Topological phases on Lieb Lattice

Abstract

We show that a Mott transition is possible in our model with a dimer placed on each site of a Lieb lattice. To illustrate this, we map the lattice problem to an impurity problem. Then we solve the impurity problem to show the Mott transition. We then investigate the band structure of the non-interacting problem using the tight binding approximation. We show that the band structure is topologically non-trivial. To check the stability of BCPs, we introduce di erent hoppings. We get quadratic band crossing points(QBCPs), tilted Dirac cones in the band structure. Then we introduce the electric eld in the system in z direction to see the e ect of inversion symmetry breaking. As the inversion symmetry is broken, we then introduce Rashba spin orbit coupling type interaction in the Hamiltonian to check its e ect on the BCPs. Finally, the model is mapped to a two orbital per site model. We are able to show that the topologically non-trivial features can be found in a system having an odd and an even parity orbital at each site.