Spin-Valley Anderson Impurity in Moiré Systems: Phase Diagram, Pairing, and Pseudogap

Recent experiments support that the magic-angle graphene family can be modeled by a periodic array of correlated quantum impurities immersed in a Dirac sea. This work analytically demonstrates that, with (anti-) Hund’s interactions that can originate from electron-phonon couplings, a single impurity can exhibit novel quantum phase transitions, and readily nurture the pairing potential and pseudogap phenomenon relevant to this moiré family. For broad applicability, we tackle a spin-valley Anderson impurity with general symmetry-allowed (anti-) Hund’s parameters (J_D, J_S), and derive its full phase diagram at half-filling. While the model reduces to well-known Kondo problems in certain limits, we uncover that in the large J_D regime, the low-energy physics is controlled by a novel “pair-Kondo” coupling between the bath and an impurity valley-doublet. Using bosonization–refermionization mapping, we show there is a BKT transition from a Fermi liquid with pairKondo resonance, into an anisotropic doublet phase that exhibits a non-analytic zero-energy kink in the impurity spectral function, and non-universal power-law scaling in impurity susceptibilities. Importantly, by analyzing the pairing potentials across the phase diagram, we unveil ubiquitous existence of attractive channels under general (anti-) Hund’s interactions. More crucially, we analytically reveal the pseudogap shoulders represent multiplet excitations induced by the injected electron or hole, and derive ansätze of correlation self-energy that reproduce the pseudogap phenomenon in the lattice. All results are established analytically, with further verification by numerical renormalization group calculations.