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| A '''quantum point contact''' (QPC) is a narrow constriction between two wide [[Electrical conduction|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.'')
| | The author is known by the name of Figures Lint. Puerto Rico is exactly where he and his spouse reside. What I adore doing is to gather badges but I've been taking on new things recently. Bookkeeping is my occupation.<br><br>Here is my webpage - [http://www.youronlinepublishers.com/authWiki/AudreaocMalmrw www.youronlinepublishers.com] |
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| == Fabrication ==
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| There are several different ways of fabricating a QPC. It can be realized in a [[break-junction]] by pulling apart a piece of [[conductor (material)|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]] [[heterostructure]]s. 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 dot]]s 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.
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| == Properties ==
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| Geometrically, a quantum point contact is a constriction in the transverse direction which presents a [[Electrical resistance|resistance]] to the motion of [[electron]]s. Applying a voltage <math>V</math> across the point contact induces a current to flow, the magnitude of this current is given by <math>I=GV</math>, where <math>G</math> is the [[Electrical conductance|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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| At low temperatures and voltages, electrons contributing to the current have a certain energy/momentum/wavelength called Fermi energy/momentum/wavelength. Much like in a [[waveguide]], the transverse confinement in the quantum point contact results in a "quantization" of the transverse motion—the transverse motion cannot vary continuously, but has to be one of a series of discrete modes. The electron wave can only pass through the constriction if it interferes constructively, which for a given width of constriction, only happens for a certain number of modes <math>N</math>. The current carried by such a [[quantum state]] is the product of the velocity times the electron density. These two quantities by themselves differ from one mode to the other, but their product is mode independent. As a consequence, each state contributes the same amount <math>e^2/h</math> per spin direction to the total conductance
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| :<math> G=N G_Q </math>.
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| This is a fundamental result; the conductance does not take on arbitrary values but is quantized in multiples of the [[conductance quantum]] <math>G_Q=2e^2/h</math>, which is expressed through the [[electron charge]] <math>e</math> and the [[Planck constant]] <math>h</math>. The integer number <math>N</math> is determined by the width of the point contact and roughly equals the width divided by half the electron [[wavelength]]. As a function of the width of the point contact (or gate voltage in the case of GaAs/AlGaAs heterostructure devices), the conductance shows a staircase behavior as more and more modes (or channels) contribute to the electron transport. The step-height is given by <math>G_Q</math>.
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| An external [[magnetic field]] applied to the quantum point contact lifts the [[Spin (physics)|spin]] degeneracy and leads to half-integer steps in the conductance. In addition, the number <math>N</math> of modes that contribute becomes smaller. For large magnetic fields, <math>N</math> is independent of the width of the constriction, given by the theory of the [[quantum Hall effect]]. An interesting feature, not yet fully understood, is a plateau at <math>0.7G_Q</math>, the so-called 0.7-structure.
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| == Applications ==
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| Apart from studying fundamentals of charge transport in [[mesoscopic]] conductors, quantum point contacts can be used as extremely sensitive charge detectors. Since the conductance through the contact strongly depends on the size of the constriction, any potential fluctuation (for instance, created by other electrons) in the vicinity will influence the current through the QPC. It is
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| possible to detect single electrons with such a scheme. In view of [[quantum computation]] in [[Solid state physics|solid-state]] systems, QPCs may be used as readout devices for the state of a [[quantum bit]] (qubit).
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| == References ==
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| * {{cite journal
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| | author=H. van Houten and C.W.J. Beenakker
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| | year=1996
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| | title=Quantum point contacts
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| | journal=Physics Today
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| | volume=49| issue=7 |pages=22–27
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| | arxiv= cond-mat/0512609
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| | doi=10.1063/1.881503
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| |bibcode = 1996PhT....49g..22V }}
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| * {{cite journal
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| | author=C.W.J.Beenakker and H. van Houten
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| | year=1991
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| | title=Quantum Transport in Semiconductor Nanostructures
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| | journal=Solid State Physics
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| | volume=44
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| | arxiv= cond-mat/0412664
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| |bibcode = 2004cond.mat.12664B
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| | pages=1 }}
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| * {{cite journal
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| | author=B.J. van Wees et al.
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| | year=1988
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| | title=Quantized conductance of point contacts in a two-dimensional electron gas
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| | journal=Physical Review Letters
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| | volume=60 | pages=848–850
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| | doi=10.1103/PhysRevLett.60.848
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| | pmid=10038668
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| | bibcode=1988PhRvL..60..848V
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| | issue=9
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| }}
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| * {{cite journal
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| | author=D.A. Wharam et al.
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| | year=1988
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| | title=One-dimensional transport and the quantization of the ballistic resistance
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| | journal=J. Phys. C
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| | volume=21 | pages=L209
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| | doi=10.1088/0022-3719/21/8/002
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| |bibcode = 1988JPhC...21L.209W
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| | issue=8 }}
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| * {{cite journal
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| | author=J.M. Elzerman et al.
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| | year=2003
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| | title=Few-electron quantum dot circuit with integrated charge read out
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| | journal=Physical Review B
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| | volume=67 | pages=161308
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| | doi=10.1103/PhysRevB.67.161308
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| |arxiv = cond-mat/0212489 |bibcode = 2003PhRvB..67p1308E
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| | issue=16 }}
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| * {{cite journal
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| | author=K. J. Thomas et al.
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| | year=1996
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| | title=Possible spin polarization in a one-dimensional electron gas
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| | journal=Physical Review Letters
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| | volume=77 | issue=1 | pages=135
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| | doi=10.1103/PhysRevLett.77.135
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| | pmid=10061790
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| | bibcode=1996PhRvL..77..135T
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| |arxiv = cond-mat/9606004 }}
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| * {{cite journal
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| | author=Nicolás Agraït, Alfredo Levy Yeyati, Jan M. van Ruitenbeek
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| | year=2003
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| | title=Quantum properties of atomic-sized conductors
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| | journal=Physics Reports
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| | volume=377 | pages=81
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| | doi=10.1016/S0370-1573(02)00633-6
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| |arxiv = cond-mat/0208239 |bibcode = 2003PhR...377...81A
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| | issue=2–3 }}
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| *{{cite journal
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| | author=C.C.Dean and M. Pepper
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| | year=1982
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| | title=The transition from two- to one-dimensional electronic transport in narrow silicon accumulation layers
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| | journal=J. Phys. C
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| | volume=15 | pages=L1287
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| | doi= 10.1088/0022-3719/15/36/005
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| | issue=36
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| }}
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| *{{cite journal
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| | author=K-F. Berggren et al
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| | year=1986
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| | title=Magnetic Depopulation of 1D Subbands in a Narrow 2D Electron Gas in a GaAs:AlGaAs Heterojunction
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| | journal=Physical Review Letters
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| | volume=57| issue=14 | pages=1769
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| | doi=10.1103/PhysRevLett.57.1769
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| | pmid=10033540
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| | bibcode=1986PhRvL..57.1769B
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| }}
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| *{{cite journal
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| | author=T. J. Thornton ''et al.''
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| | year=1986
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| | title=One-Dimensional Conduction in the 2D Electron Gas of a GaAs-AlGaAs Heterojunction
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| | journal=Physical Review Letters
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| | volume=56| issue=11 | pages=1198
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| | doi=10.1103/PhysRevLett.56.1198
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| | pmid=10032595
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| | bibcode=1986PhRvL..56.1198T
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| }}
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| *{{cite doi|10.1016/S0080-8784(08)62393-5}}
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| [[Category:Quantum mechanics]]
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| [[Category:Nanoelectronics]]
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| [[Category:Quantum electronics]]
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| [[Category:Mesoscopic physics]]
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The author is known by the name of Figures Lint. Puerto Rico is exactly where he and his spouse reside. What I adore doing is to gather badges but I've been taking on new things recently. Bookkeeping is my occupation.
Here is my webpage - www.youronlinepublishers.com