1. localization properties in disordered 2- and 3-dimensional lieb lattices and their extensions

Rudolf Roemer

University of Warwick, UK

30 March 2021 Tue 5 pm

                                      IBS Center for Theoretical Physics of Complex Systems (PCS), Administrative Office (B349), Theory Wing, 3rd floor

                                      Expo-ro 55, Yuseong-gu, Daejeon, South Korea, 34126 Tel: +82-42-878-8633                     

We study the localization properties of generalized, two- and three-dimensional Lieb lattices at energies corresponding to flat and dispersive bands using the transfer matrix method (TMM) and finite size scaling (FSS). We find that the scaling properties of the flat bands are different from scaling in dispersive bands for all studied Lieb lattices. For the d = 3 dimensional case, states are extended for very small disorder at the flat bands, indicating that the disorder can lift the degeneracy of the flat bands quickly. The phase diagram with periodic boundary condition for the simplest 3-dimensional Lieb lattice looks similar to the one for hard boundaries. We present the critical disorder at energy E = 0 and find it shows a decreasing value for increasing complexity of the Lieb lattices. Last, we give a table of FSS parameters including so-called irrelevant variables.