The presence of spin-orbit coupling affects the spontaneously flowing persistent currents in mesoscopic conducting rings. Here we analyze their dependence on magnetic flux with emphasis on identifying possibilities to prove the presence and extract the strength of Rashba spin splitting in low-dimensional systems. Effects of disorder and mixing between quasi-one-dimensional ring subbands are considered. The spin-orbit coupling strength can be inferred from the values of flux where sign changes occur in the persistent charge current. As an important consequence of the presence of spin splitting, we identify a nontrivial persistent spin current that is not simply proportional to the charge current. The different flux dependences of persistent charge and spin currents are a unique signature of spin-orbit coupling affecting the electronic structure of the ring.

We investigate the shot noise generated by particle emission from a mesoscopic capacitor into an edge state coupled to another edge state at a quantum point contact (QPC). For a capacitor subject to a periodic voltage the resulting shot noise is proportional to the number of particles (both electrons and holes) emitted during a period. The shot noise is proportional to the driving frequency, however it is independent of the applied voltage. If two capacitors are coupled to a QPC at different sides then the resulting shot noise is maximally the sum of noises produced by each of the capacitors. However, the noise is suppressed if particles of the same kind are emitted simultaneously.

We present a general formalism to study adiabatic pumping through interacting quantum dots. We derive a formula that relates the pumped charge to the local, instantaneous Green’s function of the dot. This formula is then applied to the infinite-$U$ Anderson model for both weak and strong tunnel-coupling strengths.

In this paper, we investigate the thermoelectric performance of a double-dot device driven by time-dependently modulated gate voltages. We show that if the modulation frequency $$\Omega${}$ is sufficiently small, not only quantized charge pumping can be realized, but also the heat current flowing in the leads is quantized and exhibits plateaux in units of $\frac{$\Omega${}}{2$\pi${}}\phantom{\rule{0.16em}{0ex}}{k}_{\mathrm{B}}T\mathrm{ln}2$. The factor $\mathrm{ln}2$ stems from the degeneracy of the double-dot states involved in transport. This opens the possibility of using the pumping cycle to transfer heat against a temperature gradient or to extract work from a hot reservoir with Carnot efficiency. However, the performance of a realistic device is limited by dissipative effects due to leakage currents and finite-frequency operation, which we take into account rigorously by means of a generalized master equation approach in the regime where the double dot is weakly coupled to the leads. We show that despite these effects, the efficiency of a double-dot charge pump performing work against a dc source can reach of up to 70$%$ of the ideal value.

With the development of single-atom transistors, consisting of single dopants, nanofabrication has reached an extreme level of miniaturization. Promising functionalities for future nanoelectronic devices are based on the possibility of coupling several of these dopants to each other. This already allowed to perform spectroscopy of the donor state by d.c. electrical transport. The next step, namely manipulating a single electron over two dopants, remains a challenge. Here we demonstrate electron pumping through two phosphorus donors in series implanted in a silicon nanowire. While quantized pumping is achieved in the low-frequency adiabatic regime, we observe remarkable features at higher frequency when the charge transfer is limited either by the tunnelling rates to the electrodes or between the two donors. The transitions between quantum states are modelled involving a Landau–Zener transition, allowing to reproduce in detail the characteristic signatures observed in the non-adiabatic regime.

We present a diagrammatic real-time approach to adiabatic pumping of electrons through interacting quantum dots. Performing a systematic perturbation expansion in the tunnel-coupling strength, we compute the charge pumped through a single-level quantum dot per pumping cycle. The combination of coulomb interaction and quantum fluctuations, accounted for in contributions of higher order in the tunnel coupling, modifies the pumping characteristics via an interaction-dependent renormalization of the quantum-dot level. The latter is even responsible for the dominant contribution to the pumped charge when pumping via time-dependent tunnel-coupling strengths.