Speaker
Description
TBG and moire system have attracted huge interest in both experimantal and theoretical community due to its exotic strong correlated properties and rich phase diagram. However there is still lack of a general theory for arbitrary twisted angle without commensurate approximation. And the superconductive pairing mechanism in TBG is still controversial.
We propose a new kind of geometric theory for TBG. By using vierbein formalism one can
consider the coupling between Dirac fermion and effective curved space-time in single valley. The spin connection will act as a compact SU(2) gauge field to induce Landau level. This formalism is in principle valid for any twisted angle without dislocation. Numerical calculation indicates there are flat bands at the first magic angle θm1=1.05°with band width about 5meV, which is coincide with former results. When this effective curved space is embedded intothe background Euclidean space, the band will be non-hermitian in general. Moreover, such theory can be generalized to the situation for rotating bilayer graphene (RBG). RBG is hardly described by former theories. By investigating the Bott index for finite size RBG, we can relate the Bott index with corresponding charge pumping per driven period (as 2d Thouless pump). This theory may be verified by certain transportation experiment.
