Magnetic-Field Asymmetry of Electron Wave Packet Transmission in Bent Channels Capacitively Coupled to a Metal Gate

We study the electron wave packet moving through a bent channel. We demonstrate that the packet transmission probability becomes an asymmetric function of the magnetic field when the electron packet is capacitively coupled to a metal plate. The coupling occurs through a nonlinear potential which translates a different kinetics of the transport for opposite magnetic-field orientations into a different potential felt by the scattered electron.

Figure 1

(a) Backscattered trajectories for $\pm B$. For $-B$ ($+B$) the trajectories are deflected to the right (left) by the Lorentz force. (b) The electron along the axis of the straight wire that is covered [blue (dark gray) lines] and uncovered [red (medium gray) lines] by a metal plate. (c) Dots show the position of the centers of the basis function [Eq. (2)] defining the channel. Shaded area shows the channel range determined as the region where the sum of the absolute values of the basis functions is larger than 6.5% of its maximum value. The horizontal lines show the range of the bent part $y\in [330\mathrm{nm},726\mathrm{nm}]$.

Figure 2

Snapshots of the motion of the electron packet injected into the bent wire from the lower lead for opposite $B$ orientations. Later moments in time correspond to lower plots. Solution of the linear Schrödinger equation (a–h) is presented for $t=2.1$, 4.8, 6.7 and 9.5 ps and the solution including the nonlinear term of the wave packet-metal interaction (i–p) is given for $t=3.4$, 5.8, 7.7 and 9.7 ps. Green (light gray) lines delimit the channel as defined in Fig. 1c.

Figure 3

The snapshots of the packet density along $x=0$ for the electron interacting with metal for $B=-0.75\mathrm{T}$, 0 and 0.75 T in (a), (b), and (c), respectively. In (b) the incoming, reflected and transmitted packets are marked by $i$, $r$, and $t$, respectively.

Figure 4

Same as Fig. 3 for the normal wave packet (a) and the packet interacting with metal (b).

Figure 5

Parts of the wave packet before, after, and inside the bent part of the wire for the electron density uncoupled (a) and coupled (b) to the metal plate. Solid lines show the results for $B>0$ and dashed lines for $B<0$. In (a) the part before the packet for $B<0$ is given by the symbols. (c) Lower (solid) and upper (dashed) curves are bounds for the wave packet transfer probability for $B>0$ [blue (dark gray) lines] and $B<0$ [red (medium gray) lines].