearest-neighbor AAA site distance for structural relaxation calculation withqTM= 1.5° andqBM= 1.69°. Scale
bar, 50 nm. (H) Histogram of the twist angles present in (G) showing three populations corresponding to
plaquette, soliton, and twiston sites.

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