Quantum critical scaling and superconductivity in heavy electron materials

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.