Time-dependent magnetotransport in an interacting double quantum wire with window coupling

We present a double quantum wire system containing a coupling element in the middle barrier between the two parallel quantum wires. We explicitly account for the finite length of the double quantum wire with a time-dependent switching-on potential coupling the double-wire system and the leads. By tuning the magnetic field and the coupling window between the wires, we analyze the time-dependent current and the charge distribution of the Coulomb interacting many-electron states in order to explore interwire transfer effects for developing efficient quantum interference nanoelectronics.

Figure 1

(Color online) (Upper panel) Schematic of the coupling of the lateral DWs to the external leads and their internal coupling through a coupling element. (Lower panel) The potential defining the window-coupled DW system, $\hslash {\Omega }_0=1.0\text{meV}$, $B=0\text{T}$, and $a_w=33.74\text{nm}$.

Figure 2

(Color online) Energy spectrum of the leads (solid red) versus wave number $q$ (left panel) and energy spectrum of the window-coupled DW system (cross dot) versus the SES number $n$ (right panel). The five lowest SESs are used to construct the 32 MESs that are used in the exact diagonalization of the interacting Hamiltonian (11). Magnetic field $B=0.5\text{T}$, and the chemical potentials in the leads are ${\mu }_{\text{L}}=1.65\text{meV}$ and ${\mu }_{\text{R}}=0.75\text{meV}$ (dashed green) such that $\Delta \mu =0.9\text{meV}$. The window of relevant states ${\Delta }_E=1.5\text{meV}$ is defined by the dotted blue lines.

Figure 3

(Color online) The interacting net current $I_{Q,I}$ (solid red), the noninteracting net current $I_{Q,0}$ (solid blue), the noninteracting left current $I_{\text{L},0}$ (dashed green), and the noninteracting right current $I_{\text{R},0}$ (dashed light blue) are plotted as a function of time: (a) short-time response; (b) long-time response. The magnetic field $B=0.5\text{T}$, the length of the coupling window $L_{\text{w}}=100\text{nm}$, the system-lead coupling constant $g_0^l{a}_w^{3/2}=60\text{meV}$, and the contact size parameters ${\delta }_x^l={\delta }_y^l=4.4\times {10}^{-4}{\text{nm}}^{-2}$.

Figure 4

(Color online) The many-electron charge density for the noninteracting (left panel) and interacting system (right panel) for $B=0.5\text{T}$. The other parameters are the same as Fig. 3.

Figure 5

(Color online) The interacting net current $I_{Q,I}$ versus time for $L_{\text{w}}=0$ (dotted black), 50 (dashed blue), and 100 nm (solid red): (a) short-time response; (b) long-time response for $B=0.5\text{T}$. The other parameters are the same as Fig. 3.

Figure 6

(Color online) The spatial distribution of the interacting many-electron charge density with different coupling window: $L_{\text{w}}=0.0\text{nm}$ (left), $L_{\text{w}}=50\text{nm}$ (middle), and $L_{\text{w}}=100\text{nm}$ (right) at time $t=14$, 31.2, 100, and 200 ps. $B=0.5\text{T}$ and the other parameters are the same as Fig. 3.

Figure 7

(Color online) The interacting net current $I_{Q,I}$ for cases of $B=0.0\text{T}$ (dotted black), 0.5 T (dashed blue), and 1.0 T (solid red) are plotted as a function of time: (a) short-time response; (b) long-time response. The other parameters are the same as Fig. 3.