Magnetotransport in a double quantum wire: Modeling using a scattering formalism built on the Lippmann-Schwinger equation

We model electronic transport through a double quantum wire in an external homogeneous perpendicular magnetic field using a scattering formalism built on the Lippmann-Schwinger equation. In the scattering region a window is opened between the parallel wires allowing for inter- and intrawire scattering processes. Due to the parity breaking of the magnetic field the ensuing subband energy spectrum of the double wire system with its regimes of hole- and electronlike propagating modes leads to a more structure rich conductance as a function of the energy of the incoming waves than is seen in a single parabolically confined quantum wire. The more complex structure of the evanescent modes of the system also leaves its marks on the conductance.

Figure 1

(Color online) A section of the double quantum wire showing the scattering potential and the window between the wires. The color scale on the right shows the potential height in meV. The effective magnetic confinement length $a_w=33.7\mathrm{nm}$, and other parameters are in the text.

Figure 2

(Color online) The energy spectrum of the propagating electronic states (solid red) vs the Fourier parameter $q$, and the energy spectrum of the evanescent states (dotted blue) vs $iq$, in the asymptotically free regions of the quantum wire. $D$ is an overall multiplicative factor to the deviation $V_{\delta }\left(y\right)$ from the parabolic confinement. $B=0\mathrm{T}$.

Figure 3

(Color online) The energy spectrum of the propagating electronic states (solid red) vs the Fourier parameter $q$, and the energy spectrum of the evanescent states (dotted blue) vs $iq$, in the asymptotically free regions of the quantum wire. $D$ is an overall multiplicative factor to the deviation $V_{\delta }\left(y\right)$ from the parabolic confinement. $B=0.5\mathrm{T}$.

Figure 4

(Color online) (Upper panel) The conductance of an ideal weakly $(D=0.6)$ modulated double quantum wire without a window (dashed green), and with a window between the wires (solid red). (Lower panel) The energy spectrum of the propagating electronic states (solid red) vs the Fourier parameter $q$, and the energy spectrum of the evanescent states (dotted blue) vs $iq$, in the asymptotically free regions of the quantum wire. $B=0.5\mathrm{T}$, $\alpha =0.0002{\mathrm{nm}}^{-2}$, and $V_0=-1.2\mathrm{meV}$.

Figure 5

(Color online) (Upper panel) The conductance of a double quantum wire with a window between the wires of different lengths indicated by the three different values of $\alpha$ used for the scattering potential (3). (Lower panel) The energy spectrum of the propagating electronic states (solid red) vs the Fourier parameter $q$, and the energy spectrum of the evanescent states (dotted blue) vs $iq$, in the asymptotically free regions of the quantum wire. $B=0.5\mathrm{T}$, $D=1.0$, and $V_0=-2.0\mathrm{meV}$.

Figure 6

(Color online) The energy spectrum of the two lowest propagating electronic subbands vs the Fourier parameter $q$ in the asymptotically free regions of the quantum wire. The two horizontal dashed green lines represent the energies $E=2.155\mathrm{meV}$ and $E=3.417\mathrm{meV}$. The active transport modes are labeled for these two energies with the notation $n_i$, where $i$ is the number of the active mode in subband number $n$. $D=1$ and $B=0.5\mathrm{T}$.

Figure 7

(Color online) The electron probability density for the $n_i=0_2$ electronlike mode at input energy $E=2.155\mathrm{meV}$ (a), for the mode at $E=2.902\mathrm{meV}$ (b), and for the holelike mode at $E=2.942\mathrm{meV}$ (c). $B=0.5\mathrm{T}$, $\alpha =0.0002{\mathrm{nm}}^{-2}$, and $D=1.0$ corresponding to the solid red curve in the upper panel of Fig. 5.

Figure 8

(Color online) The electron probability density for the mode $n_i=1_2$ at input energy $E=3.212\mathrm{meV}$. $B=0.5\mathrm{T}$, $\alpha =0.0002{\mathrm{nm}}^{-2}$, and $D=1.0$ corresponding to the solid red curve in the upper panel of Fig. 5.

Figure 9

(Color online) The electron probability density at input energy $E=3.417\mathrm{meV}$ for mode $n_i=0_2$ (a), $n_i=1_2$ (b), $n_i=1_4$ (c), and $n_i=1_6$ (d). See Fig. 6 for the labeling of the modes. $B=0.5\mathrm{T}$, $\alpha =0.0002{\mathrm{nm}}^{-2}$, and $D=1.0$ corresponding to the solid red curve in the upper panel of Fig. 5.

Figure 10

(Color online) The electron probability density at input energy $E=3.761\mathrm{meV}$ for mode $n_i=1_2$. $B=0.5\mathrm{T}$, $\alpha =0.0002{\mathrm{nm}}^{-2}$, and $D=1.0$ corresponding to the solid (red) curve in the upper panel of Fig. 5.