Time-dependent current partition in mesoscopic conductors

Abstract

The currents at the terminals of a mesoscopic conductor are evaluated in the presence of slowly oscillating potentials applied to the contacts of the sample. The need to find a charge and current conserving solution to this dynamic current partition problem is emphasized. We present results for the electro-chemical admittance describing the long range Coulomb interaction in a Hartree approach. For multiply connected samples we discuss the symmetry of the admittance under reversal of an Aharonov-Bohm flux.

Dynamic Conductance of Carbon Nanotubes

“…Moreover, the induced charges within a conductor, on a nearby gate, or on the surface of an electron reservoir can all play an important role in determining ac transport. These features all give rise to significant complications in the formulation of transport theory at the nanometer length scale, and are the focus of current, ongoing theoretical research [15,16]. In this Letter, we report on a theoretical investigation of the dynamic conductance of single-wall carbon nanotubes, both with and without defects.…”

“…Under ac conditions, electrodynamics shows that displacement currents are induced, which can substantially alter the transport properties of the system [15]. In order to predict the dynamic conductance of nanoscale conductors such as the carbon nanotubes, the inclusion of these displacement currents into the theoretical formalism is absolutely necessary for two fundamental reasons.…”

Numerical toolkit for electronic quantum transport at finite frequency

“…We refer to the response function dn(i, 1ω, m )/dV ac as the generalized injectivity. It is a straightforward generalization of the injectivity defined in 43,47 at small frequency and it reads 76 ,…”

“…(16), will become obvious. Last, we introduce the frequency-dependent Lindhard function 43,47 that relates a change of density on site j to the perturbation on site j as 76 ,…”

Landauer-Büttiker formula for time-dependent transport through resonant-tunneling structures: A nonequilibrium Green’s function approach

“…[5][6][7] As a matter of fact, the importance of the displacement current was first noted by Büttiker and co-workers. [8][9][10] To analyze the electron transport in the presence of ac fields, they developed a linear, low-frequency theory 8,9 based on the scattering matrix formulation, in which current conservation and gauge invariance are guaranteed. Very recently, Wang et al 7 further studied the ac problem by means of nonequilibrium Green's functions and also derived an expression for the linear dynamic conductance that conserves electric current and satisfies the gauge invariance.…”