Universality in cuprates: a gauge approach

TL;DR

This paper presents a gauge-theoretic model for high-$T_c$ cuprates that explains the universal behavior of in-plane resistivity and superfluid density through spin-charge separation and gauge flux binding, aligning with experimental observations.

Contribution

It introduces a spin-charge gauge approach to cuprates that accounts for universality in response functions via spinon and holon contributions, emphasizing the dominance of spinons in underdoped regions.

Findings

The model reproduces universal in-plane resistivity and superfluid density behaviors.

Spinons dominate response functions in the underdoped regime, explaining non-Fermi-liquid universality.

Theoretical results align well with experimental data on cuprates.

Abstract

In high-$T_c$ cuprates many quantities exhibit a non-Fermi liquid universality hinting at a very peculiar structure of the underlying pairing mechanism for superconductivity: in this work we focus on the universality for the in-plane resistivity and for the superfluid density. We outline the previously developed spin-charge gauge approach to superconductivity in hole-doped cuprates: we decompose the hole of the $t-t'-J$ model for the $\mathrm{Cu}\mathrm{O}_2$ planes as the product of a spinful, chargeless gapped spinon and of a spinless, charged holon with Fermi surface. Each one of these particle excitations is bound to a statistical gauge flux, allowing one to optimize their statistics. We show that this model allows for a natural interpretation of the universality: within this approach, under suitable conditions, the spinonic and holonic contributions to a response function sum up according to a Ioffe-Larkin rule. We argue that, if the spinonic contribution dominates, then one should expect strongly non-Fermi-liquid-like universality, due to the insensitivity of spinons to Fermi surface details. The in-plane resistivity and superfluid density are indeed dominated by the spinons in the underdoped region. We theoretically derive these quantities, discussing their universal behaviours and comparing them with experimental data.