to the extrinsic toughening mechanisms. In wet
conditions, microscale and nanoscale liquid
bridges facilitated capillary-assisted and suction-
based energy dissipation. This, along with the
toughening mechanisms associated with direct
solid-solid contact, improved the adhesion per-
formance. Using this multiscale interfacial strat-
egy, the lizard carefully balances attachment
and detachment, achieving the“just right”con-
nection in its tail that is neither too weak nor
too strong for its best chance of survival.
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ACKNOWLEDGMENTS
We thank A. Bauer for helpful discussions on the biology of tail
autotomy; P. Salmon from Bruker Belgium for CT scanning the
lizard tail; the NYU Abu Dhabi graduate office for providing N.S.B.
with a Global Ph.D. Fellowship; and the NYU Abu Dhabi Core
Technology Platform, especially R. Pasricha and J. Weston, for
providing us access and help with the SEM study.Funding:This
work was supported by an annual research grant provided by NYU
Abu Dhabi.Author contribution:N.S.B. conducted SEM analysis,
high-speed videography and analysis, biomimetic sample
preparation, characterization and results analysis, and finite
element simulations. A.O. fabricated masters for the biomimetic
model. S.K. was in charge of lizard biology and evolution and
assisted in capturing, identifying, and performing high-speed
videography of autotomy. C.J.S assisted and checked finite
element simulations. Y.A.S planned, guided, and coordinated the
project. All authors contributed to the writing of the manuscript.
Competing interests:The authors declare no competing interests.
S.K is also affiliated with the Museum für Naturkunde Berlin,
Leibniz Institute for Evolution and Biodiversity Science, Berlin
(Germany) as a guest researcher, but this affiliation has no
competing interests for the current paper.Data and materials
availability:All data and materials are available in the main
manuscript or the supplementary materials.SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.abh1614
Materials and Methods
Supplementary Text 1 to 7
Figs. S1 to S32
Tables S1 to S4
References ( 13 – 31 )
Movies S1 to S12
Accepted 20 December 2021
21 February 2021; resubmitted 5 November 2021
Accepted 20 December 2021
10.1126/science.abh16142D MATERIALS
Isospin magnetism and spin-polarized
superconductivity in Bernal bilayer graphene
Haoxin Zhou^1 , Ludwig Holleis^1 , Yu Saito^1 , Liam Cohen^1 , William Huynh^1 , Caitlin L. Patterson^1 ,
Fangyuan Yang^1 , Takashi Taniguchi^2 , Kenji Watanabe^3 , Andrea F. Young^1 *
In conventional superconductors, Cooper pairing occurs between electrons of opposite spin. We observe
spin-polarized superconductivity in Bernal bilayer graphene when doped to a saddle-point van Hove
singularity generated by a large applied perpendicular electric field. We observe a cascade of
electrostatic gate-tuned transitions between electronic phases distinguished by their polarization within
the isospin space defined by the combination of the spin and momentum-space valley degrees of
freedom. Although all of these phases are metallic at zero magnetic field, we observe a transition to a
superconducting state at finite magnetic fieldB‖≈150 milliteslas applied parallel to the two-dimensional
sheet. Superconductivity occurs near a symmetry-breaking transition and exists exclusively above
theB‖limit expected of a paramagnetic superconductor with the observed transition critical
temperatureTC≈30 millikelvins, consistent with a spin-triplet order parameter.
S
pin-triplet superconductors are rare in
nature. This scarcity is traceable, at
least in part, to the inapplicability of
Anderson’s theorem ( 1 ), which renders
conventional superconductors immune
to disorder. Realizing spin-triplet supercon-
ductivity therefore places stringent bounds
on materials’quality. Experimentally, one of
the most notable manifestations of triplet
superconductivity is resilience to applied
magnetic fields, which may exceed the limit
set by comparing the Zeeman energy with the
superconducting gap ( 2 , 3 ). Prominent exam-
ples of candidate spin-triplet superconductors
observed to violate this limit include uranium-
based compounds ( 4 ), such as URhGe ( 5 )
and UTe 2 ( 6 ). Recently, graphene-based, two-
dimensional materials have emerged as a plat-
form for superconductivity ( 7 – 11 ). In particular,
two varieties of graphene trilayer—one rota-
tionally faulted ( 12 ) and one in a metastable
rhombohedral stacking order ( 11 )—have shown
superconducting states that persist above the
paramagnetic limit ( 2 , 3 ), suggestive of a spin-
triplet order parameter. However, neither of
these materials represents a structural ground
state. Rotationally faulted structures are gen-
erally unstable, which limits sample uniform-
ity and, consequently, reproducibility ( 13 ).
Rhombohedral stacking orders, meanwhile,
are only metastable, which allows uniform
structures to be produced, but at great cost in
the practical yield of working devices. These
drawbacks hamper efforts to systematicallyvary experimental parameters and to build
more-complex devices making use of the
array of gate-tuned phases available in these
materials.
Here, we report magnetic field–induced
superconductivity in Bernal bilayer graphene
(BBG); the crystal structure is shown in Fig. 1A.
Bilayer graphene has been the subject of hun-
dreds of experimental studies since its original
experimental description in 2006 ( 14 ). How-
ever, prior explorations of electron correla-
tion physics have focused on instabilities of
the parabolic band touching that occurs in
the absence of an applied displacement field
( 15 – 18 ). When a perpendicular electric dis-
placement field (D) is applied, the parabolic
band touching is replaced by a bandgap (Fig.
1B), with van Hove singularities characterized
by divergent single-particle density of states
appearing near the band edge. Energy bands
and associated single-particle density of states
calculated within a four-band tight-binding
model ( 19 )areplottedinFig.1,BandC.Figure
1D shows the calculated density of states and
select Fermi contours at an interlayer poten-
tial difference of 50 meV, corresponding ( 20 ) to
D≈0.5 V nm−^1. A van Hove singularity occurs
at a carrier density ofne≈−0.5 × 10^12 cm−^2 ,
where three low-density Fermi pockets merge
into an annulus. Our choice of tight-binding
parameters, derived from numerical band struc-
ture modeling ( 19 ), has not been quantitatively
benchmarked to experiment in the regime of
interest. However, the existence of a saddle-
point van Hove singularity in this approximate
density regime is expected to be generic.
The electronic structure of BBG resembles
that of rhombohedral graphite multilayers
( 21 , 22 ). However, BBG is considerably easier
to manufacture owing to its structural sta-
bility. Our devices consist of a BBG channel
encapsulated in single-crystal hexagonal boron774 18 FEBRUARY 2022•VOL 375 ISSUE 6582 science.orgSCIENCE
(^1) Department of Physics, University of California at Santa
Barbara, Santa Barbara, CA 93106, USA.^2 International
Center for Materials Nanoarchitectonics, National Institute for
Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan.
(^3) Research Center for Functional Materials, National Institute
for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan.
*Corresponding author. Email: [email protected]
†Present address: Department of Applied Physics and Material
Science, California Institute of Technology, Pasadena, CA 91125, USA.
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