The role of quantum fluctuations in the t-J model: Implications for cuprate superconductors

Abstract

The physics of strongly correlated electron systems is among the central problems of condensed matter physics. One of the outstanding problems in this category is that of the high-Tc superconductivity obtained by doping of insulating parent materials like some layered copper oxides. Since its discovery in 1986, this unconventional class of superconductors has motivated extensive experimental and theoretical studies. In the context of hole doped cuprates, most of the theories have focused on d-wave superconductivity, which is characterized by the presence of nodes in its gap structure. However, recent experiments suggest that underdoped cuprates can support node-less superconductivity. In a similar vein, while early experiments on cuprates had found that these materials don’t break time reversal symmetry, recent improved experiments reveal clear signatures of microscopic time reversal symmetry breaking in underdoped cuprates, manifesting in a non-zero Polar Kerr Effect (PKE) signal. In this thesis we aim to elucidate a mechanism to account for some of the important aspects of the above mentioned experiments, within the slave-particle formulation of the widely used t-J model. We show that in the presence of strong correlations, a d-wave superconductor (d-SC) on a 2D square lattice is generically susceptible to large fluctuations of its internal phase mode. Within a large-N extension of the t-J model, these fluctuations, at zero temperature, reduce the mean field d-wave pairing scale substantially in the underdoped region. This is in contrast with the experimentally observed pseudogap scale which increases almost linearly with underdoping, and hence, suggests that the physics of the cuprate pseudogap may not solely be attributable to preformed d-wave pairs. This may also help in understanding recent ARPES and STM experiments on cuprates which do report two distinct single particle gaps in the system. Furthermore, we present a fluctuation-consistent theory of the t-J model at zero temperature wherein we find that the inclusion of the quantum fluctuations leads to a d-SC to (d + is)-SC transition at a doping of ∼ 0.12 holes per unit cell, as one moves from the overdoped to the underdoped region. The qualitative behaviour of the d-SC pairing scale on the overdoped side is similar to that obtained in the large-N theory described before. The similarity and differences of these results with respect to other theories of the t-J model like those using cluster extensions of DMFT are discussed. We also describe how these results can help in understanding the phenomenology of underdoped cuprates. One of the important messages that come out of our study is that competing non-superconducting orders may not be essential to explain the fragility of the d-SC in the underdoped region. Rather, they might be arising opportunistically when the d-SC becomes unstable to its internal phase mode fluctuations, and makes a transition to the (d + is)-SC. Overdoped cuprate superconductors are also quite unusual, and, contrary to the general belief, have a small superfluid stiffness. The stiffness has also been shown to have peculiar dependence on temperature. We perform the relevant finite temperature calculations within the t-J model, and indeed, find that the superfluid stiffness thus obtained can, qualitatively, explain the unusual features of overdoped cuprates. We have also found that the Van Hove singularity in the electronic density of states seems to be one of the important factors behind the unusual nature of the superfluid stiffness in overdoped cuprates. Overall, this thesis brings forth some notable and interesting possibilities in understanding the physics of cuprate superconductors. An idea that stands out is that underdoped cuprates may have a prominent presence of (d + is) pairing. This will have important implications for the competing or intertwined order scenario proposed for underdoped cuprates, where typically a d-SC is assumed to be competing (intertwined) with other orders. The physics of moderately overdoped and underdoped cuprates at finite temperatures will also have to be revisited to incorporate the effect of soft internal phase mode fluctuations more carefully.