Gauge Fields, Geometric Phases, and Quantum Adiabatic Pumps

Details Gauge Fields, Geometric Phases, and Quantum Adiabatic Pumps Gauge Fields, Geometric Phases, and Quantum Adiabatic Pumps

2003-04-09

arxiv.org/abs/cond-mat/0304205v2

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

1 table, 1 figure, and 5 pages. Connection between the geometric phase and the pumping currents is clarified

Scientific paper

10.1103/PhysRevLett.91.186803

Quantum adiabatic pumping of charge and spin between two reservoirs (leads) has recently been demonstrated in nanoscale electronic devices. Pumping occurs when two or more system parameters are varied in a cyclic manner and sufficiently slowly that the quantum system always remains in its ground state. We show that quantum pumping has a natural geometric representation in terms of gauge fields (both Abelian and non-Abelian) defined on the space of system parameters. We make explicit the similarities and differences with Berry's geometric phase. Tunneling from a scanning tunneling microscope tip through a magnetic atom could be used to demonstrate the non-Abelian character of the gauge field.

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