Spin-Orbit Enhanced Superconductivity in Graphene Heterostructures

Flat electronic bands in moire and crystalline graphene multilayers showcase emergent correlated phenomena including correlated insulators, superconductivity, topological orders, etc. This thesis focuses on the electrical transport characterization of superconductivity in moire and crystalline graphene, with the proximity of a layer of tungsten diselenide (WSe₂) that induces spin-orbit coupling (SOC). The interplay between spontaneous symmetry-breaking and explicit spin-orbit interactions emerges various unconventional superconducting pairing. In the case of moire graphene multilayers, superconductivity in twisted bilayer graphene persists much far away from the magic angle at which electronic correlations dominate. At the lowest twist angle 0.79°, superconductivity appears despite the absence of any insulating states. By changing the moire twist angle, the ratio between Coulomb interactions and kinetic energy is reduced, and we thus established a hierarchy of various symmetry-breaking orders. Importantly, superconductivity is tightly related to the half-filling symmetry-breaking reconstructions. We further generalize the twisted moire graphene to trilayer, quadrilayer and pentalayer cases. Characterizations around their respective magic angle show that superconductivity is more prominent in filling phase space when the number of layers is increased. We then investigated the effect of SOC on correlated phases in crystalline Bernal-stacked bilayer graphene. Surprisingly, placing monolayer WSe₂ on bilayer graphene promotes Cooper pairing to an extraordinary degree: field-induced superconductivity is stabilized at zero magnetic field, exhibits an order of magnitude enhancement in critical temperature and occurs over a density range that is wider by a factor of eight. The superconductivity descends from a broken-symmetry parent state with two out of the four spin-valley flavors being predominantly populated. Moreover, the superconductivity arises only for perpendicular electric fields that push hole wavefunctions toward WSe₂, indicating that proximity-induced Ising spin-orbit coupling plays a key role in stabilizing the pairing. The last part of the thesis focuses on a new degree of freedom: interfacial twisting between graphene and WSe₂. We experimentally demonstrate the "moireless" tuning of superconductivity in Bernal bilayer graphene proximitized by WSe₂. The precise alignment between the two materials systematically controls the strength of the induced Ising SOC, profoundly altering the phase diagram. As Ising SOC is increased, superconductivity onsets at a higher displacement field and features a higher critical temperature, reaching up to 0.5K. Within the main superconducting dome and in the strong Ising SOC limit, we find an unusual phase transition characterized by a nematic redistribution of holes among trigonally warped Fermi pockets and enhanced resilience to in-plane magnetic fields. Moreover, we identify two additional superconducting regions, one of which descends from an inter-valley coherent normal state and exhibits a Pauli-limit violation ratio exceeding 40, among the highest for all known superconductors.