Classical vortices are relevant to the Berezenskii–Kosterlitz–Thouless transition in two-dimensional XY model.
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More accurately, the vortices bound to electrons produce their own geometric phases which partly cancel the Aharonov–Bohm phase due to the external magnetic field to generate a net geometric phase that can be modeled as an Aharonov–Bohm phase in an effective magnetic field
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When electrons are confined to two dimensions, cooled to very low temperatures, and subjected to a strong magnetic field, their kinetic energy is quenched due to Landau level quantization.
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