# Dimensional crossover of quantum critical behavior in CeCoIn$_5$

## TL;DR

This study investigates the quantum critical behavior of CeCoIn$_5$ using low-temperature thermal expansion, revealing a dimensional crossover at a specific temperature and field, influenced by disorder, which alters the nature of quantum criticality.

## Contribution

It provides evidence for a dimensional crossover in quantum critical fluctuations in CeCoIn$_5$ and explores how disorder affects this crossover and the critical behavior.

## Key findings

- Identification of a crossover scale T* around 0.3 K at 5 T
- Observation of a change from T^{-1} to T^{-1/2} divergence in thermal expansion
- Disorder shifts T* to higher temperatures, affecting quantum criticality

## Abstract

The nature of quantum criticality in CeCoIn$_5$ is studied by low-temperature thermal expansion $\alpha(T)$. At the field-induced quantum critical point at H=5 T a crossover scale $T^\star\approx 0.3$ K is observed, separating $\alpha(T)/T\propto T^{-1}$ from a weaker $T^{-1/2}$ divergence. We ascribe this change to a crossover in the dimensionality of the critical fluctuations which may be coupled to a change from unconventional to conventional quantum criticality. Disorder, whose effect on quantum criticality is studied in CeCoIn$_{5-x}$Sn$_x$ ($0\leq x\leq 0.18$), shifts $T^\star$ towards higher temperatures.