| quantum Hall effect | |
|---|---|
| Name | Quantum Hall Effect |
| Field | Condensed matter physics |
quantum Hall effect
The quantum Hall effect is a quantum mechanical phenomenon that occurs in two-dimensional systems, where the Hall conductance exhibits quantized plateaus at integer multiples of the fundamental constant e^2/h. This effect is of great importance in the field of Quantum Physics, as it has led to a deeper understanding of the behavior of electrons in solid-state systems and has numerous applications in materials science and electronics. The quantum Hall effect is closely related to the integer quantum Hall effect and the fractional quantum Hall effect, which have been extensively studied by physicists such as Robert Laughlin and Horst Störmer. Research in this area has been conducted at institutions such as the University of California, Berkeley and the Massachusetts Institute of Technology.
Quantum Hall Effect The quantum Hall effect is a phenomenon that occurs in two-dimensional electron systems, where the Hall conductivity exhibits quantized plateaus at integer multiples of the fundamental physical constant e^2/h. This effect was first observed in the 1980s by Klaus von Klitzing, who was awarded the Nobel Prize in Physics in 1985 for his discovery. The quantum Hall effect is closely related to the integer quantum Hall effect and the fractional quantum Hall effect, which have been extensively studied by physicists such as Robert Laughlin and Horst Störmer. The effect has been observed in a variety of materials, including semiconductors and graphene, and has been studied using techniques such as magnetotransport and scanning tunneling microscopy. Researchers at institutions such as the University of California, Berkeley and the Massachusetts Institute of Technology have made significant contributions to the understanding of the quantum Hall effect.
The theoretical background of the quantum Hall effect is based on the quantum mechanical description of electrons in two-dimensional electron systems. The Schrödinger equation is used to describe the behavior of electrons in the presence of a magnetic field, and the Landau levels are used to describe the energy levels of the electrons. The Fermi-Dirac statistics are used to describe the distribution of electrons in the system, and the Green's function is used to calculate the Hall conductivity. Theoretical models, such as the Kubo formula and the Boltzmann equation, have been developed to describe the quantum Hall effect, and have been used to make predictions about the behavior of the Hall conductivity in different materials and under different conditions. Researchers such as Lev Landau and Werner Heisenberg have made significant contributions to the theoretical understanding of the quantum Hall effect, and institutions such as the Institute for Theoretical Physics and the European Organization for Nuclear Research have supported research in this area.
The experimental discovery of the quantum Hall effect was made by Klaus von Klitzing in 1980, using a silicon-based field-effect transistor. The experiment involved measuring the Hall conductivity of the two-dimensional electron system as a function of the magnetic field, and observing the quantized plateaus in the Hall conductivity. Since then, numerous experiments have been performed to study the quantum Hall effect, using a variety of materials and techniques. The integer quantum Hall effect and the fractional quantum Hall effect have been observed in semiconductors, graphene, and other materials, and the effect has been studied using techniques such as magnetotransport, scanning tunneling microscopy, and photoluminescence spectroscopy. Researchers at institutions such as the University of California, Los Angeles and the Stanford University have made significant contributions to the experimental study of the quantum Hall effect, and have used facilities such as the National High Magnetic Field Laboratory to conduct their research.
The quantum Hall states and plateaus are the characteristic features of the quantum Hall effect. The Hall conductivity exhibits quantized plateaus at integer multiples of the fundamental physical constant e^2/h, and the Longitudinal conductivity exhibits minima at the same values of the magnetic field. The quantum Hall states are described by the Laughlin wave function, which is a many-body wave function that describes the behavior of the electrons in the two-dimensional electron system. The fractional quantum Hall effect is characterized by the formation of quasiparticles, such as the Laughlin quasiparticle, which are excitations of the quantum Hall fluid. Researchers such as Robert Laughlin and Horst Störmer have made significant contributions to the understanding of the quantum Hall states and plateaus, and institutions such as the Princeton University and the Harvard University have supported research in this area.
The mathematical formulation of the quantum Hall effect is based on the quantum mechanical description of electrons in two-dimensional electron systems. The Schrödinger equation is used to describe the behavior of electrons in the presence of a magnetic field, and the Landau levels are used to describe the energy levels of the electrons. The Kubo formula and the Boltzmann equation are used to calculate the Hall conductivity and the Longitudinal conductivity, and the Green's function is used to describe the behavior of the electrons in the two-dimensional electron system. Theoretical models, such as the Hartree-Fock method and the density functional theory, have been developed to describe the quantum Hall effect, and have been used to make predictions about the behavior of the Hall conductivity in different materials and under different conditions. Researchers such as Lev Landau and Werner Heisenberg have made significant contributions to the mathematical formulation of the quantum Hall effect, and institutions such as the Institute for Theoretical Physics and the European Organization for Nuclear Research have supported research in this area.
in Quantum Physics The quantum Hall effect has numerous applications and implications in Quantum Physics. The effect is used to define the SI unit of electrical resistance, the ohm, and is used in the development of quantum computing and quantum information processing. The quantum Hall effect is also used in the study of topological insulators and topological phases of matter, and has implications for our understanding of the behavior of electrons in solid-state systems. Researchers such as David Thouless and Michael Kosterlitz have made significant contributions to the understanding of the applications and implications of the quantum Hall effect, and institutions such as the University of Cambridge and the University of Oxford have supported research in this area. The quantum Hall effect has also been studied in the context of condensed matter physics and materials science, and has been used to develop new materials and devices with unique properties.
The quantum Hall effect is related to several other phenomena and analogues in Quantum Physics. The integer quantum Hall effect and the fractional quantum Hall effect are closely related to the quantum Hall effect, and the spin Hall effect and the valley Hall effect are analogous phenomena that occur in two-dimensional electron systems. The quantum Hall effect is also related to the quantum spin Hall effect and the topological insulators, which are materials that exhibit topological phases of matter. Researchers such as Charles Kane and Eugene Mele have made significant contributions to the understanding of the related phenomena and analogues of the quantum Hall effect, and institutions such as the University of Pennsylvania and the University of California, Santa Barbara have supported research in this area. The study of the quantum Hall effect and its related phenomena has led to a deeper understanding of the behavior of electrons in solid-state systems and has numerous applications in materials science and electronics. Category:Quantum Hall effect Category:Condensed matter physics Category:Quantum mechanics