Trions in Twisted Bilayer Graphene

TL;DR

This paper investigates the existence and properties of trion bound states in twisted bilayer graphene, revealing their role as low-energy charge excitations and analyzing their dependence on system parameters and screening lengths.

Contribution

It demonstrates that trion bound states are the lowest charge +1 excitations at certain fillings and explores their existence conditions across various parameters in twisted bilayer graphene.

Findings

Trion bound states are lowest charge +1 excitations at specific fillings.

Existence of trions depends on momentum range and system parameters.

Trions disappear at realistic coupling ratios, indicating limited stability.

Abstract

The strong coupling phase diagram of magic angle twisted bilayer graphene (TBG) predicts a series of exact one particle charge $\pm 1$ gapped excitations on top of the integer-filled ferromagnetic ground-states. Finite-size exact diagonalization studies showed that these are the lowest charge $\pm 1$ excitations in the system (for $10$nm screening length), with the exception of charge $+1$ at filling $-1$ in the chiral limit. In the current paper we show that this "trion bound state", a $3$-particle, charge $1$ excitation of the insulating ferromagnetic ground-state of the projected Hamiltonian of TBG is the lowest charge $+1$ overall excitation at $\nu=-1$, and also for some large ($\approx 20$nm) screening lengths at $\nu=-2$ in the chiral limit and with very small binding energy. At other fillings, we show that trion bound states do exist, but only for momentum ranges that do not cover the entire moir\'e Brillouin zone. The trion bound states (at different momenta) exist for finite parameter range $w_0/w_1$ but they all disappear in the continuum far below the realistic values of $w_0/w_1= 0.8$. We find the conditions for the existence of the trion bound state, a good variational wavefunction for it, and investigate its behavior for different screening lengths, at all integer fillings, on both the electron and hole sides.