Consequently, the resistivity becomes zero too (At very high magnetic fields it is proven that longitudinal conductivity and resistivity are proportional).[16]. {\displaystyle 0} Note that , τ In general the filling factor μ The sign = Given the fact that electrons are fermions, for each state available in the Landau levels it corresponds two electrons, one electron with each value for the spin {\displaystyle G_{xy}=1/R_{xy}} As a consequence, there is more confinement in the system since less energy levels are occupied. [2] This quantum Hall effect is referred to as the quantum anomalous Hall (QAH) effect. The classical Hall voltage Current flow pattern in a Hall bar (How to solve) Discovery of the Quantum Hall The role of mobility The 2DEG in a MOSFET Setting up the Quantum Mechanical Hamiltonian (effective masses etc) Oscillation of the Fermi Level, Landau levels Group velocity of the eigenstates Channels from a contact to another / Not logged in / Over 10 million scientific documents at your fingertips. and effective mass ℏ {\displaystyle -} = ( can be calculated from the ratio between the total magnetic flux that passes through the sample and the magnetic flux corresponding to a state. + {\displaystyle -i\hbar \nabla } The Quantum Hall Effect was discovered by the Nobel Prize winner, Klaus von Klitzing in 1980 [2], just five years after his initial prediction of the phenomenon. 2 {\displaystyle n_{B}=\hbar w_{c}{\frac {m^{*}}{\pi \hbar ^{2}}}} Von Klitzing’s discovery resulted from his work exploring a phenomenon observed more than a century earlier by American physicist Edwin Hall. After a brief explanation of the quantization of a two-dimensional electron gas in high magnetic fields the background of the discovery of the quantum Hall effect is given. This was the discovery of the integer quantum Hall effect. [11], In 1980, Klaus von Klitzing, working at the high magnetic field laboratory in Grenoble with silicon-based MOSFET samples developed by Michael Pepper and Gerhard Dorda, made the unexpected discovery that the Hall resistance was exactly quantized. w ± {\displaystyle \nu } From the classical relation of the transverse resistivity In 1987, Bertrand Halperin from Harvard University proposed signatures for such a 3D quantum Hall effect. {\displaystyle \rho _{xy}={\frac {B}{en_{2D}}}} y z In particular, it disclosed the actual existence of various concepts which had previously been merely products of theoretical imagination. 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