Weak phase stiffness and mass divergence of superfluid in underdoped cuprates

TL;DR

This paper introduces a simple, solvable model for underdoped cuprates that explains the soft phase fluctuations, mass divergence, and quantum critical point by mapping superconductivity to a dilute bosonic superfluid, aligning well with experimental observations.

Contribution

It proposes a new low-energy model that captures the superfluid behavior and phase softness in underdoped cuprates without free parameters, offering fresh insights into longstanding puzzles.

Findings

Prediction of a mass divergence at the quantum critical point

Reproduction of superfluid properties consistent with experiments

Identification of incoherent p-wave pairs dominating below 5.2% doping

Abstract

Despite more than two decades of intensive investigations, the true nature of high temperature (high-$T_c$) superconductivity observed in the cuprates remains elusive to the researchers. In particular, in the so-called `underdoped' region, the overall behavior of superconductivity deviates $qualitatively$ from the standard theoretical description pioneered by Bardeen, Cooper and Schrieffer (BCS). Recently, the importance of phase fluctuation of the superconducting order parameter has gained significant support from various experiments. However, the microscopic mechanism responsible for the surprisingly soft phase remains one of the most important unsolved puzzles. Here, opposite to the standard BCS starting point, we propose a simple, solvable low-energy model in the strong coupling limit, which maps the superconductivity literally into a well-understood physics of superfluid in a special dilute bosonic system of local pairs of doped holes. In the prototypical material (La$_{1-\delta}$Sr$_\delta$)$_2$CuO$_4$, without use of any free parameter, a $d$-wave superconductivity is obtained for doping above $\sim 5.2\%$, below which unexpected incoherent $p$-wave pairs dominate. Throughout the whole underdoped region, very soft phases are found to originate from enormous mass enhancement of the pairs. Furthermore, a striking mass divergence is predicted that dictates the occurrence of the observed quantum critical point. Our model produces properties of the superfluid in good agreement with the experiments, and provides new insights into several current puzzles. Owing to its simplicity, this model offers a paradigm of great value in answering the long-standing challenges in underdoped cuprates.