CMSA Quantum Matter in Mathematics and Physics: Symmetry, Insulating States and Excitations of Twisted Bilayer Graphene with Coulomb Interaction

CMSA EVENTS

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October 29, 2020 10:30 am - 12:00 pm
via Zoom Video Conferencing
Speaker:

Biao Lian - Princeton

The twisted bilayer graphene (TBG) near the magic angle around 1 degree hosts topological flat moiré electron bands, and exhibits a rich tunable strongly interacting physics. Correlated insulators and Chern insulators have been observed at integer fillings nu=0,+-1,+-2,+-3 (number of electrons per moiré unit cell). I will first talk about the enhanced U(4) or U(4)xU(4) symmetries of the projected TBG Hamiltonian with Coulomb interaction in various combinations of the flat band limit and two chiral limits. The symmetries in the first chiral and/or flat limits allow us to identify exact or approximate ground/low-energy (Chern) insulator states at all the integer fillings nu under a weak assumption, and to exactly compute charge +-1, +-2 and neutral excitations. In the realistic case away from the first chiral and flat band limits, we find perturbatively that the ground state at integer fillings nu has Chern number +-mod(nu,2), which is intervalley coherent if nu=0,+-1,+-2, and is valley polarized if nu=+-3. We further show that at nu=+-1 and +-2, a first order phase transition to a Chern number 4-|nu| state occurs in an out-of-plane magnetic field. Our calculation of excitations also rules out the Cooper pairing at integer fillings nu from Coulomb interaction in the flat band limit, suggesting other superconductivity mechanisms. These analytical results at nonzero fillings are further verified by a full Hilbert space exact diagonalization (ED) calculation. Furthermore, our ED calculation for nu=-3 implies a phase transition to possible translationally breaking or metallic phases at large deviation from the first chiral limit.

Zoom: https://harvard.zoom.us/j/977347126