Abstract
The anomalous spatial shifts at interface scattering, first studied in geometric optics, recently found their counterparts in the electronic systems. It was shown that both the longitudinal and transverse shifts, analogous to the Goos-Hänchen and Imbert-Fedorov shifts in optics, can exist when electrons are scattered at a junction interface. There, the incident and the scattered beams are of the same kind of particles, e.g., a photon is scattered as a photon, an electron is scattered as an electron. More interestingly, at a normal-metal/superconductor interface, an incoming electron from the normal-metal side can be reflected as a hole. Notably, the incident andthe scattered particles do not share the same identity, and this electron-hole conversion process is known as Andreev reflection. Whether the anomalous spatial shifts exist in Andreev reflection has never been explored before. Our works predict for the first time that the anomalous spatial shifts universally exist in Andreev reflection and also unveil new phenomenon that cannot be realized in pure electronic and optic systems. It provides a fundamentally new effect in physics. Our key findings can be summarized as follows: 1. We find that a transverse shift, analogous to the Imber-Fedorov shift in optics, can generally exist in Andreev reflection due to the effect of spin-orbit-coupling in the normal metal. Particularly, we demonstrate that the shift is pronounced for a lightly doped Weyl semimetal via different approaches. Notably, the shift is opposite for incoming electrons of opposite chirality, leading to a chirality Hall effect for holes. This spatial shift is not limited to Weyl systems, but occurs for a general three-dimensional spin-orbit-coupled metal interfaced with a superconductor. 2. Remarkably, we also discovery that a sizable transverse shift could be induced solely by the unconventional pairings in the superconductor side. Notably, the transverse shift happening at such a junction is sensitive to the superconductor gap structure, showing characteristic features for each pairing type, which can be used as a method to probe the structure of unconventional pairings. Our work not only discovers a fundamentally new effect, but also suggests a powerful new technique capable of probing the gap structure of unconventional pairings. 3. A transverse shift is predicated for a crossed Andreev reflection, a nonlocal scattering process occurring at a normal-metal/superconductor/normal-metal structure. We reveal that the effect is quite general and depends on the spin-orbitvi coupling of the two normal-metal terminals. It provides a new mechanism to detect the crossed Andreev reflection. 4. At a normal-metal/superconductor interface, we also discover for the first time that a pronounced longitudinal shift, analogous to the Goos-Hänchen shift in optics, can generally happen in both normal reflection and Andreev reflection, leading to measurable effects. Finally, based on the features of these anomalous spatial shifts, we propose several experimental setups to detect them.