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Berry phase in magnetic systems with point perturbations

Pavel Exner·Vladimir A. Geyler
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Abstract

We study a two-dimensional charged particle interacting with a magnetic field, in general non-homogeneous, perpendicular to the plane, a confining potential, and a point interaction. If the latter moves adiabatically along a loop the state corresponding to an isolated eigenvalue acquires a Berry phase. We derive an expression for it and evaluate it in several examples such as a homogeneous field, a magnetic whisker, a particle confined at a ring or in quantum dots, a parabolic and a zero-range one. We also discuss the behavior of the lowest Landau level in this setting obtaining an explicit example of the Wilczek-Zee phase for an infinitely degenerated eigenvalue.

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Pavel Exner, Vladimir A. Geyler. 1999-11-13. Berry phase in magnetic systems with point perturbations. https://doi.org/10.1016/s0393-0440(00)00020-6

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