# Spin Liquids and Pseudogap Metals in $SU(4)$ Hubbard Model in Moir\'e Superlattice

## TL;DR

This paper explores novel Mott insulating phases and pseudogap metals in an $SU(4)$ Hubbard model on moiré superlattices, revealing potential unconventional metallic states with small Fermi surfaces and phase transitions.

## Contribution

It introduces symmetry-based constraints and parton mean field theories to identify new symmetric spin liquids and pseudogap metals in the $SU(4)$ Hubbard model relevant to moiré materials.

## Key findings

- Existence of symmetric, featureless pseudogap metals with small Fermi surfaces.
- Identification of two symmetric $Z_2$ spin liquids at the $SU(4)$ symmetric point.
- Proposal of a phase evolution from pseudogap metal to Fermi liquid via deconfined metal.

## Abstract

Motivated by the realization of spin-valley Hubbard on triangular moir\'e superlattice in ABC trilayer graphene aligned with hexagon boron nitride (hBN) and possibly also in twisted transition metal dichalcogenide homobilayers, we study possible Mott insulating phases and pseudogap metals based on symmetry constraint and parton mean field theories. First we show that Luttinger constraint allows two distinct symmetric and featureless Fermi liquids when there is an inter-valley Hund's term breaking $SU(4)$ spin rotation. Especially, there exists a symmetric and featureless "pseudogap metal" with small Fermi surfaces. Then we suggest to search for such an unconventional metallic state by doping the Mott insulator at $\nu_T=2$. For this purpose, we study the $\nu_T=2$ Mott insulator using $SO(6)$ Schwinger boson or Schwinger fermion parton. At the $SU(4)$ symmetric point, we find two symmetric $Z_2$ spin liquids. With a large anti inter-valley Hund's term, a featureless Mott insulator is natural. Next we show that doping the featureless Mott insulator or a $Z_2$ spin liquid can lead to featureless or orthogonal "pseudogap metal" with small Fermi surfaces proportional to the doping. Besides, we also provide one scenario for the evolution from "pseudogap metal" to the conventional Fermi liquid through an intermediate exotic "deconfined metal" phase. Last, we give brief comments on the possibility of $U(1)$ spinon fermi surface state or $Z_4$ spin liquid at $\nu_T=1$.