We give a gauge description of the adiabatic charge pumping in closed systems, both in Abelian and non-Abelian processes, and by means of asymptotic Wilson loops in a suitable parameter manifold. Our geometric formulation provides new insights into this issue, and a very simple algorithm for numerical computations. Indeed, as we show first, discretized Berry--Wilczeck--Zee holonomies are easy to implement. Finally, we study non-Abelian pumping in a solvable four-state model, already used in several contexts, to demonstrate the relevance of our approach.
Topological pumping of edge states in finite crystals or quasicrystals with non-trivial topological phases provides a powerful means for robust excitation transfer. In most schemes of topological pumping, the edge states become delocalized and immersed into the continuum during the adiabatic cycle, requiring extremely slow evolution to avoid nonadiabatic effects. Here a scheme of topological pumping based on adiabatic passage of edge and interface states is proposed, which is more robust against nonadiabatic effects and avoids delocalization of the state over the entire adiabatic cycle. The sc…
The adiabatic charge pumping of a non-equilibrium state of spinless fermions in a one-dimensional lattice is investigated, with an emphasis placed on its usefulness in revealing many-body interaction effects on interband coherence. For a non-interacting system, the pumped charge per adiabatic cycle depends not only on the topology of the occupied bands but also on the interband coherence in the initial state. This insight leads to an interesting opportunity for quantitatively observing how quantum coherence is affected by many-body interaction that is switched on for a varying duration prior t…
Adiabatic pumping is a fundamental concept in the time-dependent transport of mesoscopic devices. To maximize pumping performance, i.e., the amount of pumping per unit time, it is necessary to carefully manage the driving speed, which should be sufficiently less than the {\it limited speed}, an upper bound of the driving speed below which non-adiabatic effects are negligible. In general, the amount of pumping increases as the contour of the driving parameter lengthens, however a long contour diminishes the pumping power because it requires more time per cycle under the limited speed constraint…
Periodic driving can create topological phases of matter absent in static systems. In terms of the displacement of the position expectation value of a time-evolving wavepacket in a closed system, a type of adiabatic dynamics in periodically driven systems is studied for general initial states possessing coherence between different Floquet bands. Under one symmetry assumption, the displacement of the wavepacket center over one adiabatic cycle is found to be comprised by two components independent of the time scale of the adiabatic cycle: a weighted integral of the Berry curvature summed over al…
We investigate adiabatic pumping via a single level quantum dot induced by periodic modulation of thermodynamic variables of reservoirs, i.e., temperatures and electrochemical potentials. We consider the impurity Anderson model and derive analytical formulas for coherent adiabatic charge pumping applicable to the strong dot-reservoir coupling within first-order perturbation with respect to Coulomb interaction. We show that charge pumping is induced by rectification effect due to delayed response of the quantum dot to time-dependent reservoir parameters. The presence of interaction is necessary…
We formulate adiabatic charge pumping via a single-level quantum dot (QD) induced by reser- voir parameter driving, i.e., temperature and electrochemical potential driving. Our formulation describes arbitrary strength of dot-reservoir coupling and Coulomb interaction in the QD, and is applicable to the low-temperature regime, where the Kondo effect becomes important. The adia- batic charge pumping is expressed by the Berry connection and is related to delayed response of the QD. We calculate the pumped charge by the renormalized perturbation theory, and discuss how the Coulomb interaction affe…
We use exact techniques to demonstrate theoretically the pumping of fractional charges in a single-level non-interacting quantum dot, when the dot-reservoir coupling is adiabatically driven from weak to strong coupling. The pumped charge averaged over many cycles is quantized at a fraction of an electron per cycle, determined by the ratio of Lamb shift to level-broadening; this ratio is imposed by the reservoir band-structure. For uniform density of states, half an electron is pumped per cycle. We call this "adiabatic almost-topological pumping", because the pumping's Berry curvature is sharpl…
Based on the Floquet scattering theory, we analytically investigate the topological spin pumping for an exactly solvable model. Floquet spin Chern numbers are introduced to characterize the periodically time-dependent system. The topological spin pumping remains robust both in the presence and in the absence of the time-reversal symmetry, as long as the pumping frequency is smaller than the band gap, where the electron transport involves only the Floquet evanescent modes in the pump. For the pumping frequency greater than the band gap, where the propagating modes in the pump participate in the…
A generalization of the Aubry-André-Harper (AAH) model is developed, containing a tunable phase shift between on-site and off-diagonal modulations. A localization transition can be induced by varying just this phase, keeping all other model parameters constant. The complete localization phase diagram is obtained. Unlike the original AAH model, the generalized model can exhibit a transition between topologically trivial bandstructures and topologically non-trivial bandstructures containing protected boundary states. These boundary states can be pumped across the system by adiabatic variations i…
We consider charge pumping in a system of parafermions, implemented at fractional quantum Hall edges. Our pumping protocol leads to a noisy behavior of the pumped current. As the adiabatic limit is approached, not only does the noisy behavior persist but the counting statistics of the pumped current becomes robust and universal. In particular, the resulting Fano factor is given in terms of the system's topological degeneracy and the pumped quasiparticle charge. Our results are also applicable to the more conventional Majorana fermions.
In a mesoscopic system, under zero bias voltage, a finite charge is transferred by quantum adiabatic pumping by adiabatically and periodically changing two or more control parameters. We obtained expressions for the pumped charge for a ring of three quantum dots (QDs) by choosing the magnetic flux penetrating the ring as one of the control parameters. We found that the pumped charge shows a steplike behavior with respect to the variance of the flux. The value of the step heights is not universal but depends on the trajectory of the control parameters. We discuss the physical origin of this beh…
