Influence Of Flatband Structure On The Robustness Of Superfluidity:Creutz Lattices As An Example

Band dispersion of electrons in flat band does not depend on momentum,and the electrons in the flat band range have a great density of states,as a result,flat band leads to strong correlation.Superfluidity is a typical strong correlation phenomenon.Researches have shown that systems exhibit flat bands are more rubust on superfluidity.Cruetz lattice with flat band on its ground state is a typical example of flat band structure.As a contrast,two-legs ladder lattice,the ground state of which is dispensional band,is also researched.In this work,we use attractive Hubbard model to research the two lattices.Quenched disorders are added to both two-legs ladder lattice and Creutz lattice so that the robustness of superconductivity can be researched.Observes we calculated include binding energy,Drude Weight and several correlation functions.Numerical method we use includes density matrix renormalization group(DMRG)and various matrix product state(MPS)algorithmsIntroducing disorder to lattices will localize electrons and lead to superconductorinsulator transition.Different results are given on the effect of disorder to superconducting states:some researchers suggest that disorder will first break paring,changing the system into metal phase.As the disorder increase,the system enters the single particle localized insulating state.Other research implied that disorder will directly destroy the coherence of paring.The system turns into Cooper pair insulator.Our results suggest that paring and superconductivity of Creutz lattice are more robust.What is more,different types of disorder effect differently on superconductivity.For random chemical potential on sites,influence on paring is weak,while effects on Drude weight and correlation function are significant.On the other hand,random Zeeman field on sites will break paring and coherent almost simultaneously without passing through the metal phase.