maximum field of our experimental setup, is
thus well in excess of this limit.
We conclude that the Zeeman effect is not
pair breaking for the superconductor, con-
sistent with a spin-triplet order parameter.
The negligible strength of spin-orbit coupling
in graphene plays a key role in drawing this
conclusion. In transition metal dichalcogenides
2H-NbSe2 ( 28 ) and 2H-MoS2 ( 29 ), for example,
similarly large violations of the paramagnetic
limit are also observed but are not thought to
imply spin-triplet order parameters. Instead,
those observations were interpreted in terms
of Ising superconductivity ( 30 ), where the
strong spin orbit coupling locks the spins
perpendicular to the sample plane, rendering
them immune to magnetic fields smaller than
the spin-orbit coupling strengthlSO. For a sim-
ilar mechanism to apply in graphene would
requirelSO≫ 100 meV, the largest Zeeman
energy reached in our experiment. This is much
larger than expected from previous theoretical
and experimental literature ( 31 , 32 ). In many
spin-triplet superconductors, nonmagnetic im-
purities play the role of magnetic impurities
in conventional superconductors. To assess
whether such exotic superconducting order is
plausible, we estimate the disorder strength
parameterized by the ratiod¼x=‘mf( 33 ) of
the superconducting coherence lengthxand
the electronic mean free path in the normal
state‘mf.xmay be estimated from the upper
critical field at base temperature ofBc⊥≈
5 mT (Fig. 2, E and F) from the relation ( 34 )
x¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
F 0 =ðÞ 2 pBc⊥p
≈250 nm (whereF 0 is the
superconducting magnetic flux quantum).
This value is comparable to that of RTG ( 11 ) and
is much longer than that in moiré graphene
multilayers ( 7 , 12 ).
We may estimate‘mffrom the magnetic
field where quantum oscillations are first
observed. This corresponds to‘mf≈ 2 pkF‘^2 B,
the circumference of a cyclotron orbit ( 35 )
(where‘Bis the magnetic length andkFis the
Fermi wave vector). Figure 3 shows quantum
oscillation data in the vicinity of the super-
conducting state. Atne≈−0.57 × 10^12 cm−^2 ,
on the cusp of the superconducting state,
two oscillation frequencies are observed.
Taking the higherffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi fn≲^1 = 2 , we estimatekF¼
2 pfnjjnep
¼ 0 :13nm ^1. In this regime, the
onset field is found to be≈140 mT (fig. S6),
giving‘mf≈ 5 mm. This estimate is compara-
ble to device dimensions ( 36 ), so we conclude
thatd< 0.05, placing superconductivity deep
in the clean limit. Exotic superconducting order
parameters are thus not ruled out by disorder
considerations.
BBG and RTG share the same crystal sym-
metries, differing only in quantitative details.It is likely then that, just as for RTG, the bare
fact that superconductivity occurs at a mag-
netic transition in BBG can be explained by
both conventional electron-phonon as well as
electronically mediated attraction ( 37 – 46 ). We
therefore turn our attention to previously un-
recognized constraints offered by BBG on
theories of the superconducting state that seek
to capture the qualitative details of the phase
diagram.
In contrast to superconductors in RTG, the
fermiology indicates that the superconducting
state in BBG emerges from a partially isospin-
polarized normal state with both majority and
minority Fermi surfaces. In the domain of the
superconducting state, both a high-frequency
and a low-frequency oscillation are evident
(Fig. 3, A and B, and additional data in fig. S7),
evolving continuously from the peaks in the
PIP 2 phase. The normal state has a somewhat
distinct fermiology from that of the PIP 2 state
observed at higherjjne, with the two phases
showing contrastingnedependence of both
the low- and high-frequency oscillations. In the
PIP 2 state, dfn=dneis negative for the low-fn
oscillation and positive for the high-fnoscilla-
tion, with these trends reversing abruptly at
the boundary of the superconducting state.
Notably, the low-frequency peak in the super-
conducting regime continuously interpolatesSCIENCEscience.org 18 FEBRUARY 2022•VOL 375 ISSUE 6582 777
-0.55
ne (10^12 cm-2)B(T)100 200 300 400GH-0.65 -0.6 -0.5-0.55
ne (10^12 cm-2)-0.65 -0.6 -0.50257550100150200250300350-10 0 10
I (nA)-0.65 -0.6 -0.55 -0.5
00.20.40.60.81ne (10^12 cm-2)Ispin- polarized
SCPIP 2 Sym 12spin-unpoloarized phaseA0150300R(xx)B = 0
B = 0.165T0 200 400-10010I (nA)PIP 2 Sym 12-10010I (nA)BCDEFPIP 2 Sym 12dV/dI ()^04500450dV
/d
I (
)B(mT)R^0450
xx ( )dV/dI ()^0450-15 -10 -5 0 5 10 15
I (nA)J00.10.20.3B(T)B(mT)0257550100dV/dI ()T (mK)^1060Rxx ()Fig. 4. Magnetic fieldÐinduced phase transitions.(A)ne-dependent
resistivity measured atD=1.02Vnm−^1 andB‖=0.165T(blue)orzero
magnetic field (black). (B) Nonlinear resistivity atne=−0.59 × 10^12 cm−^2 ,
D=1.02Vnm−^1 , and zero magnetic field for variableT.(C)ne-dependent
nonlinear dV/dImeasured atD=1.02Vnm−^1 and zero magnetic field.
(D)dV/dIas a function ofImeasured atnevalues indicated by arrows in (C).
(E) Same as (C), but withB‖= 0.165 T. (F)Sameas(D),butwithB‖= 0.165 T.
(G)dV/dIas a function ofB⊥atne=−0.59 × 10^12 cm−^2 ,D=1.02Vnm−^1 ,
andB‖= 0. (H) Same as (G), but as a function ofB‖withB⊥= 0. (I)B‖
dependence of linear response resistivity measured atD=1.02Vnm−^1
andB⊥= 0. SC, superconductivity. (J)dV/dImeasured along the trajectory
shown by the dashed line in (I).RESEARCH | REPORTS