Vibronic Polarons and Electric Current Generation by a Berry Phase in Cuprate Superconductors

Abstract

High temperature superconductivity in cuprates occurs upon hole doping in half-filled antiferromagnetic insulating parent compounds. This insulating state is often called, a “Mott insulator” state, in which strong on-site Coulomb repulsion is the origin of the insulating behavior. Superconductivity occurs upon hole (or electron) doping in this state. In addition to the strong on-site Coulomb repulsion, a number of experimental and theoretical results indicate that strong hole-lattice interactions are present; the interactions are so strong that doped-holes become small polarons at low temperatures. In this review, we discuss the small polaron formation and its consequences in the superconductivity in cuprates. First, we will present some experimental and theoretical results that indicate the presence of strong interactions between doped-holes and the underlying lattice; especially, it is worth mentioning that a recent EXAFS experiment on La_{1. 85}Sr_{0. 15}Cu_{1 − x} M _x O₄ (M=Mn, Ni, Co) reveals a direct connection between the local lattice distortion and superconductivity. When small polarons are formed, the mobility of the holes becomes very small; then, the system behaves as an “effectively half-filled Mott insulator (EHMI)” to an external perturbation whose interaction time is much shorter than the hole-hopping life-time. We argue that this EHFMI state is adequate for explaining the magnetic excitation spectrum in the cuprate; actually, the “hourglass-shaped magnetic excitation spectrum” is explained due to spin-wave excitations in the presence of spin–vortices with their centers at hole-occupied sites. The spin-wave excitations are composed of two types: the first (Mode I) is the one exhibits antiferromagetic dispersion for high energy excitations, and the other (Mode II), which is a novel one, is the one has a sharp commensurate peak at the maximum excitation energy, and a broadened dispersion at energies below; this novel spin-wave excitations explain the Drude-like peak in the optical conductivity. Next, we will present a novel current generation mechanism that is compatible with the small polaron and spin–vortex formations. The unit of the current is a loop current around each spin–vortex; and a macroscopic current is generated as a collection of loop currents. The existence of such loop currents in the cuprate is supported by the fact that the enhanced Nernst signal observed in the pseudogap phase is explained by the flow of the loop currents. Lastly, we present an implication of the new current generation mechanism in the cuprate superconductivity; we will show that the superconducting transition in the underdoped cuprate is explained as an order–disorder transition of the loop currents.