Andreev reflection (AR), named after the Russian physicist Alexander F. Andreev, is a type of particle

scattering Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including ...

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 In solid-state physics, an energy gap is an energy range in a solid where no electron states exist, i.e. an energy range where the density of states vanishes. Especially in condensed-matter physics, an energy gap is often known more abstractly as ...

Overview

The process involves an electron (hole) incident on the interface from the normal state material at energies less than the superconducting

. The incident electron (hole) forms a

Cooper pair In condensed matter physics, a Cooper pair or BCS pair (Bardeen–Cooper–Schrieffer pair) is a pair of electrons (or other fermions) bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Cooper ...

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 Spin or spinning most often refers to: * Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning * Spin, the rotation of an object around a central axis * Spin (propaganda), an intentionally b ...

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 Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials a ...

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 Niobium is a chemical element with chemical symbol Nb (formerly columbium, Cb) and atomic number 41. It is a light grey, crystalline, and ductile transition metal. Pure niobium has a Mohs hardness rating similar to pure titanium, and it has sim ...

antimony Antimony is a chemical element with the symbol Sb (from la, stibium) and atomic number 51. A lustrous gray metalloid, it is found in nature mainly as the sulfide mineral stibnite (Sb2S3). Antimony compounds have been known since ancient time ...

lead Lead is a chemical element with the symbol Pb (from the Latin ) and atomic number 82. It is a heavy metal that is denser than most common materials. Lead is soft and malleable, and also has a relatively low melting point. When freshly cu ...

) is placed into contact with a normal material at temperatures below the

critical temperature Critical or Critically may refer to: *Critical, or critical but stable, medical states **Critical, or intensive care medicine *Critical juncture, a discontinuous change studied in the social sciences. *Critical Software, a company specializing in ...

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. In an AR process, the phase difference between the electron and hole is −π/2 plus the phase of the superconducting

order parameter In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...

Crossed Andreev reflection

Crossed Andreev reflection, or CAR, also known as non-local Andreev reflection occurs when two spatially separated normal state material electrodes form two separate junctions with a superconductor, with the junction separation of the order of the BCS superconducting coherence length of the material in question. In such a device, retroreflection of the hole from an Andreev reflection process, resulting from an incident electron at energies less than the superconducting gap at one lead, occurs in the second spatially separated normal lead with the same charge transfer as in a normal AR process to a Cooper pair in the superconductor. For CAR to occur, electrons of opposite spin must exist at each normal electrode (so as to form the pair in the superconductor). If the normal material is a ferromagnet this may be guaranteed by creating opposite spin polarization via the application of a magnetic field to normal electrodes of differing

coercivity Coercivity, also called the magnetic coercivity, coercive field or coercive force, is a measure of the ability of a ferromagnetic material to withstand an external magnetic field without becoming demagnetized. Coercivity is usually measured in ...

. CAR occurs in competition with elastic cotunneling or EC, the quantum mechanical tunneling of electrons between the normal leads via an intermediate state in the superconductor. This process conserves electron spin. As such, a detectable CAR potential at one electrode on the application of current to the other may be masked by the competing EC process, making clear detection difficult. In addition, normal Andreev reflection may occur at either interface, in conjunction with other normal electron scattering processes from the normal/superconductor interface. The process is of interest in the formation of solid-state

quantum entanglement Quantum entanglement is the phenomenon that occurs when a group of particles are generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the group cannot be described independently of the state of ...

, via the formation of a spatially separated entangled electron-hole (Andreev) pair, with applications in

spintronics Spintronics (a portmanteau meaning spin transport electronics), also known as spin electronics, is the study of the intrinsic spin of the electron and its associated magnetic moment, in addition to its fundamental electronic charge, in solid-sta ...

and

quantum computing Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...

Overview

Crossed Andreev reflection

References

Further reading