Quantum pumping and dissipation: From closed to open systems

Abstract

Current can be pumped through a closed system by changing parameters (or fields) in time. The Kubo formula allows to distinguish between dissipative and non-dissipative contributions to the current. We obtain a Green function expression and an S matrix formula for the associated terms in the generalized conductance matrix: the "geometric magnetism" term that corresponds to adiabatic transport; and the "Fermi golden rule" term which is responsible to the irreversible absorption of energy. We explain the subtle limit of an infinite system, and demonstrate the consistency with the formulas by Landauer and Büttiker, Prétre and Thomas. We also discuss the generalization of the fluctuation-dissipation relation, and the implications of the Onsager reciprocity.

Floquet scattering theory for current and heat noise in large amplitude adiabatic pumps

“…38 For our model, Eq. (35), and for well separated transmission resonances each time only one resonance contributes to the pumped charge and noise. If the Fermi energy EF changes then the corresponding resonance line [in the plane of pump parameters (V1, V2)] can leave the pumping contour [the trace of the point with coordinates (V1(t), V2(t)) ].…”

“…This mechanism is relevant not only for open (i.e., connected to external particle reservoirs) systems but also for closed (ring-like) mesoscopic systems. 34,35,36 The possibility 5,14,37−44 to achieve quantized transport, not only of charge but in addition heat 14,22,45,46 and spin 3,47−60 currents, makes pumping interesting also in view of possible applications. Quantum pumping has been investigated in systems of strongly correlated electrons 8,47,55,61 , for systems in the quantum Hall regime 62,63 and in hybrid superconducting-normal structures.…”

Spin pumping by a field-driven domain wall

“…4 Currently, the activity in this field is mostly concentrated on the effects of interactions, 5 dissipation, 6 and nonadiabaticity. 7 Complementary to these developments, the emission of spin current by a precessing ferromagnet-called spin pumping-has been studied theoretically and experimentally in single-domain magnetic nanostructures.…”

Nonadiabatic charge pumping by oscillating potentials in one dimension: Results for infinite system and finite ring

“…Most studies of charge pumping have also been limited to infinite systems in which the left and right sides of the system (called the leads or reservoirs) are associated with certain chemical potentials and temperatures. Charge pumping on a finite ring has been studied in a few papers for adiabatic [13][14][15][16] and nonadiabatic situations [23,25,26].…”

“…For the case of non-interacting electrons, theoretical studies of this phenomenon have used adiabatic scattering theory [9][10][11][12][13][14][15][16][17], Floquet scattering theory [21][22][23], the nonequilibrium Green function formalism [24][25][26][27], and the equation of motion approach [36,37]. The case of interacting electrons has been studied using a renormalization group method for weak interactions [50], and the method of bosonization for arbitrary interactions [51][52][53][54][55][56][57][58][59][60][61].…”