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UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2024-11-22 1:35 |
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Conference: Bucharest University Faculty of Physics 2021 Meeting
Section: Theoretical Physics and Applied Mathematics
Title:
The quantum Hall effect - topological properties of the single-particle wave function. The Hall resistance
Authors:
Maria-Cătălina IȘFAN (1)
Affiliation:
1) Faculty of Physics, University of Bucharest, Romania
E-mail
maria.isfan@s.unibuc.ro
Keywords:
Hall effect, wave function, Hall resistance, topology
Abstract:
The quantum Hall effect is a phenomenon which consists in the quantification of the Hall resistance of a heterostructure in which an injection current flows and is placed in an external magnetic field. I present in the quantum formalism the solution of the time independent Schrodinger equation for an electron which is placed in a magnetic field and confined to two dimensions, using Landau, respectively symmetric gauges, aiming for discussing the physical interpretations of the wave functions. The degeneracy order is independent of gauge and it can be linked to the magnetic flux quantum interpretation. This idea is the precursor of Laughlin’s argument for the quantum Hall effect, which I explained in detail. Then, I analyzed what happens with the single particle if the electron is placed in a real probe, with finite dimensions and disorder. At the interface that occurs between two semiconductors with different energy gaps the bi-dimensional electron gas is formed. The finite width of the probe leads to a potential barrier that keeps the electrons inside, but doesn’t modify the single particle wave function. The disorder induces localized states, so that only the edge electrons produce Hall effect. I showed how the Hall resistance quantifies multiple times, using different approaches. Next, I studied the semiclassical limit of the single particle wavefunction in symmetric gauge and I found out that for large absolute values of the quantum numbers, the electron can be thought as having a circular motion along an orbit; the orbit has undetermined center coordinates.
Acknowledgement:
I would like to thank my three coordinating teachers, Lect. Dr. Roxana ZUS, Prof. Dr. Virgil BĂRAN and Conf. Dr. Mădălina BOCA for coaching and supporting me while elaborating this paper.
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