The single-particle density of states and a resonance in the Aharonov-Bohm potential

Details The single-particle density of states and a resonance in the Aharonov-Bohm potential The single-particle density of states and a resonance in the Aharonov-Bohm potential

1996-02-07

arxiv.org/abs/cond-mat/9602041v1

Mod. Phys. Lett. B9, 1407-1417 (1995)

Physics

Condensed Matter

14 pages, plain latex, 1 figure, uuencoded

Scientific paper

The single-particle densitity of states (DOS) for the Pauli and the Schr\"{o}dinger Hamiltonians in the presence of an Aharonov-Bohm potential is calculated for different values of the particle magnetic moment. The DOS is a symmetric and periodic function of the flux. The Krein-Friedel formula can be applied to this long-ranged potential when regularized with the zeta function. We have found that whenever a bound state is present in the spectrum it is always accompanied by a resonance. The shape of the resonance is not of the Breit-Wigner type. The differential scattering cross section is asymmetric if a bound state is present and gives rise to the Hall effect. As an application, propagation of electrons in a dilute vortex limit is considered and the Hall resistivity is calculated.

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