  The t-J model is a paradigmatic model for the study of strongly correlated
electron systems. In particular, it has been argued that it is an appropriate
model to describe the cuprate high-Tc superconductors. It turns out that a
comprehensive understanding of the gamut of physics encoded by the t-J model is
still an open problem. In recent years some remarkable experiments on the
cuprates, for example, discovery of nodeless superconductivity in underdoped
samples (PNAS 109, 18332 (2012)), discovery of s-wave like gap in the pseudogap
phase (Phys. Rev. Lett. 111, 107001 (2013)), and observation of polar Kerr
effect (PKE) (Phys. Rev. Lett. 112, 047003 (2014)), have thrown up new
challenges for this model. Here, we present results demonstrating that, within
the slave-particle formulation of the t-J model, the d-wave superconductor is
unstable at low doping to its own anti-symmetric phase mode fluctuations when
the effect of fluctuations is treated self-consistently. We then show that this
instability gives way to a time reversal symmetry broken d + is-SC in the
underdoped region which has superfluid stiffness consistent with Uemura
relation, even with a large pair amplitude. We show that our results are
consistent with existing experiments on cuprates and suggest that Josephson
(SQUID interferometry) experiments can clearly distinguish the d+is-SC from a
host of other possibilities alluded to be contributing to the physics of
underdoped cuprates. We also comment on other theoretical studies vis-a-vis
ours.
