Stroboscopic Wave-Packet Description of Nonequilibrium Many-Electron Problems

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.

Figure 1

Squared amplitudes of orthogonal stroboscopic wave packets obtained by time propagation of the initial WP (in the center) by a constant time-step $\tau$ for free electrons in 1D. The right- (blue, or solid) and left-going (red, or dashed) WPs belonging from the same energy band (inset) are shown. These, together with the WPs coming from the bands covering the rest of the spectrum, form a complete orthogonal basis set.

Figure 2

Abrupt switching on of the bias in a 1D wire. In response to the bias $\Delta V$, the right-going WPs for $x>0$ (white, the previously unoccupied band) start to fill the WPs from the left and the occupied left-going WPs for $x<0$ become empty. The finite extent of each WP causes oscillations, with period $\tau$, of the resulting occupancy $N_m(t)$ and hence the current measured at the fixed position of the $m$th bulk WP, $x_m=v_{F}m\tau$ (below).