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Alternative theories of cuprate superconductivity
Published in J. R. Waldram, Superconductivity of Metals and Cuprates, 2017
The semion approach [22] grew out of the successful explanation by Laughlin [23] and others of the fractional quantum Hall effect in two-dimensional semiconductors, and only works for essentially two-dimensional systems. The idea there was that in a tranverse magnetic field the single-electron wavefunctions may be coherent enough for flux-line vortices to form, much as in a conventional superconductor. We then suppose that an electron is for some reason bound to some vortices, to make a composite of one electron coupled to m vortices. Such composites have interesting statistics. When a single electron is moved once around a flux line the phase changes by π. It follows that when two such entities change places the phase changes by ±(m + 1)π, allowing for the Fermi character of the electrons, the sign depending on whether the paths loop clockwise or anticlockwise. We see that if m is odd the joint entity is a boson. If we now add a single vortex as an excitation to this system, a screening hole will develop around it which will contain 1/m electrons. Investigation shows, intriguingly, that such an entity is an any on having fractional statistics. When two such entities are interchanged the phase changes by ±(1 + 1/m)π. The existence of such excitations provides a natural explanation of the fractional quantum Hall effect.
Special Topics
Published in James J Y Hsu, Nanocomputing, 2017
The fractional quantum Hall effect has two main theories: Fractionally-charged quasi-particle, proposed by Laughlin, allows a ratio of electrons to magnetic flux-quanta of υ = p/q, where p and q are integers with no common factors. Composite Fermion model, proposed by Jain (1989), attaches an even number of flux quantato each electron, forming integer-charged quasiparticles. Tsui, Stormer, and Laughlin were awarded the1998 Nobel Prize for their work on FQHE. The fractional charges, exhibiting neither bosonic nor fermionic but anyonic statistics, were indirectly observed through measurements of quantum shot noise. Figure 9.2
The Boltzmann equation and the relaxation time approximation
Published in DAVID K. FERRY, Semiconductor Transport, 2016
and plateaux, in which the resistance is a fraction of hie1 (Tsui et al., 1982). This fractional quantum Hall effect is theorized to arise from the condensation of the interacting electron system into a new many-body state characteristic of an incompressible fluid (Laughlin, 1983). Tsui, Stormer, and Laughlin shared the Nobel Prize for this discovery. However, the properties of this many-body ground state are clearly beyond the present level, and we leave this topic to discuss more properties of the quantum Hall effect itself.
Sign-changing solutions for the nonlinear Chern–Simons–Schrödinger equations
Published in Applicable Analysis, 2020
Jackiw and Pi in [1,2] introduced a nonrelativistic model that the nonlinear Schrödinger dynamics is coupled with the Chern–Simons gauge terms as follows: Here, i denotes the imaginary unit, , , for , is a complex scalar filed, is the gauge filed and is the covariant derivative for κ running over 0,1,2, and is a constant representing the strength of interaction potential. The Chern–Simons gauge theory describes the nonrelativistic thermodynamic behavior of large number of particles in an electromagnetic field. This feature of the model is important for the study of the high temperature superconductor, Aharovnov–Bohm scattering and the fractional quantum Hall effect.