The discovery of magic-angle twisted trilayer graphene (tTLG) adds a new twist to the family of graphene moire. The additional graphene layer unlocks a series of intriguing properties in the superconducting phase, such as the violation of Pauli limit and re-entrant superconductivity at large in-plane magnetic field. In this work, we integrate magic-angle tTLG into a double-layer structure to study the superconducting phase. Utilizing proximity screening from the adjacent metallic layer, we examine the stability of the superconducting phase and demonstrate that Coulomb repulsion competes against the mechanism underlying Cooper pairing. Furthermore, we use a combination of transport and thermodynamic measurements to probe the isospin order, which shows that the isospin configuration at half moire filling, and for the nearby fermi surface, is spin-polarized and valley-unpolarized. In addition, we show that valley isospin plays a dominating role in the Pomeranchuk effect, whereas the spin degree of freedom is frozen, which indicates small valley isospin stiffness and large spin stiffness in tTLG. Taken together, our findings provide important constraints for theoretical models aiming to understand the nature of superconductivity. A possible scenario is that electron-phonon coupling stabilizes a superconducting phase with a spin-triplet, valley singlet order parameter.
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