Quantum critical scaling and superconductivity in heavy electron materials

Yi-feng Yang, David Pines, and N. J. Curro

Phys. Rev. B 92, 195131 – Published 17 November 2015

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.

Received 2 October 2014
Revised 2 November 2015

DOI:https://doi.org/10.1103/PhysRevB.92.195131

Authors & Affiliations

Yi-feng Yang^1,2,*, David Pines^3,4, and N. J. Curro³

¹Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
²Collaborative Innovation Center of Quantum Matter, Beijing 100190, China
³Department of Physics, University of California, Davis, California 95616, USA
⁴Santa Fe Institute, Santa Fe, New Mexico 87501, USA

^*yifeng@iphy.ac.cn

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 92, Iss. 19 — 15 November 2015

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
The scaling of the spin-lattice relaxation rate with temperature normalized by the superconducting transition temperature for a number of heavy electron superconductors at pressures near that at which $T_{c}$ is maximum [1, 2]. The solid line represents an approximate scaling relation for $T_{c} < T < T^{*} / 2$ , see Eq. (6). The analysis is extended to higher temperatures in the inset, where the arrows indicate $T^{*}$ . The pressure $p_{L}$ at which $T_{c}$ is maximum is not known for ${PuCoGa}_{5}$ ; it is 1.4 GPa for ${CeCoIn}_{5}$ and 2.4 GPa for ${CeRhIn}_{5}$ , values that differ somewhat from those for which data is currently available.
Reuse & Permissions
Figure 2
A schematic phase diagram for heavy electron superconductors that is based on the application of the two-fluid model to the pressure-induced changes in the behavior of ${CeCoIn}_{5}$ and ${CeRhIn}_{5}$ [13, 14]. It shows the coherence temperature $T^{*} (> 30 T_{c})$ at which itinerant heavy electrons emerge to form a Kondo liquid and the delocalization line $T_{L}$ that marks the boundary between fully itinerant and partially localized heavy electron quasiparticles. Note that $T_{c}$ is maximum at the pressure $p_{L}$ at which $T_{c} = T_{L}$ , and, as shown in the text, this provides a link between $T_{c}$ and $T^{*}$ . Importantly, at $p_{L}$ , between $T^{*}$ and $T_{c}$ , both the hybridized local spin liquid and the itinerant Kondo liquid contribute to the spin lattice relaxation rate.
Reuse & Permissions
Figure 3
Probing quantum critical scaling behavior in a number of heavy electron materials [1, 2, 16, 17, 18] by plotting the spin-lattice relaxation rate against ${(1 - T / T^{*})}^{3 / 2}$ . The arrows indicate the temperature where the scaling fails. Note that temperature decreases from $T^{*}$ to zero as one goes from right to left on the horizontal axis. While in most of these materials the spin-lattice relaxation rate decreases as the temperature falls below $T^{*}$ and scales with the strength of the heavy electron component down to some low temperature (indicated by arrows), note that ${CeCu}_{2} {Si}_{2}$ and ${YbRh}_{2} {Si}_{2}$ exhibit markedly different behavior.
Reuse & Permissions
Figure 4
Comparison of theory and experiment for the spin-lattice relaxation rate in several heavy electron superconductors. (a) The scaling of $T_{1}$ as a function of $T / T^{*}$ . The solid line is the proposed scaling formula with $t_{0} = 2.7$ . (b) The total $1 / T_{1}$ and the Kondo liquid contribution for ${CeRhIn}_{5}$ at 2.7 GPa. The inset shows the intrinsic Kondo liquid term $1 / T_{1}^{K L}$ derived after subtracting the spin liquid contribution. The (solid and dashed) lines are fit to experiment using $T_{1}^{K L} T \sim (T + T_{0})$ with $T_{0} = 3$ K for ${CeRhIn}_{5}$ .
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics