Anomalous shift in Andreev reflection from side incidence

Abstract

Andreev reflection at a normal-superconductor interface may be accompanied with an anomalous spatial shift. The studies so far are limited to the top incidence configuration. Here, we investigate this effect in the side incidence configuration, with the interface parallel to the principal axis of superconductor. We find that the shift exhibits rich behaviors reflecting the character of pair potential. It has two contributions: one from the $k$-dependent phase of pair potential, and the other from the evanescent mode. For chiral $p$-wave pairing, the pairing phase contribution is proportional to the chirality of pairing and is independent of excitation energy, whereas the evanescent mode contribution is independent of chirality and is nonzero only for excitation energy below the gap. The two contributions also have opposite parity with respect to the incident angle. For $d_{x^{2}-y^{2}}$-wave pairing, only the evanescent mode contribution exists, and the shift exhibits suppressed zones in incident angles, manifesting the superconducting nodes. The dependence of the shift on other factors, such as the angle of incident plane and Fermi surface anisotropy, are discussed.