Charge pair hopping and Bose-Einstein condensation in underdoped Mott insulators

Abstract

Recently, a renormalized Hamiltonian has been derived by continuing spin states from the Mott limit of the $t$-$J$ model to the underdoped region. We show that it naturally leads to a pairing mechanism in which the pair has a dual character. Its spin part is a spinon singlet that condenses at ${T}^{*}$. The charge part is a real-space holon pair formed at ${T}_{p}l{T}^{*}$, which undergoes a Bose-Einstein condensation at ${T}_{c}l{T}_{p}$. While neither is observable separately, the combination is predicted to be observable as a sharp excitation above and below ${T}_{c}$. The mechanism is consistent with the small superfluid density, the decline of ${T}_{c}$ at small doping, and the existence of pairs above ${T}_{c}$ in cuprates, indicated by the observation of diamagnetism and Nernst effect.