Research Projects

Flat band semimetal has been under consideration from theoretical perspective for a long time, as such system exhibits high density of states which can cause electron-electron interaction dominated physics like superconductivity or Mott's insulating state, at low temperature. In fact in early 90's, it was predicted that such semimetal might open-up a new route to high-Tc superconductor. It was theoretically predicted in 2011 that the twisted bilayer graphene (TBG) can exhibit such flat band at certain twist angle. The superconductivity in such flat band semimetal-like the TBG was discovered recently in 2018 and in twisted trilayer graphene in 2021. After the experimental works, several theoretical investigations about the mechanism and the origin of the superconductivity were carried out based on BCS approach, however the microscopic picture still remains unclear as several follow up experiments indicated unusual observations . The objectives of this project are multifold, firstly we want to study the electronic band structure of TBG and TTG made of deformed monolayer graphenes and examine how the magic angles are affected by lattice deformation. The lattice deformation might arise while giving a twist between the layers. Another intrinsic and unavoidable feature of moire’s lattice (the lattice structure of twisted bilayer or trilayer graphene) is the presence of angle disorderness. The role of such angle disorderness will be studied in a nanoribbon as well as in the bulk of a twisted layer materials, particularly in presence of irradiation. Subsequently we want to develop a theory of superconductivity within non-equilibrium frame- work for such twisted layered material at magic angle where flat band emerges. Here, we will take into account the space inhomogeneity of the superconducting order parameter. To do so we will adopt well-known Gorkov’s Green’s function approach followed by Eilenberger’s quasiclassical approximation, instead of BCS type. Then we will take into account the random disorder effects for which we adopt Usadel’s approach for dirty limit. After this we will include the effects of lattice deformation and angle disorderness in the electronic band structure and study the equilibrium superconductivity by using standard mandy-body path integral approach as well as non-equilibrium quasi-classical approximation, individually. We shall include the magnetic field also to study the Meissner effect. Lastly, we will include the effects of spin-orbit interaction term, external laser field and investigate topological aspects in presence of lattice deformation, above the superconducting critical temperature and very near to magic angle. The study will bring out a clear picture of microscopic origin of superconductivity and other low temperature quantum phenomena.