{\displaystyle \varphi _{xy}=u(x)e^{iky}} The Quantum Hall Effect was discovered by the Nobel Prize winner, Klaus von Klitzing in 1980, just five years after his initial prediction of the phenomenon. c = x {\displaystyle \nu } {\displaystyle \Delta E=\pm {\frac {1}{2}}g\mu _{B}B} 2 {\displaystyle L_{x}\times L_{y}} A striking model of much interest in this context is the Azbel–Harper–Hofstadter model whose quantum phase diagram is the Hofstadter butterfly shown in the figure. The quantum Hall effect has provided an amazingly accurate method for calibrating resistance. A quantum Hall effect in three dimensions is a long-sought phase of matter and has inspired many efforts and claims. -direction spaced equally along the q / {\displaystyle -} This value is independent of the material, geometry and microscopic details of the semiconductor. are degenerate. 2 ε δ It is possible to relate the filling factor to the resistivity and hence, to the conductivity of the system: When The discovery of the quantum Hall effect in 2D systems opens the door to topological phases of matter. The larger the magnetic field is, the more states are in each Landau level. z − The quantum theory of atomic structure, which is the concept that energy is available in discrete, whole packets at the subatomic level, had predicted the quantum Hall effect as early as 1975. The 1980 discovery of the quantum version was a surprise whose theoretical basis still contains some puzzles. By substituting this Ansatz into the Schrödinger equation one gets the one-dimensional harmonic oscillator equation centered at Since Investigating the conductance properties of two-dimensional electron gases at very low temperature and high magnetic fields, his group obtained curious results: The Hall conductance of such a system plotted as a function of the ratio 0 {\displaystyle k} e ± The colors represent the integer Hall conductances. x [12][9] For this finding, von Klitzing was awarded the 1985 Nobel Prize in Physics. Klaus von Klitzing is a Nobel laureate who won the prestigious award in 1985 for his discovery of the quantized Hall effect, sometimes referred to as the quantum Hall effect. y k i Its practical significance, however, was immediately obvious, and today the quantum Hall effect, recognized in the 1985 Nobel Prize in physics, is the basis of the standard definition of the unit of electrical resistance, the ohm. ). ν States with the same This means that electronics and technology using quantum mechanics in the future will be more energy-efficient and powerful. ε c Note, however, that the density of states in these regions of quantized Hall conductance is zero; hence, they cannot produce the plateaus observed in the experiments. quantum Hall effect or anomalous quantum Hall effect] which remains visible up to room temperature. ( = This service is more advanced with JavaScript available, The Quantum Hall Effect The quantum Hall effect also provides an extremely precise independent determination of the fine-structure constant, a quantity of fundamental importance in quantum electrodynamics. Unable to display preview. The discovery's roots lie in the workings of the quantum Hall effect- a form of topological effect which was the subject of the Nobel Prize in Physics in 1985. Since the discovery of the quantum Hall effect (QHE) in the 1980s it has been one of the fundamental quantum phenomena in solid state physics. {\displaystyle \mathbf {A} =(0,Bx,0)} and the wavefunctions are sinusoidal. Introduction. m ) has the important property of being exceedingly precise. and {\displaystyle g} ARTICLE OPEN Quantum anomalous Hall effect in two-dimensional magnetic insulator heterojunctions Jinbo Pan1,6, Jiabin Yu2,3,6, Yan-Fang Zhang1,4,5, Shixuan Du4, Anderson Janotti 5, Chao-Xing Liu 2 and Qimin Yan 1 Recent years have witnessed tremendous success in the discovery … being k The quantum Hall effect (QHE) and its relation to fundamental physical constants was discovered in 1980 by Klaus von Klitzing for which he received a Nobel prize in 1985. The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance Rxy exhibits steps that take on the quantized values at certain level. [17] This process can be expressed through a metaphor of photons bouncing between multiple mirrors. B B = Robert B. Laughlin, (born November 1, 1950, Visalia, California, U.S.), American physicist who, with Daniel C. Tsui and Horst Störmer, received the Nobel Prize for Physics in 1998 for the discovery that electrons in an extremely powerful magnetic field can form a quantum fluid in … ℏ {\displaystyle s=\pm {\frac {1}{2}}} . In order to get the number of occupied Landau levels, one defines the so-called filling factor It is interesting to notice that if the magnetic field is very small, the longitudinal resistivity is a constant which means that the classical result is reached. From the expression for the Landau levels one notices that the energy depends only on In this perspective, we review our proposal that guarantees a 3D quantum Hall effect. ε ∗ Or anomalous quantum Hall effect ( QHE ) marked a turning point condensed-matter... Levels are occupied it disclosed the actual existence of various phenomena, the. 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