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 Rxy exhibits steps that take on the quantized values
where VHall is the Hall voltage, Ichannel is the channel current, e is the elementary charge and h is Planck's constant. The divisor ν can take on either integer (ν = 1, 2, 3,...) or fractional (ν = 1/3, 2/5, 3/7, 2/3, 3/5, 1/5, 2/9, 3/13, 5/2, 12/5,...) values. Here, ν 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 ν 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 corresponds to one where the Fermi level is an energy with a finite density of states, though these states are localized (see Anderson localization).
The fractional quantum Hall effect is more complicated and still considered an open research problem. Its existence relies fundamentally on electron–electron interactions. In 1988, it was proposed that there was quantum Hall effect without Landau levels. This quantum Hall effect is referred to as the quantum anomalous Hall (QAH) effect. There is also a new concept of the quantum spin Hall effect which is an analogue of the quantum Hall effect, where spin currents flow instead of charge currents.
The quantization of the Hall conductance () has the important property of being exceedingly precise. Actual measurements of the Hall conductance have been found to be integer or fractional multiples of e2/h to nearly one part in a billion. It has allowed for the definition of a new practical standard for electrical resistance, based on the resistance quantum given by the von Klitzing constant RK.
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Graphene (ˈgræfiːn) is an allotrope of carbon consisting of a single layer of atoms arranged in a hexagonal lattice nanostructure. The name is derived from "graphite" and the suffix -ene, reflecting the fact that the graphite allotrope of carbon contains numerous double bonds. Each atom in a graphene sheet is connected to its three nearest neighbors by σ-bonds and a delocalised π-bond, which contributes to a valence band that extends over the whole sheet.
The elementary charge, usually denoted by or , is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . The symbol e has another useful mathematical meaning due to which its use as label for elementary charge is avoided in theoretical physics. For example, in quantum mechanics one wants to be able to write compactly plane waves with the use of Euler's number .
The fractional quantum Hall effect (FQHE) is a physical phenomenon in which the Hall conductance of 2-dimensional (2D) electrons shows precisely quantized plateaus at fractional values of . It is a property of a collective state in which electrons bind magnetic flux lines to make new quasiparticles, and excitations have a fractional elementary charge and possibly also fractional statistics.
Explores the fundamental concepts of modes and states in quantum optics, covering topics such as optical frequency combs, homodyne detection, and quantum resource like squeezed states.
The aim of the course is to review mathematical concepts learned during the bachelor cycle and apply them, both conceptually and computationally, to concrete problems commonly found in engineering and
The aim of this course is to provide an introduction to the theory of a few remarkable phenomena of modern condensed matter physics ranging from the quantum Hall effects to superconductivity.
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