Ancilla Theory of Mott Physics: from Cuprate to Twisted Bilayer Graphene

I will introduce a new formalism to capture (partial) Mott localization in both the conventional Hubbard model and in topological flat band relevant to  the twisted bilayer graphene (TBG).    I will first demonstrate that this framework reproduces the known results of the Mott insulator.  Then I will show two applications on more exotic  states which are challenging to describe using conventional methods.  (1) In the context of high Tc cuprate, we can construct a fractional fermi liquid (FL*) phase  which host both small hole pocket and localized  spin moments at filling n=1-p.  Our theory may provide an explanation of the ‘Fermi arcs’ observed in under doped cuprate;  (2) In TBG,  ancilla theory can capture Mott physics directly in momentum space without the need of a lattice model with Wannier orbital.   In this language, Mott gap is the hybridization gap between the physical band and an ancilla band.  In TBG, the hybridization is equal to U at momentum away from Gamma, but is constrained to have a node at Gamma point, leading to a Mott semimetal instead of insulator at nu=0.  At nu=-1, -2, -3, there is a transition from a correlated insulator to Mott semimetal upon decreasing interaction.   Most interestingly, we propose a small Fermi surface pseudogap metal state at filling nu=-2-x, which may be the normal state of the superconductor.  At x=0 limit, the quasiparticle is dominated by a composite polaron with vanishing overlap with physical electron.  If time allowed, I will also comment on the potential mechanism of superconductivity in this framework.