Superconductivity phase diagram in the gauge-field description of thet-Jmodel

We analyze the effect that the gauge field has on the superconducting transition temperature in the t-J model. Mean-field theories of the t-J model tend to predict d-wave superconductivity at a very high temperature of the order of Tc⁰{}0.15 J. We will show that this transition temperature is suppressed, if one takes a fluctuating gauge field into account. The underlying idea is that there is a significant reduction of free energy due to gauge-field fluctuations, which is partly lost when a superconducting gap opens up. This cost of energy prevents the system from going into a superconducting state. Superconductivity is only possible at an intermediate range of doping, when the superfluid density of holons is sufficiently large to stiffen the gauge field. These ideas are supported by a numerical analysis. We obtained a phase diagram in the doping-temperature plane, that shows that for t/J=3 the optimal Tc occurs at a doping of x{}0.15. One consequence of our analysis is that in this model the spin-gap phase is completely destroyed by gauge-field fluctuations.