Many-body effects in twisted bilayer graphene at low twist angles

TL;DR

This paper investigates the many-body electronic properties of twisted bilayer graphene at the first magic angle, revealing interaction-induced band splitting, doping-dependent spectra, and emergent nematic states that align with recent experimental observations.

Contribution

The study introduces a model with excitonic order parameters showing how interactions lift degeneracies and produce doping-dependent spectral features in twisted bilayer graphene.

Findings

Interactions partially lift band degeneracy.

Doping causes oscillations in the density of states.

Emergence of a many-body nematic state near half-filling.

Abstract

We study the zero-temperature many-body properties of twisted bilayer graphene with a twist angle equal to the so-called `first magic angle'. The system low-energy single-electron spectrum consists of four (eight, if spin label is accounted) weakly-dispersing partially degenerate bands, each band accommodating one electron per Moir{\'{e}} cell per spin projection. This weak dispersion makes electrons particularly susceptible to the effects of interactions. Introducing several excitonic order parameters with spin-density-wave-like structure, we demonstrate that (i)~the band degeneracy is partially lifted by the interaction, and (ii)~the details of the low-energy spectrum becomes doping-dependent. For example, at or near the undoped state, interactions separate the eight bands into two quartets (one quartet is almost filled, the other is almost empty), while for two electrons per Moir\'{e} cell, the quartets are pulled apart, and doublets emerge. When the doping is equal to one or three electrons per cell, the doublets split into singlets. Hole doping produces similar effects. As a result, electronic properties (e.g., the density of states at the Fermi energy) demonstrate oscillating dependence on the doping concentration. This allows us to reproduce qualitatively the behavior of the conductance observed recently in experiments [Cao et al., Nature {\bf 556}, 80 (2018)]. Near half-filling, the electronic spectrum loses hexagonal symmetry indicating the appearance of a many-body nematic state.