Andreev reflection

Andreev reflection (AR), named after the Russian physicist Alexander F. Andreev, is a type of particle scattering which occurs at interfaces between a superconductor (S) and a normal state material (N). It is a charge-transfer process by which normal current in N is converted to supercurrent in S. Each Andreev reflection transfers a charge 2e across the interface, avoiding the forbidden single-particle transmission within the superconducting energy gap.

The process involves an electron (hole) incident on the interface from the normal state material at energies less than the superconducting energy gap. The incident electron (hole) forms a Cooper pair in the superconductor with the retroreflection of a hole (electron) of opposite spin and velocity but equal momentum to the incident electron (hole), as seen in the figure. The barrier transparency is assumed to be high, with no oxide or tunnel layer which reduces instances of normal electron-electron or hole-hole scattering at the interface. Since the pair consists of an up and down spin electron, a second electron (hole) of opposite spin to the incident electron (hole) from the normal state forms the pair in the superconductor, and hence the retroreflected hole (electron). Through time-reversal symmetry, the process with an incident electron will also work with an incident hole (and retroreflected electron).

The process is highly spin-dependent – if only one spin band is occupied by the conduction electrons in the normal-state material (i.e. it is fully spin-polarized), Andreev reflection will be inhibited due to inability to form a pair in the superconductor and impossibility of single-particle transmission. In a ferromagnet or material where spin-polarization exists or may be induced by a magnetic field, the strength of the Andreev reflection (and hence conductance of the junction) is a function of the spin-polarization in the normal state.

The spin-dependence of AR gives rise to the Point Contact Andreev Reflection (or PCAR) technique, whereby a narrow superconducting tip (often niobium, antimony or lead) is placed into contact with a normal material at temperatures below the critical temperature of the tip. By applying a voltage to the tip, and measuring differential conductance between it and the sample, the spin polarization of the normal metal at that point (and magnetic field) may be determined. This is of use in such tasks as measurement of spin-polarized currents or characterizing spin polarization of material layers or bulk samples, and the effects of magnetic fields on such properties.

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