## Heavy fermion superconductivity

### Publications

M. P. Allan & F. Massee et al., Nature Physics**9**, 468 (2013)

*Imaging Imaging Cooper pairing of heavy fermions in CeCoIn*

_{5}J. S. Van Dyke et al., PNAS

**111**, 11663 (2014)

*Direct evidence for a magnetic f-electron–mediated pairing mechanism of heavy-fermion superconductivity in CeCoIn*

_{5}Fig. 1: Atomically resolved surface structure of CeCoIn

_{5}.### Imaging Cooper pairing of heavy fermions in CeCoIn_{5}

The discovery of superconductivity in heavy fermion materials marked the birth of unconventional superconductivity. As with the subsequently found cuprates and iron pnictides, the Cooper pairing mechanism of heavy-fermion superconductors, while long hypothesized as due to spin fluctuations, has not been determined. It is the momentum space (k-space) structure of the superconducting energy gap Δ(k) that encodes specifics of this pairing mechanism. However, because the energy scales are so low, it has not been possible to directly measure Δ(k) for any heavy-fermion superconductor. Bogoliubov quasiparticle interference (QPI) imaging, a proven technique for measuring the energy gaps of high-T_{c}superconductors, has been proposed by Akbardi et al. (PRB

**84**, 134505 (2011)) as a new method to measure Δ(k) in heavy-fermion superconductors, specifically CeCoIn

_{5}.

Fig. 2: Δ(k) for CeCoIn

By implementing this method, we detect a superconducting energy gap whose nodes are oriented along k||(±1,±1)π/a_{5}._{0}directions. Moreover, we determine the detailed structure of its multiband energy gaps Δ

_{i}(k). For CeCoIn

_{5}, this information includes: the complex band structure and Fermi surface of the hybridized heavy bands, the fact that largest magnitude Δ(k) opens on a high-k band so that the primary gap nodes occur at unforeseen k-space locations, and that the Bogoliubov quasiparticle interference patterns are most consistent with d

_{x2-y2}gap symmetry. Such quantitative knowledge of both the heavy band-structure and superconducting gap-structure will be critical in identifying the microscopic pairing mechanism of heavy fermion superconductivity.

For more information, see Nature Physics

**9**, 468 (2013).

### Magnetically mediated superconductivity

Using the experimentally determined band structure of CeCoIn_{5}, we reveal quantitatively the momentum space (k-space) structure of the f-electron magnetic interactions. Then, with the assumption that these magnetic interactions are mediating Cooper pairing, the coupled superconducting gap equations are solved on the two heavy-fermion bands E

_{α,β}(k). The resulting calculated momentum space structure of the superconducting gap, Δ

_{α,β}(k) is in remarkable good agreement with the experimentally determined one. Furthermore, our phase sensitive quasi particle interference scattering measurements are in good agreement with a sign change of the superconducting order parameter, which provides additional strong indications for a d-wave superconducting gap in CeCoIn

_{5}.

From the k-space structure of the f-electron magnetic interactions, a variety of characteristics for unconventional superconductivity driven by them can be calculated. We show that the calculated superconducting transitions temperature, the spin resonance seen by neutron scattering, and the spin relaxation rate are all qualitatively in good agreement with experiment, providing direct evidence that the heavy fermion Cooper pairing in this material is indeed mediated by f-electron magnetism.

For more information, see PNAS

**111**, 11663 (2014).

Fig. 3: Phase sensitive QPI on CeCoIn

_{5}.