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The fractional quantum Hall effect is more complicated and still considered an open research problem. [2] Its existence relies fundamentally on electron–electron interactions. In 1988, it was proposed that there was a quantum Hall effect without Landau levels. [3] This quantum Hall effect is referred to as the quantum anomalous Hall (QAH) effect.
For a two-dimensional electron system which can be produced in a MOSFET, in the presence of large magnetic field strength and low temperature, one can observe the quantum Hall effect, in which the Hall conductance σ undergoes quantum Hall transitions to take on the quantized values.
The fractional quantum Hall effect (FQHE) is a collective behavior in a 2D system of electrons. In particular magnetic fields, the electron gas condenses into a remarkable liquid state, which is very delicate, requiring high quality material with a low carrier concentration, and extremely low temperatures.
Quantum Hall transitions are the quantum phase transitions that occur between different robustly quantized electronic phases of the quantum Hall effect. The robust quantization of these electronic phases is due to strong localization of electrons in their disordered, two-dimensional potential. But, at the quantum Hall transition, the electron ...
Quantum anomalous Hall effect (QAHE) is the "quantum" version of the anomalous Hall effect. While the anomalous Hall effect requires a combination of magnetic polarization and spin-orbit coupling to generate a finite Hall voltage even in the absence of an external magnetic field (hence called "anomalous"), the quantum anomalous Hall effect is ...
The fractional quantum Hall effect of electrons is thus explained as the integer quantum Hall effect of composite fermions. [5] It results in fractionally quantized Hall plateaus at =, with given by above quantized values. These sequences terminate at the composite fermion Fermi sea.
Klaus von Klitzing (German: [ˈklaʊs fɔn ˈklɪtsɪŋ] ⓘ; born 28 June 1943) is a German physicist, known for discovery of the integer quantum Hall effect, for which he was awarded the 1985 Nobel Prize in Physics. [3] [4]
The semicircle law, in condensed matter physics, is a mathematical relationship that occurs between quantities measured in the quantum Hall effect.It describes a relationship between the anisotropic and isotropic components of the macroscopic conductivity tensor σ, and, when plotted, appears as a semicircle.