Additional Dirac Matrix in Quantum Hall Effect
- Department of Physics, University of Malaya, Kuala Lumpur 50603 (Malaysia)
We find that the predictions of the Dirac equation agree with the idea of fractional charges. We have introduced the combination of spin and orbital quantum numbers, including the negative sign for spin, in such a way that there occur fractional charges through the Bohr magneton. This leads to doubling of eigen values so that we define an additional matrix the properties of which are important when magnetic field is present. There is a spin-charge coupling so that spin (1/2) particle can have the zero or one charge. The Dirac equation can accommodate not only charges of 0 and {+-}e but also fractional values such as 1/3 and 2/3. For spin (1/2) there are two eigen values, {+-}(1/2)g{mu}{sub B}H but when two different g values are taken into account, there are four eigen values, {+-}(1/2)g{+-}{mu}{sub B}H, which are fractionally charged. The Hall resistivity becomes spin dependent. The spin (1/2) particle with zero orbital angular momentum, has two values of resistivity, 3h/e{sup 2} and 3h/(2e{sup 2}) which means that when magnetic field is varied the resistivity can change by a factor of 2. If the spin is 3/2, the value of (1/2)g+ = (1/2)+(3/2) so that g = 4 arises which substituted in the series, {+-}(1/2)g{mu}{sub B}H, {+-}(3/2)g{mu}{sub B}H, {+-}(5/2)g{mu}{sub B}H, ..., gives 2, 6, 10, etc which are the correct numbers found experimentally.
- OSTI ID:
- 21143318
- Journal Information:
- AIP Conference Proceedings, Vol. 1017, Issue 1; Conference: PERFIK 2007: National physics conference 2007 on current issues of physics in Malaysia, Kuala Terengganu (Malaysia), 26-28 Dec 2007; Other Information: DOI: 10.1063/1.2940677; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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