Orbital Orders and non-Fermi Liquid in Moir\'{e} systems

TL;DR

This paper investigates three potential orbital orders in Moiré systems, highlighting how their quantum fluctuations near phase transitions can lead to unique non-Fermi liquid behaviors and complex phase interactions.

Contribution

It introduces a novel effective theory for nematic order in Moiré systems, revealing unique non-Fermi liquid behavior and exploring the interplay among multiple orbital orders.

Findings

Distinct non-Fermi liquid behavior near nematic transition

Effective theory differs from standard Hertz-Millis formalism

Competition between orbital orders and superconductivity

Abstract

Motivated by recent observation of nematicity in Moir\'{e} systems, we study three different orbital orders that potentially can happen in Moir\'{e} systems: (1) the nematic order; (2) the valley polarization; and (3) the "compass order". Each order parameter spontaneously breaks part of the spatial symmetries of the system. We explore physics caused by the quantum fluctuations close to the order-disorder transition of these order parameters. Especially, we recognize that the symmetry of the Moir\'{e} systems leads to a crucial difference of the effective theory describing the nematic order from the standard Hertz-Millis formalism. We demonstrate that this key difference may lead to a special non-Fermi liquid behavior near the order-disorder nematic transition, different from the standard non-Fermi liquid behavior usually expected when a Fermi surface is coupled to the critical fluctuations of orbital orders. We also discuss the interplay of the three order parameters and the possible rich phase diagram at finite temperature. Within the three orbital orders, the valley polarization and the "compass order" likely strongly compete with the superconductor.