Superconductivity without insulating states in twisted bi-
layer graphene stabilized by monolayer WSe
2
Harpreet Singh Arora
1
,
2
∗
, Robert Polski
1
,
2
∗
, Yiran Zhang
1
,
2
,
3
∗
, Alex Thomson
2
,
3
,
4
, Youngjoon
Choi
1
,
2
,
3
, Hyunjin Kim
1
,
2
,
3
, Zhong Lin
5
, Ilham Zaky Wilson
5
, Xiaodong Xu
5
,
6
, Jiun-Haw Chu
5
,
Kenji Watanabe
7
, Takashi Taniguchi
7
, Jason Alicea
2
,
3
,
4
and Stevan Nadj-Perge
1
,
2
†
1
T. J. Watson Laboratory of Applied Physics, California Institute of Technology, 1200 East Cali-
fornia Boulevard, Pasadena, California 91125, USA
2
Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, Cal-
ifornia 91125, USA
3
Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
4
Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, Cal-
ifornia 91125, USA
5
Department of Physics, University of Washington, Seattle, Washington 98195, USA
6
Department of Materials Science and Engineering, University of Washington, Seattle, WA 98195,
USA
7
National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305 0044, Japan
*These authors contributed equally to this work
†
Correspondence: s.nadj-perge@caltech.edu
Magic-angle twisted bilayer graphene (TBG), with rotational misalignment close to 1.1°, fea-
tures isolated flat electronic bands that host a rich phase diagram of correlated insulating,
superconducting, ferromagnetic, and topological phases
1–6
. The origins of the correlated
insulators and superconductivity, and the interplay between them, are particularly elusive
due to the sensitivity of these correlated states to microscopic details. Both states have been
previously observed only for angles within
±
0.1° from the magic-angle value and occur in
adjacent or overlapping electron density ranges; nevertheless, it is still unclear how the two
states are related. Beyond the twist angle and strain, the dependence of the TBG phase dia-
gram on the alignment
4, 6
and thickness of insulating hexagonal boron nitride (hBN)
7, 8
used
to encapsulate the graphene sheets indicates the importance of the microscopic dielectric en-
vironment. Here we show that adding an insulating tungsten-diselenide (WSe
2
) monolayer
between hBN and TBG stabilizes superconductivity at twist angles much smaller than the
established magic-angle value. For the smallest angle of
θ
= 0.79°, we still observe clear su-
perconducting signatures, despite the complete absence of the correlated insulating states
and vanishing gaps between the dispersive and flat bands. These observations demonstrate
that, even though electron correlations may be important, superconductivity in TBG can ex-
ist even when TBG exhibits metallic behaviour across the whole range of electron density.
Finite-magnetic-field measurements further reveal breaking of the four-fold spin-valley sym-
metry in the system, consistent with large spin-orbit coupling induced in TBG via proximity
to WSe
2
. The survival of superconductivity in the presence of spin-orbit coupling imposes
additional constraints on the likely pairing channels. Our results highlight the importance of
1
arXiv:2002.03003v1 [cond-mat.supr-con] 7 Feb 2020
symmetry breaking effects in stabilizing electronic states in TBG and open new avenues for
engineering quantum phases in moir
́
e systems.
Strongly correlated electron systems often exhibit a variety of quantum phases with simi-
lar ground-state energies, separated by phase boundaries that depend sensitively on microscopic
details. Twisted bilayer graphene, with twist angle close to the magic angle
θ
M
≈
1.1°, has re-
cently emerged as a highly tunable platform with an exceptionally rich phase diagram
1, 2
hosting
correlated insulating states, superconductivity, and ferromagnetism
3–6
. Strong correlations in TBG
originate from the non-dispersive (flat) bands that are created by the hybridization of the graphene
sheets
9
and are isolated from the rest of the energy spectrum by an energy gap
∼
30 meV
10, 11
.
Previous transport experiments on magic-angle TBG found that the correlated insulators are often
accompanied by superconductivity in a narrow range
±
0.1° around
θ
M
1, 3, 7, 8, 12
, with signatures of
these states observed down to 0.93°
13
. Close to
θ
M
, the correlated insulators develop at electron
densities that correspond to an integer number
ν
of electrons per moir
́
e unit and are surrounded
by intermittent pockets of superconductivity
5
; both phases appear most frequently around
ν
=
±
2
2, 3
. Away from
θ
M
, however, both phases are suppressed as the effects of electron-electron in-
teractions quickly diminish due to a rapid increase of the flat-band bandwidth and corresponding
dominance of kinetic energy
1, 9
. In addition to the TBG twist angle, the physics of the correlated
phases is also affected by the hBN employed as a high-quality dielectric. In particular, since hBN
and graphene exhibit similar crystal lattices, the relative alignment between the hBN and TBG is
critical. For example, a ferromagnetic state near
ν
= +3 was observed in devices where hBN aligns
with TBG
4, 6
. However, in such devices the band structure of the flat bands is strongly altered
6
,
and superconductivity—typically observed when hBN and TBG are misaligned—is absent. Re-
cent work using a very thin hBN layer separating a back gate from TBG additionally suggests
that electrostatic screening plays a prominent role in the appearance of insulating and supercon-
ducting states
7
. These experiments exemplify the effects of hBN layers on the phase diagram in
hBN-TBG-hBN structures and highlight the importance of understanding how microscopic details
of the dielectric environment alter the properties of correlated phases.
Here, instead of the usual hBN-TBG-hBN structures, we investigate devices made from
hBN-TBG-WSe
2
-hBN van der Waals stacks in which a monolayer of WSe
2
resides between the
top hBN and TBG (Fig. 1a). Our stacks are assembled using a modified ‘tear and stack’ technique
where the ‘tearing’ and ‘stacking’ of TBG is facilitated by monolayer WSe
2
; see Methods and
Extended Data Fig. 1 for fabrication details. Like hBN, flakes of transition metal dichalcogenides,
such as WSe
2
, can be used as a high-quality insulating dielectric for graphene-based devices
14
;
however, the two van der Waals dielectrics differ in several ways that may alter the TBG band
structure. First, unlike hBN, the WSe
2
and graphene lattice constants differ significantly (0.353
nm for WSe
2
and 0.246 nm for graphene, Fig. 1b). This mismatch implies that the moir
́
e pattern
formed between TBG and WSe
2
has a maximum lattice constant
∼
1 nm, in other words, much
smaller than that formed in small-angle TBG (
>
10 nm). Second, it is well-established that WSe
2
can induce a spin-orbit interaction (SOI) in graphene via van der Waals proximity
15, 16
. And finally,
due to hybridization effects, WSe
2
may also change both the Fermi velocity of the proximitized
2
graphene sheet and the system’s phonon spectrum. We chose to use monolayer WSe
2
in particular
because of its large band gap
17
that allows applying a large range of gate voltages. It has also been
suggested previously that a monolayer induces larger spin-orbit coupling in graphene compared to
a few-layer WSe
2
18
.
We have studied three TBG-WSe
2
devices and show results for two of them in the main text
(see Extended Data Fig. 4 for data from an additional device). Surprisingly, we find robust super-
conductivity in all studied TBG-WSe
2
structures, even for twist angles far outside of the previously
established range. Fig. 1c-e shows the temperature dependence of resistance over three TBG re-
gions corresponding to angles
θ
= 0.97°,
θ
= 0.87° and
θ
= 0.79°; in all cases superconducting
transitions are clearly visible. Aside from the drop in R
xx
to zero, we also observe well-resolved
Fraunhofer-like patterns for all three angles (Figs. 1f-1h), qualitatively similar to the typical hBN-
TBG-hBN devices
2, 3, 5
. The small periodic modulations of the critical current in magnetic field
have been previously attributed to the presence of Josephson junctions in the system, indepen-
dently corroborating the presence of superconducting correlations. In our devices, we typically
see periods of 1.5-3 mT that, if interpreted as the effective junction area
S
∼
0.67–1.33 μm
2
, are
consistent with the device geometry.
For the largest angle
θ
= 0.97°, a superconducting pocket emerges on the hole side near
ν
= –
2 with a maximal transition temperature T
c
≈
0.8 K. To our knowledge, this already is the smallest
angle for which superconductivity has been observed for hole doping. Careful inspection reveals
another weak superconductivity pocket close to
ν
= +2 (the behavior at low fields is displayed
in Extended Data Fig. 6). However, despite the small twist angle—falling outside the
θ
M
±
0.1°
range—the observed phase diagram resembles that of regular high-quality magic-angle hBN-TBG-
hBN structures
2, 5
. For this angle, correlated insulating states are also observed for filling factors
ν
= +2, +3 with activation gaps of
∆
+2
= 0.68 meV and
∆
+3
= 0.08 meV, whereas at other filling
factors correlated states are less developed and do not show insulting behavior (see Fig. 2f and
Extended Data Fig. 3).
Although superconductivity persists for all three angles, the correlated insulators are quickly
suppressed as the twist angle is reduced. This suppression is not surprising, as for angles be-
low
θ
M
, the bandwidth increases rapidly and, moreover, the characteristic correlation energy scale
e
2
/
4
πL
m
also diminishes due to an increase in the moir
́
e periodicity
L
m
=
a/sin
(
θ/
2)
(
a
= 0.246
nm denotes the graphene lattice constant)
1, 9, 10, 19–21
. For the lower angle of
θ
= 0.87° correlated-
insulating behavior is heavily suppressed at all filling factors. In Fig. 1d a peak in longitudinal
resistance versus density is visible only around
ν
= +2 above the superconducting transition (
T
c
= 600–800 mK). Data for a larger temperature range (Fig. 2a-b) shows that the resistance peak
near
ν
= +2 survives up to
T
= 30 K, and also reveals a new peak near
ν
= +1 in the temperature
range 10-35 K. These observations suggest that electron correlations remain strong, though the
corresponding states appear to be metallic as the overall resistance increases with temperature. For
this angle, we measure activation gaps at full filling (i.e., at
ν
=
±
4
) of
∆
+4
= 8.3 meV and
∆
−
4
=
2.8 meV (Fig. 2e) —far smaller than the gaps around
θ
M
, in line with previous results that report a
3
disappearance of the band gap separating dispersive and flat bands at around
θ
= 0.8°
11, 22
.
At the smallest angle,
θ
= 0.79°, along with the lack of insulating states at any partial fill-
ing, the resistance at full filling is even more reduced (Fig. 2c-d). The relatively low resistances
<
2 k
Ω
measured at full filling—which are less than
15%
of the resistance at the charge neutrality
point (CNP)—suggest a semi-metallic band structure around full filling, consistent with theoretical
expectations for TBG at
θ
= 0.79°
22
and the resistivity of a dilute 2D electron gas
23
. We empha-
size, however, that despite the absence of both full-filling band gaps and correlated insulators, the
superconducting low-resistance pocket near
ν
= +2
is clearly resolved (Figs. 1e and 1h).
Both the disappearance of the correlated insulators and the vanishing gap between flat and
dispersive bands for low angles suggest that the additional WSe
2
monolayer does not significantly
change the magic angle. Since superconductivity survives to much lower angles compared to cor-
related insulating states, the two phenomena appear to have different origins
7, 8
. Note also that the
close proximity of the dispersive bands does not seem to have a major impact on the supercon-
ducting phase. While these findings are not consistent with a scenario wherein superconductivity
descends from a Mott-like insulating state as in high-T
c
superconductors
24
, we do emphasize that
electron correlations may still prove essential for the development of superconductivity. For in-
stance, even for the smallest angle of
θ
= 0.79°, the superconducting pocket is seemingly pinned
to the vicinity of
ν
= 2. Additionally, as shown in Fig. 2, at higher temperatures residual R
xx
peaks
can still appear at certain integer filling factors despite the absence of gapped correlated insulating
states. It is thus hard to rule out the possibility that superconductivity arises from correlated states
of metallic nature that may be present at smaller angles and near integer values of
ν
in analogy to
other exotic superconducting systems
25–27
.
Measurements in finite magnetic field reveal further insights into the physics of TBG-WSe
2
structures (Fig. 3). Surprisingly, for all three angles we find that even at modest magnetic fields,
above
B
= 1 T, gaps between Landau levels are well-resolved, showing a fan diagram that diverges
from the CNP. The slopes of the dominant sequence of R
xx
minima correspond to even-integer
Landau level fillings
±
2,
±
4,
±
6
, etc.—indicating broken four-fold (spin-valley flavor) symme-
try. By contrast, the majority of previous transport experiments
2, 3
near the magic angle report a
Landau-fan sequence
±
4,
±
8,
±
12 at the CNP, with broken-symmetry states being only occasion-
ally observed at the lowest Landau level (corresponding to the
±
2 sequence)
4, 5, 28
. In addition to
R
xx
minima corresponding to the gaps between Landau levels, we also measured quantized Hall
conductance plateaus, further corroborating the two-fold symmetry and indicating the low disorder
in the measured TBG areas. Note also that for the smallest angle (
θ
= 0.79° ) we do not observe
obvious signatures of correlated insulating states near
ν
= 2 up to
B
= 4 T.
The observed two-fold degeneracy is consistent with a scenario in which the TBG band struc-
ture is modified by the spin-orbit interaction (SOI) inherited from the WSe
2
monolayer (Fig. 4).
Previous works established that WSe
2
can induce large SOI of both Ising and Rashba type into
4
monolayer and bilayer graphene
15, 16
, and it is therefore reasonable to assume that the SOI is sim-
ilarly generated in the upper (proximitized) layer of TBG in our devices. Continuum-model cal-
culations taking into account this effect show that the SOI lifts the degeneracy of both flat and
dispersive bands, thereby breaking four-fold spin-valley symmetry. In a finite magnetic field, the
resulting Landau levels then descend from Kramer’s states that are only two-fold degenerate. Odd
steps—which are not generated by the SOI—are occasionally observed for low angles. We at-
tribute these steps to additional symmetry breaking, possibly due to correlation effects originating
either from flat-band physics or simply a magnetic-field-induced effect at low electronic densities.
Induced SOI can additionally constrain the nature of the TBG phase diagram. In particu-
lar, the SOI acts as an explicit symmetry-breaking field that further promotes instabilities favoring
compatible symmetry-breaking patterns while suppressing those that do not. The relative robust-
ness of the
ν
= 2 correlated insulator in our
θ
= 0.97° device suggests that interactions favor
re-populating bands
29, 30
in a manner that also satisfies the spin-orbit energy. Furthermore, the sur-
vival of superconductivity with SOI constrains the plausible pairing channels—particularly given
the dramatic spin-orbit-induced Fermi-surface deformations that occur at
ν
= +2 (Fig. 4). Su-
perconductivity in our low-twist-angle devices, for instance, is consistent with Cooper pairing of
time-reversed partners that remain resonant with SOI. Thus the stability of candidate insulating and
superconducting phases to the SOI provides a nontrivial constraint for theory
31–35
. The integration
of monolayer WSe
2
demonstrates the impact of the van der Waals environment and proximity
effects on the rich phase diagram of TBG. In a broader context, this approach opens the future
prospect of controlling the range of novel correlated phases available in TBG and similar struc-
tures by carefully engineering the surrounding layers, and it highlights a key tool for disentangling
the mechanisms driving the different correlated states.
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Acknowledgments:
We acknowledge discussions with Hechen Ren, Ding Zhong, Yang Peng, Gil
Refael, Felix von Oppen, Jim Eisenstein, and Patrick Lee. The device nanofabrication was per-
formed at the Kavli Nanoscience Institute (KNI) at Caltech.
Funding:
This work was supported
7
by NSF through program CAREER DMR-1753306 and grant DMR-1723367, Gist-Caltech memo-
randum of understanding and the Army Research Office under Grant Award W911NF-17-1-0323.
Nanofabrication performed by Y.Z. has been supported by DOE-QIS program (de-sc0019166).
J.A. and S.N.-P. also acknowledge the support of IQIM (NSF funded physics frontiers center).
A.T. and J.A. are grateful for support from the Walter Burke Institute for Theoretical Physics at
Caltech and the Gordon and Betty Moore Foundation’s EPiQS Initiative, Grant GBMF8682. The
material synthesis at UW was supported as part of Programmable Quantum Materials, an Energy
Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science,
Basic Energy Sciences (BES), under award de-sc0019443 and the Gordon and Betty Moore Foun-
dation’s EPiQS Initiative, Grant GBMF6759 to J.-H.C.
Author Contribution:
H.A., R.P., Y.Z., and S.N.-P. designed the experiment. H.A. made the TBG-
WSe
2
devices assisted by Y.Z., H.K. and Y.C. H.A. and R.P., performed the measurements. Y.Z.
performed measurements on initial TBG devices. H.A., R.P., and S.N.-P. analyzed the data. A.T.
and J.A. developed the continuum model that includes spin-orbit interaction and performed model
calculations. Z.L., I.Z.W., X.X., and J.-H.C. provided WSe
2
crystals. K.W. and T.T. provided
hBN crystals. H.A., R.P., Y.Z., A.T., J.A., and S.N.-P. wrote the manuscript with input from other
authors. S.N.-P. supervised the project.
Data availability:
The data that support the findings of this study are available from the corre-
sponding authors on reasonable request.
8
Figure 1
|
Superconductivity in small-angle TBG-WSe
2
structures. a
, Schematic of the TBG-
WSe
2
structure showing the crystal lattice of two graphene layers (red and blue) and WSe
2
(yellow
and cyan). Inset: Complete structure including encapsulating hBN layers on top and bottom and
a gold back-gate.
b
, Top view of WSe
2
and graphene, indicating different unit-cell sizes.
c-e
,
Longitudinal resistance R
xx
vs. temperature and electron density, expressed as a flat-band filling
factor
ν
, for devices D1 and D2 and angles
θ
= 0.97°,
c
;
θ
= 0.87°,
d
; and
θ
= 0.79°,
e
. In device
D2, adjacent sets of electrodes have slightly different twist angle, as explained in the Methods
section. Superconducting domes (SC) are indicated by a dashed line that delineates half of the
resistance measured at 2 K (except for the electron-side dome for 0.97°, for which the normal
temperature used was taken at 1K).
f-h
, Fraunhofer-like interference patterns, typically observed
in TBG superconducting devices, for the three contact pairs (
θ
= 0.97°,
ν
= –2.40,
f
;
θ
= 0.87°,
ν
=
1.96
g
; and
θ
= 0.79°,
ν
= 2.30,
h
).
9