All electrical measurements are performed in a dilution refrigerator equipped with a 9T/1T/1T superconducting vector magnet. The vector-field control is essential for B||-dependence measurements, allowing precise control of the field direction, in particular removing residual B⊥. Transport measurements are performed using lock-in techniques at a frequency f< 45Hz to reduce the electronic noise. Low-pass electronic filtering based on "F. Kuemmeth, C. M. Marcus, Reducing noise and temperature during measurements in cryostats, US Patent US20150060190A1 (2015)" is applied to lower the electron temperature. Penetration field capacitance was measured using a capacitance bridge circuit with an FHX15X high electron mobility transistor serving as an in-situ impedance transformer, as described in "A. A. Zibrov, et al., Nature 549, 360 (2017)". An excitation frequency of 54245.12Hz was used to obtain the capacitance data. To convert the measured values to inverse electronic compressibility κ, we use low-magnetic field Landau levels as a calibration for perfect screening and perfect penetration, a procedure described in detail in "H. Zhou, et al., Nature 598, 429 (2021)".

We report the observation of spin-polarized superconductivity in Bernal bilayer graphene when doped to a saddle-point van Hove singularity generated by 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. While all of these phases are metallic at zero magnetic field, we observe a transition to a superconducting state at finite B|| ≈ 150mT applied parallel to the two dimensional sheet. Superconductivity occurs near a symmetry breaking transition, and exists exclusively above the B||-limit expected of a paramagnetic superconductor with the observed Tc ≈ 30mK, implying a spin-triplet order parameter. 

Please refer to the README.txt file and the associated manuscript.