Fermi-liquid versus non-Fermi-liquid/'strange-metal' fits to the electrical resistivity in the quantum critical magnetic regime of an unconventional superconductor

Abstract

The question of a possible quantum critical point lying inside of a superconducting phase is central for understanding unconventional superconductivity. In various unconventional superconductors, non-Fermi-liquid/'strange-metal' $T^n$ variations, with $n<2$, of the electrical resistivity have been identified as the signature of magnetic quantum criticality. However, a difficulty is to prove experimentally that a non-Fermi-liquid/'strange-metal' law identified at temperatures above the superconducting temperature is the signature of an intrinsic zero-temperature quantum critical regime. In the heavy-fermion paramagnet UTe${}_2$, unconventional superconductivity develops in the vicinity of a metamagnetic quantum phase transition induced by a magnetic field, and the quantum critical magnetic properties are suspected to play a role for the superconducting mechanism. In this work, we present a comparative analysis of electrical resistivity data collected on two UTe${}_2$ samples of different qualities, in magnetic fields tilted by angles $\hat{I}¸\simeq 35-40$~${}^{\circ }$ from $\mathbf{b}$ to $\mathbf{c}$. Fits to the data have been performed either with a Fermi-liquid function $\ddot{I}=\ddot{I}{}_0+A{T}^2$ or with a non-Fermi-liquid/'strange-metal' function $\ddot{I}=\ddot{I}{}_0+A_n{T}^n$. Near to a superconducting phase induced beyond 40~T, non-physical residual resistivities $\ddot{I}{}_0<0$ are extracted from the $T^n$ fits, revealing that a 'hidden' Fermi-liquid $T^2$ regime may be ultimately recovered at low temperature. The results obtained here highlight the importance to investigate high-quality samples with low residual resistivity to confirm - or not - the presence of a suspected 'hidden' quantum critical behavior masked by superconductivity.

7 pages, 5 figures