Thermodynamics and quantum criticality in cuprate superconductors

TL;DR

This paper uses scaling arguments to analyze thermodynamics near the quantum critical point in cuprate superconductors, revealing how specific heat and chemical potential measurements can uncover the nature of zero-temperature singularities.

Contribution

It extends the scaling analysis of the Grüneisen parameter to cuprates, providing new insights into the coupling constant scaling and the effective dimensionality.

Findings

Effective number of time dimensions equals space dimensions.

Six scaling laws govern chemical potential and temperature dependence.

Specific heat data indicates zero-temperature singularity characteristics.

Abstract

We will present elementary scaling arguments focussed on the thermodynamics in the proximity of the quantum critical point in the cuprate superconductors. Extending the analysis centered on the Gr\"uneisen parameter by Rosch, Si and coworkers to the cuprates, we demonstrate that a combination of specific heat- and chemical potential measurements can reveal the nature of the zero temperature singularity. From the known specific heat data it follows that the effective number of time dimensions has to equal the number of space dimensions, while we find a total of six scaling laws governing the temperature and density dependence of the chemical potential, revealing directly the coupling constant scaling dimension.