Andreev–Saint-James reflections: A probe of cuprate superconductors

Abstract

Electrical transport through a normal-metal/superconductor contact at biases smaller than the energy gap can occur via the reflection of an electron as a hole of opposite wave vector. The same mechanism of electron-hole reflection gives rise to low-energy states at the surface of unconventional superconductors having nodes in their order parameter. The occurrence of electron-hole reflections at normal-metal/superconductor interfaces was predicted independently by Saint-James and de Gennes and by Andreev, and their spectroscopic features were discussed in detail by Saint-James in the early sixties. They are generally called Andreev reflections but, in view of the literature, will here be referred to as Andreev--Saint-James (ASJ) reflections. This review presents a historical review of ASJ reflections and spectroscopy in conventional superconductors, and reviews their application to the high-${T}_{c}$ cuprates. The occurrence of ASJ reflections in all studied cuprates is well documented for a broad range of doping levels, implying that there is no large asymmetry between electrons and holes near the Fermi level in the superconducting state. In the underdoped regime, where the pseudogap phenomenon has been observed by other methods such as nuclear magnetic resonance (NMR), angular-resolved photoemission spectroscopy (ARPES), and Giaever tunneling, gap values obtained from ASJ spectroscopy are smaller than pseudogap values, indicating a lack of coherence in the pseudogap energy range. Low-energy surface bound states have been observed in all studied hole-doped cuprates, in agreement with a dominant $d$-wave symmetry order parameter. Results are mixed for electron-doped cuprates. In overdoped $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}\phantom{\rule{0.3em}{0ex}}(\ensuremath{\delta}<0.08)$ and ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$, ASJ spectroscopy is consistent with the presence of an additional imaginary component of the order parameter. Results of ASJ spectroscopy under applied magnetic fields are also reviewed. A short section at the end is devoted to some recent results on spin effects.