Quantum critical scaling and superconductivity in heavy electron materials

TL;DR

This paper investigates the conditions for scaling behavior in the nuclear spin-lattice relaxation rate of heavy electron superconductors, linking it to quantum critical spin fluctuations and providing a test for their presence at optimal superconductivity.

Contribution

It introduces a model-based criterion for scaling in $T_1$, connecting it to quantum critical fluctuations and the coherence temperature in heavy electron materials.

Findings

Scaling in $T_1$ occurs if quantum critical spin fluctuations are temperature-independent.

The scaling of $T_1$ correlates with the strength of the heavy electron component and $T^*$.

Optimal superconductivity is linked to quantum critical spin fluctuations near a phase transition.

Abstract

We use the two fluid model to determine the conditions under which the nuclear spin-lattice lattice relaxation rate, $T_1$, of candidate heavy quantum critical superconductors can exhibit scaling behavior and find that it can occur if and only if their "hidden" quantum critical spin fluctuations give rise to a temperature-independent intrinsic heavy electron spin-lattice relaxation rate. The resulting scaling of $T_1$ with the strength of the heavy electron component and the coherence temperature, $T^*$, provides a simple test for their presence at pressures at which the superconducting transition temperature, $T_c$, is maximum and is proportional to $T^*$. These findings support the previously noted partial scaling of the spin-lattice relaxation rate with $T_c$ in a number of important heavy electron materials and provide additional evidence that in these materials their optimal superconductivity originates in the quantum critical spin fluctuations associated with a nearby phase transition from partially localized to fully itinerant quasiparticles.