Nodal Protectorate: A Unified Theory of the ab-plane and c-axis Penetration Depths of Underdoped cuprates

TL;DR

This paper presents a unified model explaining the doping and temperature dependence of the penetration depths in underdoped cuprates, highlighting a 'nodal protectorate' where quasiparticles remain coherent.

Contribution

It introduces a phenomenological charge renormalization factor and a model of incoherent tunneling to describe penetration depths, revealing a protected nodal region shrinking with doping.

Findings

Existence of a 'nodal protectorate' region near the nodes.

Superfluid density originates mainly from the protected nodal regions.

Model aligns with experimental data on YBa2Cu3O6+δ.

Abstract

We formulate a model describing the doping ($x$) and temperature ($T$) dependence of the $ab$-plane and c-axis penetration depth of a cuprate superconductor. The model incorporates the suppression of the superfluid density with underdoping as the system approaches the Mott-Hubbard insulating state by augmenting a d-wave BCS model with a phenomenological charge renormalization factor that is vanishingly small for states away from the nodes of the d-wave pair potential but close to unity in the vicinity of the nodes. The c-axis penetration depth is captured within a model of incoherent electron tunneling between the CuO$_2$ planes. Application of this model to the recent experimental data on the high-purity single crystals of YBa$_2$Cu$_3$O$_{6+\delta}$ implies existence of a ``nodal protectorate'', a $k$-space region in the vicinity of the nodes whose size decreases in proportion to $x$, in which d-wave quasiparticles remain sharp even as the system teeters on the brink of becoming an insulator. The superfluid density, which is extremely small for these samples, also appears to come exclusively from these protected nodal regions.