TY - JOUR
T1 - Trions in twisted bilayer graphene
AU - Schindler, Frank
AU - Vafek, Oskar
AU - Bernevig, B. Andrei
N1 - Funding Information:
We thank F. Xie, S. Parameswaran, and Y. Kwan for discussions. F.S. was supported by a fellowship at the Princeton Center for Theoretical Science. O.V. was supported by NSF Grant No. DMR-1916958 and, in part, by NSF Grant No. DMR-1644779 and the state of Florida MagLab core grant. This work also received support from DOE Grant No. DE-SC0016239, the Schmidt Fund for Innovative Research, Simons Investigator Grant No. 404513, the Packard Foundation, the Gordon and Betty Moore Foundation through Grant No. GBMF8685 toward the Princeton theory program, and a Guggenheim Fellowship from the John Simon Guggenheim Memorial Foundation. Further support was provided by the NSF-MRSEC Grant No. DMR-2011750, ONR Grant No. N00014-20-1-2303, BSF Israel-US Foundation Grant No. 2018226, and the Princeton Global Network Funds.
Publisher Copyright:
© 2022 American Physical Society.
PY - 2022/4/15
Y1 - 2022/4/15
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevB.105.155135
DO - 10.1103/PhysRevB.105.155135
M3 - Article
AN - SCOPUS:85129021418
SN - 2469-9950
VL - 105
JO - Physical Review B
JF - Physical Review B
IS - 15
M1 - 155135
ER -