Integer Quantum Hall Effect
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Integer Quantum Hall Effect
The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance exhibits steps that take on the quantized values : R_ = \frac = \frac , where is the Hall voltage, is the channel current, is the elementary charge and is the Planck constant. The divisor can take on either integer () or fractional () values. Here, is roughly but not exactly equal to the filling factor of Landau levels. The quantum Hall effect is referred to as the integer or fractional quantum Hall effect depending on whether is an integer or fraction, respectively. The striking feature of the integer quantum Hall effect is the persistence of the quantization (i.e. the Hall plateau) as the electron density is varied. Since the electron density remains constant when the Fermi level is in a clean spectral gap, this situation corres ...
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Quantum Mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot. Classical physics can describe many aspects of nature at an ordinary (macroscopic and Microscopic scale, (optical) microscopic) scale, but is not sufficient for describing them at very small submicroscopic (atomic and subatomic) scales. Classical mechanics can be derived from quantum mechanics as an approximation that is valid at ordinary scales. Quantum systems have Bound state, bound states that are Quantization (physics), quantized to Discrete mathematics, discrete values of energy, momentum, angular momentum, and ot ...
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Electrical Resistance
The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual parallels with mechanical friction. The SI unit of electrical resistance is the ohm (), while electrical conductance is measured in siemens (S) (formerly called the 'mho' and then represented by ). The resistance of an object depends in large part on the material it is made of. Objects made of electrical insulators like rubber tend to have very high resistance and low conductance, while objects made of electrical conductors like metals tend to have very low resistance and high conductance. This relationship is quantified by resistivity or conductivity. The nature of a material is not the only factor in resistance and conductance, however; it also depends on the size and shape of an object because these properties are extensive rather tha ...
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Bell Labs
Nokia Bell Labs, commonly referred to as ''Bell Labs'', is an American industrial research and development company owned by Finnish technology company Nokia. With headquarters located in Murray Hill, New Jersey, Murray Hill, New Jersey, the company operates several laboratories in the United States and around the world. As a former subsidiary of the American Telephone and Telegraph Company (AT&T), Bell Labs and its researchers have been credited with the development of radio astronomy, the transistor, the laser, the photovoltaic cell, the charge-coupled device (CCD), information theory, the Unix operating system, and the programming languages B (programming language), B, C (programming language), C, C++, S (programming language), S, SNOBOL, AWK, AMPL, and others, throughout the 20th century. Eleven Nobel Prizes and five Turing Awards have been awarded for work completed at Bell Laboratories. Bell Labs had its origin in the complex corporate organization of the Bell System telepho ...
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Silicon Dioxide
Silicon dioxide, also known as silica, is an oxide of silicon with the chemical formula , commonly found in nature as quartz. In many parts of the world, silica is the major constituent of sand. Silica is one of the most complex and abundant families of materials, existing as a compound of several minerals and as a synthetic product. Examples include fused quartz, fumed silica, opal, and aerogels. It is used in structural materials, microelectronics, and as components in the food and pharmaceutical industries. All forms are white or colorless, although impure samples can be colored. Silicon dioxide is a common fundamental constituent of glass. Structure In the majority of silicon dioxides, the silicon atom shows tetrahedral coordination, with four oxygen atoms surrounding a central Si atomsee 3-D Unit Cell. Thus, SiO2 forms 3-dimensional network solids in which each silicon atom is covalently bonded in a tetrahedral manner to 4 oxygen atoms. In contrast, CO2 is a li ...
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