# Selective mass enhancement close to the quantum critical point in BaFe$_2$(As$_{1-x}$P$_x$)$_2$

## TL;DR

This study investigates the behavior of the upper critical field in BaFe$_2$(As$_{1-x}$P$_x$)$_2$ near its quantum critical point, revealing band-dependent effective mass enhancement and dual electron groups, which advances understanding of quantum criticality in superconductors.

## Contribution

The paper provides the first high-field $H_{c2}$ measurements in thin films of BaFe$_2$(As$_{1-x}$P$_x$)$_2$, demonstrating band-dependent mass enhancement near the QCP and revealing dual electron behavior.

## Key findings

- Significant charge carrier mass enhancement at the QCP.
- Identification of two electron groups with different sensitivities to the QCP.
- Evidence of band-dependent quantum critical effects in superconducting properties.

## Abstract

A quantum critical point (QCP) is currently being conjectured for the BaFe$_2$(As$_{1-x}$P$_x$)$_2$ system at the critical value $x_{\rm c} \approx$ 0.3. In the proximity of a QCP, all thermodynamic and transport properties are expected to scale with a single characteristic energy, given by the quantum fluctuations. Such an universal behavior has not, however, been found in the superconducting upper critical field $H_{\rm c2}$. Here we report $H_{\rm c2}$-data for epitaxial thin films extracted from the electrical resistance measured in very high magnetic fields up to 67 Tesla. Using a multi-band analysis we find that $H_{\rm c2}$ is sensitive to the QCP, implying a significant charge carrier effective mass enhancement at the doping-induced QCP that is essentially band-dependent. Our results point to two qualitatively different groups of electrons in BaFe$_2$(As$_{1-x}$P$_x$)$_2$. The first one (possibly associated to hot spots or whole Fermi sheets) has a strong mass enhancement at the QCP, and the second one is insensitive to the QCP. The observed duality could also be present in many other quantum critical systems.