Text: Quantum Hall Effect In 1985 Klaus von Klitzing won the Nobel Prize for discovery of the quantised Hall effect. The previous Nobel prize awarded in the area of semiconductor physics was to Bardeen, Shockley and Brattain for invention of the transistor. Everyone knows how important transistors are in all walks of life, but why is a quantised Hall effect significant? Over 100 years ago E.H. Hall discovered that when a magnetic field is applied perpendicular to the direction of a current flowing through a metal a voltage is developed in the third perpendicular direction. This is well understood and is due to the charge carriers within the current being deflected towards the edge of the sample by the magentic field. Equilibrium is achieved when the magnetic force is balanced by the electrostatic force from the build up of charge at the edge. This happens when Ey = vxBz  .The Hall coefficient is defined as RH = Ey /Bzjx and since the current density is jx = vxNq , RH =1/Nq in the case of a single species of charge carrier. RH can thus be measured to find N the density of carriers in the material. Often this transverse voltage is measured at fixed current and the Hall resistance recorded. It can easily be seen that this Hall resistance increases linearly with magnetic field. In a two-dimensional metal or semiconductor the Hall effect is also observed, but at low temperatures a series of steps appear in the Hall resistance as a function of magnetic field instead of the monotonic increase. What is more, these steps occur at incredibly precise values of resistance which are the same no matter what sample is investigated. The resistance is quantised in units of h/e2 divided by an integer. This is the QUANTUM HALL EFFECT. http://www.warwick.ac.uk/~phsbm/qhe.htm

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