Trions in twisted bilayer graphene

The strong-coupling phase diagram of magic-angle twisted bilayer graphene (TBG) predicts a series of exact one-particle charge ±1 gapped excitations on top of the integer-filled ferromagnetic ground states. Finite-size exact diagonalization studies showed that these are the lowest charge ±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 ν=-1, and also for some large (≈20 nm) screening lengths at ν=-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 moiré Brillouin zone. The trion bound states (at different momenta) exist for finite parameter range w0/w1 but they all disappear in the continuum far below the realistic values of w0/w1=0.8. We find the conditions for the existence of the trion bound state, a good variational wave function for it, and investigate its behavior for different screening lengths, at all integer fillings, on both the electron and hole sides.