# Linear in Temperature Resistivity and Associated Mysteries

## TL;DR

This paper presents a theory based on the dissipative 2D-XY model that explains various experimental observations in cuprates and heavy fermion compounds, including resistivity, specific heat, and scattering rates, through a unified quantum-critical framework.

## Contribution

It introduces a novel quantum-criticality theory using the dissipative 2D-XY model that accounts for multiple experimental phenomena with a single coupling parameter.

## Key findings

- Explains linear resistivity and specific heat behaviors.
- Identifies a common energy scale from different experiments.
- Describes the formation of a marginal Fermi-liquid state.

## Abstract

Recent experimental results: (i) the measurement of the $T \ln T$ specific heat in cuprates and the earlier such results in some heavy fermion compounds, (ii) the measurement of the single-particle scattering rates, (iii) the density fluctuation spectrum in cuprates and (iv) the long standing results on the linear temperature dependence of the resistivity, show that a theory of the quantum-criticality in these compounds based on the solution of the dissipative 2D - XY model gives the temperature and frequency dependence of each of them, and the magnitudes of all four with one dimensionless coupling parameter. These low frequency or temperature dependences persist to an upper cut-off which is measured to be about the same from the singularity in the specific heat or the saturation of the single-particle self-energy. The same two parameters are deduced in the analysis of results of photoemission experiments to give d-wave superconductivity and its transition temperature. The coupling parameter and the cut-off had been estimated in the microscopic theory to within a factor of 2. The simplicity of the results depends on the discovery that orthogonal topological excitations in space and in time determine the fluctuations near criticality such that the space and time metrics are free of each other. The interacting fermions then form a marginal Fermi-liquid.

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Source: https://tomesphere.com/paper/1908.05686