Quantum point contact

A quantum point contact (QPC) is a narrow constriction between two wide electrically conducting regions, of a width comparable to the electronic wavelength (nano- to micrometer). Quantum point contacts were first reported in 1988 by a Dutch group (Van Wees et al.) and, independently, by a British group (Wharam et al.). They are based on earlier work by the British group which showed how split gates could be used to convert a two-dimensional electron gas into one-dimension, first in silicon (Dean and Pepper) and then in gallium arsenide (Thornton et al., Berggren et al.)

There are several different ways of fabricating a QPC. It can be realized in a break-junction by pulling apart a piece of conductor until it breaks. The breaking point forms the point contact. In a more controlled way, quantum point contacts are formed in a two-dimensional electron gas (2DEG), e.g. in GaAs/AlGaAs heterostructures. By applying a voltage to suitably shaped gate electrodes, the electron gas can be locally depleted and many different types of conducting regions can be created in the plane of the 2DEG, among them quantum dots and quantum point contacts. Another means of creating a QPC is by positioning the tip of a scanning tunneling microscope close to the surface of a conductor.

Geometrically, a quantum point contact is a constriction in the transverse direction which presents a resistance to the motion of electrons. Applying a voltage ${\displaystyle V}$ across the point contact induces a current to flow, the magnitude of this current is given by ${\displaystyle I=GV}$, where ${\displaystyle G}$ is the conductance of the contact. This formula resembles Ohm's law for macroscopic resistors. However, there is a fundamental difference here resulting from the small system size which requires a quantum mechanical analysis.

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