We introduce the construction of an orthogonal wave-packet basis set, using the concept of stroboscopic time propagation, tailored to the efficient description of nonequilibrium extended electronic systems. Thanks to three desirable properties of this basis, significant insight is provided into nonequilibrium processes (both time-dependent and steady-state), and reliable physical estimates of various many-electron quantities such as density, current, and spin polarization can be obtained. Use of the wave-packet basis provides new results for time-dependent switching-on of the bias in quantum transport, and for current-induced spin accumulation at the edge of a 2D doped semiconductor caused by edge-induced spin-orbit interaction.

We demonstrate that the time operator that measures the time of arrival of a quantum particle into a chosen state can be defined as a self-adjoint quantum-mechanical operator using periodic boundary conditions and applied to wave functions in energy representation. The time becomes quantized into discrete eigenvalues; and the eigenstates of the time operator, i.e., the stroboscopic wave packets introduced recently [Phys. Rev. Lett. 101, 046402 (2008)], form an orthogonal system of states. The formalism provides simple physical interpretation of the time-measurement process and direct construction of normalized, positive definite probability distribution for the quantized values of the arrival time. The average value of the time is equal to the phase time but in general depends on the choice of zero time eigenstate, whereas the uncertainty of the average is related to the traversal time and is independent of this choice. The general formalism is applied to a particle tunneling through a resonant tunneling barrier in one dimension.

Presently, the main methods for describing a nonequilibrium charge-transporting steady state are based on time-evolving it from the initial zero-current situation. An alternative class of theories would give the statistical nonequilibrium density operator from principles of statistical mechanics, in a spirit close to Gibbs ensembles for equilibrium systems, leading to a variational principle for the nonequilibrium steady state. We discuss the existing attempts to achieve this using the maximum entropy principle based on constraining the average current. We show that the current-constrained theories result in a zero-induced drop in electrostatic potential, so that such ensembles cannot correspond to the time-evolved density matrix, unless left- and right-going scattering states are mutually incoherent.

We derive an expression for the four-point conductance of a general quantum junction in terms of the density response function. Our formulation allows us to show that the four-point conductance of an interacting electronic system possessing either a geometrical constriction and/or an opaque barrier becomes identical to the macroscopically measurable two-point conductance. Within time-dependent density-functional theory the formulation leads to a direct identification of the functional form of the exchange-correlation kernel that is important for the conductance. We demonstrate the practical implementation of our formula for a metal-vacuum-metal interface.

We characterize the role of the spin-orbit coupling between electrons and the confining potential of the edge in nonequilibrium two-dimensional homogeneous electronic gas. We derive a simple analytical result for the magnitude of the current-induced spin polarization at the edge and prove that it is independent of the details of the confinement edge potential and the electronic density within realistic values of the parameters of the considered models. While the amplitude of the spin accumulation is comparable to the experimental values of extrinsic spin-Hall effect in similar samples, the spatial extent of edge-induced effect is restricted to the distances on the order of Fermi wavelength ($\sim${}10$\hskip0.3em${}nm).

Ultrathin AlO${}_x$ layers are nowadays widely employed to make tunneling junctions and, as a common practice, experimental transport data are often rationalized in terms of analytical models invoking effective electronic and geometric properties of the oxide layer. In this paper we examine the reliability of such models by performing first-principles simulations of the transport properties of Al/AlO${}_x$/Al junctions. The band gap, effective mass, and interface width obtained from ground state density-functional calculations are used within a potential barrier model, known also as the Simmons model, and its predictions of the conductance are compared with first-principles results. We also propose an analytical expression for the conductance based on a tight-binding model of the interface oxide. We show that the success of the potential barrier model in fitting experimental transport measurements rests on its formal similarity with the tight binding model which, in contrast to the former, is directly related to the realistic electronic structure of the interface. DOI: http://dx.doi.org/10.1103/PhysRevB.87.195107 ©2013 American Physical Society