Other Josephson-Related Phenomena

Authored by: Alexander A. Golubov , Francesco Tafuri

Handbook of Superconductivity

Print publication date:  July  2022
Online publication date:  July  2022

Print ISBN: 9781439817322
eBook ISBN: 9780429179181
Adobe ISBN:


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Andreev reflection (AR) is the scattering mechanism describing how an electron excitation slightly above the Fermi level in the normal metal is reflected at the interface as a hole excitation slightly below the Fermi level [1]. The missing charge of 2e is removed as a Cooper pair. This is a branch-crossing process which converts electrons into holes and vice versa, and therefore changes the net charge in the excitation distribution. The reflected hole (or electron) has a shift in phase compared to the incoming electron (or hole) wave function: ϕhole = ϕelectsuperc+arccos(E/∆) (ϕelect = ϕhole−ϕsuperc+arccos(E/∆)), where ∆ and ϕsuperc are the gap value and the superconducting phase of the S. The macroscopic phase of the S and the microscopic phase of the quasi-particles are therefore mixed through AR. To provide an intuitive idea of effects related to AR, the Andreev-reflected holes act as a parallel conduction channel to the initial electron current, thus doubling the normal-state conductance of the S/N interface for applied voltages less than the superconducting gap eV < ∆ [2]. Blonder, Tinkham and Klapwijk [2] (BTK) introduced the dimensionless parameter Z, proportional to the potential barrier at the interface, to describe the barrier transparency. This allows the continuous passage from the tunnel limit to a transmissive barrier since the barrier transparency is defined as D ¯ = 1 / ( 1 + Z 2 ) . More elements on AR can be found in [3].

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