Superconducting Transition Temperatures for Spin-Fluctuation Promoted Superconductivity in Heavy Fermion Compounds

Abstract

The quantum critical Antiferromagnetic (AFM) fluctuation spectra measured by inelastic neutron scattering recently in two heavy fermion superconductors are used together with their other measured properties to calculate their D-wave superconducting transition temperatures $T_{\mathrm{c}}$. To this end, the linearized Eliashberg equations for D-wave superconductivity induced by AFM fluctuations are solved in models of fermions with various levels of nesting. The results for the ratio of $T_{\mathrm{c}}$ to the characteristic spin-fluctuation energy are well parametrized by a dimensionless coupling constant and the AFM correlation length. Comparing the results with experiments suggests that one may reasonably conclude that superconductivity in these compounds is indeed caused by AFM fluctuations. This conclusion is strengthened by a calculation with the same parameters of the measured coefficient of the normal state quantum-critical resistivity $\propto T^{3/2}$ characteristic of {\it gaussian} AFM quantum-critical fluctuations. The calculations give details of the superconducting coupling as a function of the correlation length and the integrated fluctuation spectra useful in other compounds.

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Cited by in corpus (13)

• Quantum-Critical Fluctuations in 2D Metals: Strange Metals and Superconductivity in Antiferromagnets and in Cuprates
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• Gap symmetry of the heavy fermion superconductor CeCu${}_2$Si${}_2$ at ambient pressure
• Quantum Criticality in Quasi-Two Dimensional Itinerant Antiferromagnets
• CeIrIn5: Superconductivity on a Magnetic Instability
• d-wave superconductivity in the frustrated two-dimensional periodic Anderson model
• Pseudogap, van Hove Singularity, Maximum in Entropy and Specific Heat for Hole-Doped Mott Insulators
• Interplay between unconventional superconductivity and heavy-fermion quantum criticality: CeCu${}_2$Si${}_2$ versus YbRh${}_2$Si${}_2$
• Quantum critical response function in quasi-two dimensional itinerant antiferromagnets
• Nearly-degenerate $p_x+i{p}_y$ and $d_{x^2-y^2}$ pairing symmetry in the heavy fermion superconductor YbRh${}_2$Si${}_2$
• The Structure of the Nucleon: Elastic Electromagnetic Form Factors
• A Simple Solvable Model for Heavy Fermion Superconductivity from the Two-Fluid Normal State
• Quantitative Determination of the Pairing Interactions for High Temperature Superconductivity in Cuprates