Gauge Fields, Geometric Phases, and Quantum Adiabatic Pumps

Abstract

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.

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

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Cited by in corpus (37)

• Berry Phase Effects on Electronic Properties
• Topological invariance and global Berry phase in non-Hermitian systems
• Thouless pumping and topology
• Adiabatic quantum pump in the presence of external ac voltages
• Spin pumping by a field-driven domain wall
• Charge transport through single molecules, quantum dots, and quantum wires
• Adiabatic pumping through a quantum dot with coulomb interactions: A perturbation expansion in the tunnel coupling
• Landau-Zener Transition in Topological Acoustic Pumping
• Spin Gauge Fields: from Berry Phase to Topological Spin Transport and Hall Effects
• Floquet scattering theory for current and heat noise in large amplitude adiabatic pumps
• Magnetic field symmetry of pump currents of adiabatically driven mesoscopic structures
• Quantum Charge Pumps with Topological Phases in Creutz Ladder
• Floquet theory of Cooper pair pumping
• Topological spin transport of photons: "magnetic monopole" gauge field in Maxwell equations and polarization splitting of rays in periodically inhomogeneous media
• Non-abelian superconducting pumps
• Adiabatic pumping in the mixed-valence and Kondo regimes
• Phase coherence, inelastic scattering, and interaction corrections in pumping through quantum dots
• Properties of 1D two-barrier quantum pump with harmonically oscillating barriers
• Interaction-induced charge and spin pumping through a quantum dot at finite bias
• Andreev interference in adiabatic pumping
• Purely electric spin pumping in one-dimension
• Gauge freedom in observables and Landsbergs nonadiabatic geometric phase: pumping spectroscopy of interacting open quantum systems
• Quantum Pumping with Ultracold Atoms on Microchips: Fermions versus Bosons
• Topological pumping in the one-dimensional Bose-Hubbard model
• Non-adiabatic topological spin pumping
• Geometric effects in non-equilibrium electron transfer statistics in adiabatically driven quantum junctions
• Measuring geometric phases of scattering states in nanoscale electronic devices
• From Anderson Localization to Mesoscopic Physics
• The Geometry of (non) abelian adiabatic pumping
• Statistics of an adiabatic charge pump
• Green's function representation of spin pumping effect
• Charge pumping in strongly-coupled molecular quantum dots
• Geometric pumping and dephasing at topological phase transition
• Pumping in quantum dots and non-Abelian matrix Berry phases
• Quantum Paddlewheel with Ultracold Atoms in Waveguides
• Dynamical Resonances and Stepped Current in an Attractive Quantum Pump
• Geometric phases of scattering states in a ring geometry: adiabatic pumping in mesoscopic devices