We analyze the nonlinear voltage dependence of electrochemical capacitance for nanoscale conductors. This voltage dependence is due to the finite density of states of the conductors. Within Hartree theory we derive an exact expression for the electrochemical capacitance-voltage curve for a parallel plate system. The result suggests a quantum scanning capacitance microscopy at the nanoscale: by inverting the capacitance-voltage expression one is able to deduce the local spectral function of the nanoscale conductor.

We theoretically put forward a spin injector, which consists of a three-terminal ferromagnetic-metal (FM) nonmagnetic-semiconductor (NS)-superconductor (SC) mesoscopic hybrid system. This device can inject not only the spin-up current but also the pure spin current into the NS lead. The crossed Andreev reflection plays a key role in this device. Such a spin injector may be realized within the reach of the present-day technology.

We present a solution to the problem of ac current partition in a multiprobe mesoscopic conductor within the nonequilibrium Green's function formalism. This allows the derivation of dynamic conductance which is appropriate for nonequilibrium situations and which satisfies the current conservation and gauge invariance requirements. This formalism presents a significant generalization to previous theory: (i) There is no limit in the frequency, and (ii) it allows detailed treatments of interactions in the mesoscopic region. The formalism is applied to calculate the dynamic conductance of tunneling structures with and without assuming a wideband limit.

We report a first-principles theory for analyzing the parametric electron pump at finite frequency. The pump is controlled by two pumping parameters with phase difference Φ In the zero-frequency limit, our theory recovers the well-known adiabatic result that the pumped current I (Φ)～sinΦ. At a finite frequency, it predicts I (Φ=0)≠0 while I (Φ=π)≈0, consistent with recent experimental data. We discuss a possible mechanism behind the nonzero pumped current at f50 from photon-assisted processes.

We report a theoretical investigation of shot noise of spin current without an accompanying charge current. For a two-probe spin pump, both cross- and autocorrelations are needed to characterize the noise. The corresponding Fano factors measure the spin unit of the quasiparticles in the spin current. The shot noise also detects open channels for spin transport, and can have qualitatively different behavior compared with the shot noise of charge current.