Point Contact Andreev-Reflection Spectroscopy : mechanisms, models and examples

Résumé :

Point-contact spectroscopy [1] in superconductors, also known as point-contact Andreev-Reflection spectroscopy (PCARS) is a simple but powerful and versatile technique that allows a direct determination of the number, the amplitude and the symmetry of the energy gap(s) in superconducting materials [2,3]. The technique is rather simple in principle, i.e. it just consists in creating a small (point-like) contact between a normal metal and a superconductor, and to measure its differential conductance as a function of the bias voltage across the junction. However, there are several complications that make this simple recipe fairly difficult to realize in practice. First of all, the contact must be in the spectroscopic regime [1,2,3], i.e. electrons from the normal metal must be injected in the superconductor with an excess energy that coincides with eV, V being the bias voltage. Hence, they must not lose energy in the banks and in the contact itself. The ideal condition is that of ballistic conduction through the N/S interface, which ensures no Joule effect and requires in turns that the contact size is smaller than both the coherence length and the electronic mean free path in the superconductor.
When these conditions are met, the conduction through the contact is dominated by Andreev reflection, a quantum phenomenon that is responsible for the conversion of the normal current into supercurrent, and occurs in a specific range of voltages (electron energies) set by the amplitude of the superconducting gap. Several models have been proposed to describe the phenomenon and are currently used to extract information on the amplitude and symmetry of the order parameter from the spectra. The simplest one [4] was only suited for superconductors with an isotropic (s-wave) gap, but has been successfully generalized to the case of layered materials with anisotropic gaps, like cuprates [5,6] or strontium ruthenate [7]) and finally to the 3D case, while taking into account the shape of the actual Fermi surface [3]. The latter generalization allows calculating the point-contact spectrum for any symmetry of the order parameter, including exotic ones with horizontal node lines.
After discussing these general aspects, I will briefly describe the application of the technique to some example materials, from the conventional multiband superconductors MgB2 [8] to unconventional ones like Pu-based heavy fermion compounds [9] or Fe-based compounds [3], to transition-metal dichalcogenides [10].

References
1. Y. G. Naidyuk and I. K. Yanson, Point-Contact Spectroscopy, Springer Series in Solid-State Sciences, Vol. 145 (Springer, 2004).
2. D. Daghero and R.S. Gonnelli, Supercond. Sci. Technol. 23, 043001 (2010).
3. D. Daghero et al., Rep. Prog. Phys. 74, 124509 (2011).
4. G. E. Blonder, M. Tinkham and T. M. Klapwijk, Phys. Rev. B 25, 4515 (1982)
5. Y. Tanaka and S. Kashiwaya, Phys. Rev. Lett. 74, 3451 (1995)
6. S. Kashiwaya and Y. Tanaka, Rep. Prog. Phys. 63, 1641 (2000).
7. M. Yamashiro, Y. Tanaka, and S. Kashiwaya, Phys. Rev. B 56, 7847 (1997)
8. R. S. Gonnelli et al., Phys Rev. Lett. 89, 247004 (2002)
9. D. Daghero et al., Nature Communications 3, 786 (2012)
10. E. Piatti et al., Materials Today Physics 59 (2025) 101883

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Contact : matteo.dastuto@neel.cnrs.fr