Quantum pumping: Coherent Rings versus Open Conductors

We examine adiabatic quantum pumping generated by an oscillating scatterer embedded in a one-dimensional ballistic ring and compare it with pumping caused by the same scatterer connected to external reservoirs. The pumped current for an open conductor, paradoxically, is non-zero even in the limit of vanishing transmission. In contrast, for the ring geometry the pumped current vanishes in the limit of vanishing transmission. We explain this paradoxical result and demonstrate that the physics underlying adiabatic pumping is the same in open and in closed systems.Comment: 4 pages, 2 figure

Backscattering off a dynamical impurity in one-dimensional Fermi systems: A perturbative computation

We investigate the problem of backscattering off a time-dependent and spatially extended barrier in a one-dimensional electron gas. By performing a perturbative expansion in the backscattering amplitude, we compute the total energy density of the system. We show how the free fermion spectrum and the conductance of the system are affected by the interplay between dynamical and geometrical properties of the impurity.Comment: 4 pages, 2 figure

Energetics of metal slabs and clusters: the rectangle-box model

An expansion of energy characteristics of wide thin slab of thickness L in power of 1/L is constructed using the free-electron approximation and the model of a potential well of finite depth. Accuracy of results in each order of the expansion is analyzed. Size dependences of the work function and electronic elastic force for Au and Na slabs are calculated. It is concluded that the work function of low-dimensional metal structure is always smaller that of semi-infinite metal sample. A mechanism for the Coulomb instability of charged metal clusters, different from Rayleigh's one, is discussed. The two-component model of a metallic cluster yields the different critical sizes depending on a kind of charging particles (electrons or ions). For the cuboid clusters, the electronic spectrum quantization is taken into account. The calculated critical sizes of Ag_{N}^{2-} and Au_{N}^{3-} clusters are in a good agreement with experimental data. A qualitative explanation is suggested for the Coulomb explosion of positively charged Na_{\N}^{n+} clusters at 3<n<5.Comment: 11 pages, 6 figures, 1 tabl

Persistent currents in ballistic normal-metal rings

Recent experiments renewed interest in persistent currents in mesoscopic normal-metal rings. We show that in ballistic rings in high magnetic fields the Zeeman splitting leads to periodic current quenching with period much larger than the period of the persistent current. Simple arguments show that this effect might be relevant for diffusive rings as well. Another aim of this paper is to discuss fluctuations of the persistent current due to thermal excitation of high energy levels. Being observed such fluctuations would witness a coherent state of an electron system at high temperatures when the persistent current is exponentially suppressed.Comment: Submitted to Special Issue of the international journal Low Temperature Physics : "Quantum coherent effects in superconductors and normal metals" devoted to 75-years anniversary of Prof. Igor Kuli

Floquet Formalism of Quantum Pumps

We review Floquet formalism of quantum electron pumps. In the Floquet formalism the quantum pump is regarded as a time dependent scattering system, which allows us to go beyond the adiabatic limit. It can be shown that the well-known adiabatic formula given by Brouwer can be derived from the adiabatic limit of Floquet formalism. We compare various physical properties of the quantum pump both in the adiabatic and in the non-adiabatic regime using the Floquet theory.Comment: Latex2e 16 pages, 6 figures. A review paper to appear in Int. J. Mod. Phys.

Floquet states and persistent currents transitions in a mesoscopic ring

We consider the effect of an oscillating potential on the single-particle spectrum and the time-averaged persistent current of a one-dimensional phase-coherent mesoscopic ring with a magnetic flux. We show that in a ring with an even number of spinless electrons the oscillating potential has a strong effect on the persistent current when the excited side bands are close to the eigen levels of a pure ring. Resonant enhancement of side bands of the Floquet state generates a sign change of the persistent current.Comment: 2 figure

Quantum pump driven fermionic Mach-Zehnder interferometer

We have investigated the characteristics of the currents in a pump-driven fermionic Mach-Zehnder interferometer. The system is implemented in a conductor in the quantum Hall regime, with the two interferometer arms enclosing an Aharonov-Bohm flux $\Phi$. Two quantum point contacts with transparency modulated periodically in time drive the current and act as beam-splitters. The current has a flux dependent part $I^{(\Phi)}$ as well as a flux independent part $I^{(0)}$. Both current parts show oscillations as a function of frequency on the two scales determined by the lengths of the interferometer arms. In the non-adiabatic, high frequency regime $I^{(\Phi)}$ oscillates with a constant amplitude while the amplitude of the oscillations of $I^{(0)}$ increases linearly with frequency. The flux independent part $I^{(0)}$ is insensitive to temperature while the flux dependent part $I^{(\Phi)}$ is exponentially suppressed with increasing temperature. We also find that for low amplitude, adiabatic pumping rectification effects are absent for semitransparent beam-splitters. Inelastic dephasing is introduced by coupling one of the interferometer arms to a voltage probe. For a long charge relaxation time of the voltage probe, giving a constant probe potential, $I^{(\Phi)}$ and the part of $I^{(0)}$ flowing in the arm connected to the probe are suppressed with increased coupling to the probe. For a short relaxation time, with the potential of the probe adjusting instantaneously to give zero time dependent current at the probe, only $I^{(\Phi)}$ is suppressed by the coupling to the probe.Comment: 10 pages, 4 figure

Persistent current noise and electron-electron interactions

We analyze fluctuations of persistent current (PC) produced by a charged quantum particle moving in a ring and interacting with a dissipative environment formed by diffusive electron gas. We demonstrate that in the presence of interactions such PC fluctuations persist down to zero temperature. In the case of weak interactions and/or sufficiently small values of the ring radius $R$ PC noise remains coherent and can be tuned by external magnetic flux $\Phi_x$ piercing the ring. In the opposite limit of strong interactions and/or large values of $R$ fluctuations in the electronic bath strongly suppress quantum coherence of the particle down to $T=0$ and induce incoherent $\Phi_x$-independent current noise in the ring which persists even at $\Phi_x=0$ when the average PC is absent.Comment: 12 pages, 8 figure

Adiabatic quantum pump in the presence of external ac voltages

We investigate a quantum pump which in addition to its dynamic pump parameters is subject to oscillating external potentials applied to the contacts of the sample. Of interest is the rectification of the ac currents flowing through the mesoscopic scatterer and their interplay with the quantum pump effect. We calculate the adiabatic dc current arising under the simultaneous action of both the quantum pump effect and classical rectification. In addition to two known terms we find a third novel contribution which arises from the interference of the ac currents generated by the external potentials and the ac currents generated by the pump. The interference contribution renormalizes both the quantum pump effect and the ac rectification effect. Analysis of this interference effect requires a calculation of the Floquet scattering matrix beyond the adiabatic approximation based on the frozen scattering matrix alone. The results permit us to find the instantaneous current. In addition to the current generated by the oscillating potentials, and the ac current due to the variation of the charge of the frozen scatterer, there is a third contribution which represents the ac currents generated by an oscillating scatterer. We argue that the resulting pump effect can be viewed as a quantum rectification of the instantaneous ac currents generated by the oscillating scatterer. These instantaneous currents are an intrinsic property of a nonstationary scattering process.Comment: 11 pages, 1 figur

Floquet scattering theory of quantum pumps

We develop the Floquet scattering theory for quantum mechanical pumping in mesoscopic conductors. The nonequilibrium distribution function, the dc charge and heat currents are investigated at arbitrary pumping amplitude and frequency. For mesoscopic samples with discrete spectrum we predict a sign reversal of the pumped current when the pump frequency is equal to the level spacing in the sample. This effect allows to measure the phase of the transmission coefficient through the mesoscopic sample. We discuss the necessary symmetry conditions (both spatial and temporal) for pumping.Comment: 11 pages, 5 figure