Spin-Valley Anderson Impurity for Moir\'e Systems: Fermi Liquid, Pairing, and Pseudogap

TL;DR

This paper analytically explores a spin-valley Anderson impurity model relevant to magic-angle graphene, revealing rich phase transitions, pairing mechanisms, and pseudogap phenomena driven by Hund's interactions, with implications for moiré systems.

Contribution

It provides a comprehensive analytical phase diagram for the spin-valley Anderson impurity, uncovering the origins of pairing and pseudogap phenomena in moiré materials.

Findings

J_D drives a BKT transition to an anisotropic doublet phase.

J_S induces a transition to a local singlet phase with a non-Fermi liquid critical point.

Pseudogap shoulders in spectral functions are multiplet excitations caused by added electrons or holes.

Abstract

Recent experiments support that the magic-angle graphene can be modeled by a periodic array of correlated quantum impurities, immersed in a Dirac sea. This work analytically tackles a spin-valley Anderson impurity, featuring a general (anti-)Hund's interaction ($J_D, J_S$) that can originate from electron-phonon couplings. We derive its full phase diagram, which encompasses rich continuous local phase transitions, and presents a unified origin for pairing potential and pseudogap. In particular, $J_D$ favors a valley doublet, and we show it drives a BKT transition out of heavy Fermi liquid, to an anisotropic doublet phase exhibiting a non-analytic zero-energy kink in the impurity spectral function. $J_S$ drives a second-order transition out of heavy Fermi liquid, to a local singlet phase, with a non-Fermi liquid critical point. We analyze the pairing potential across the phase diagram, and unveil their ubiquitous existence triggered by the (anti-)Hund's multiplet splitting. Crucially, we show the pseudogap shoulders in the spectral function represent multiplet excitations induced by an injected electron or hole. All results are obtained analytically, using techniques including bosonization-refermionization, with further verification by numerical renormalization group calculations. Then we derive the correlation self-energy ansa\"tze that account for pseudogap, and apply to the magic-angle graphene lattice.