Hidden Crossover Phenomena in Strongly Pauli Limited Multiband Superconductors ---Application to CeCu$_2$Si$_2$

TL;DR

This paper develops a theoretical framework for multiband superconductors with strong Pauli effects, explaining hidden crossover phenomena and anomalies observed in CeCu$_2$Si$_2$ and related materials.

Contribution

It introduces a self-consistent microscopic theory revealing hidden crossover phenomena in multiband superconductors under strong Pauli effects, explaining experimental anomalies.

Findings

Upper critical field remains second order despite strong Pauli effects.

Hidden first order transition manifests as a crossover within $H_{c2}$.

Explains anomalies and vortex core states observed in STM experiments.

Abstract

Motivated by recent experiments on heavy fermion materials CeCu$_2$Si$_2$ and UBe$_{13}$, we develop a framework to capture generic properties of multiband superconductors with strong Pauli paramagnetic effect (PPE). In contrast to the single band case, the upper critical field $H_{\rm c2}$ can remain second order transition even for strong PPE cases. The expected first order transition is hidden inside $H_{\rm c2}$ and becomes a crossover due to the interplay of multibandness. The present theory based on full self-consistent solutions of the microscopic Eilenberger theory explains several mysterious anomalies associated with the crossover and the "empty" vortex core state which is observed by recent STM experiment on CeCu$_2$Si$_2$.