Single hole doped strongly correlated ladder with a static impurity

TL;DR

This paper investigates how a single hole interacts with static impurities in a strongly correlated ladder system, revealing impurity-dependent bound states and pair-breaking effects through analytical and numerical methods.

Contribution

It provides analytical solutions for impurity-hole bound states in a $t-J$ ladder with both non-magnetic and magnetic impurities, highlighting impurity effects on pairing.

Findings

Bound states form in singlet sector with increasing J/t

Maximum binding energy occurs with non-magnetic impurity

Impurities can break pairs, affecting superconductivity

Abstract

We consider a strongly correlated ladder with diagonal hopping and exchange interactions described by $t-J$ type hamiltonian. We study the dynamics of a single hole in this model in the presence of a static non-magnetic (or magnetic) impurity. In the case of a non-magnetic (NM) impurity we solve the problem analytically both in the triplet (S=1) and singlet (S=0) sectors. In the triplet sector the hole doesn't form any bound state with the impurity. However, in the singlet sector the hole forms bound states of different symmetries with increasing $J/t$ values. Binding energies of those impurity-hole bound states are compared with the binding energy of a pair of holes in absence of any impurity. In the case of magnetic impurity the analytical eigenvalue equations are solved for a large (50 X 2) lattice. In this case also, with increasing $J/t$ values, impurity-hole bound states of different symmetries are obtained. Binding of the hole with the impurity is favoured for the case of a ferromagnetic (FM) impurity than in the case of antiferromagnetic (AFM) impurity. However binding energy is found to be maximum for the NM impurity. Comparison of binding energies and various impurity-hole correlation functions indicates a pair breaking mechanism by NM impurity.