Exact diagonalization study of the effects of Zn and Ni impurities on the pseudogap of underdoped cupratehigh-Tcsuperconductors

Abstract

The influence of Zn and Ni impurities on the normal-state pseudogap of underdoped $\text{high-}{T}_{c}$ cuprate superconductors is studied using exact diagonalization of effective $t\ensuremath{-}J\text{-like}$ Hamiltonians describing low energy electronic excitations of the ${\mathrm{CuO}}_{2}$ plane with some of the copper ions replaced with Zn/Ni. The Ni case Hamiltonian has been obtained by a sequence of approximations from a more complete model involving Cu $3d$, Ni $3d$, and O $2p$ orbitals. Our main findings are: (i) The width ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{PG}}$ of the pseudogap occurring in the many body density of states, and manifesting itself also in the $c\text{-axis}$ infrared conductivity, decreases with increasing Zn concentration as a consequence of a suppression of short range spin correlations. (ii) In the case of one hole and one Ni impurity, the hole is---for realistic values of the model parameters---weakly bound to the Ni site. This causes a slight increase of ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{PG}}$ with respect to the pure case. (iii) Based on this result and further results for 1--2 holes and 1--2 Ni impurities, we suggest that in the real Ni substituted ${\mathrm{CuO}}_{2}$ plane ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{PG}}$ is larger than in the pure case due to the binding of the doped holes to the Ni sites and effective underdoping. Our findings clarify the trends observed in the $c\text{-axis}$ infrared conductivity data of Zn and Ni substituted (Sm,Nd)${\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ crystals.