U(1) Gauge Field, t′-J Model and Superconductivity

Abstract

We argue that the physics of the oxide superconductors may be represented by the t-t′-J model, where J is the exchange, t_ij is the hopping between opposite sublattices and t′_ij is the hopping between the same sublattice. Here the sublattices A and B are introduced as labels only, without assuming long range antiferromagnetic order. The hopping terms t and t′ have very different physical consequences. The t term disorders the local antiferromagnetic ordering as the hole hops. This leads to an enhancement of the hole mass for the coherent motion of the hole. At the same time, the t term may lead to a spiral structure, as described by Shraiman and Siggia. Thus the t term may be responsible for the destruction of long range order upon doping. The t′ term, on the other hand, allows the hole to hop without disordering the spin. Nevertheless, as the hole makes a closed loop on one sublattice, it is subject to a slowly varying spin quantization axis and the hole wavefunction picks up a phase equal to half the solid angle subtended by the spin orientations around the loop. The phase can be represented by an Aharonov-Bohm flux, resulting in a U(1) gauge theory, as first pointed out by Wiegmann. There is a natural attraction between holes on opposite sublattices because they experience opposite Aharonov-Bohm fluxes. We treat the gauge theory in the presence of a finite concentration of holes and describe the resulting superconductivity. The gauge field also enhances coupling to particle-hole excitations, leading to a T^4/3 law for the normal state resistivity.