Electron transport through quantum wires and point contacts

We have studied quantum wires using the Green’s function technique within density-functional theory, calculating electronic structures and conductances for different wire lengths, temperatures, and bias voltages. For short wires, i.e., quantum point contacts, the zero-bias conductance shows as a function of the gate voltage and at a finite temperature a plateau at around $0.7G_0$. ($G_0=2e^2∕h$ is the quantum conductance.) The behavior, which is caused in our mean-field model by spontaneous spin polarization in the constriction, is reminiscent of the so-called 0.7 anomaly observed in experiments. In our model the temperature and the wire length affect the conductance–gate-voltage curves similarly as in experiments.

Figure 1

2D quantum wire between two electrodes. The gray areas denote the rigid positive background charge of the electrodes. The electrodes continue to infinity outside the calculation region. The uniform background charge density is varied in the black wire region in order to model the effects of the gate voltage.

Figure 2

(a) Total electron density and (b) difference between the spin-up and spin-down electron densities at zero temperature for a system with dimensions $S=5a_0^{*}$, $L=7a_0^{*}$, $W=20a_0^{*}$, $A=47a_0^{*}$ (see Fig. 1) and for the gate voltage of $12.4\mathrm{mV}$.

Figure 3

Conductance as a function of the gate voltage for QW’s with width $S=5a_0$ and with different lengths $L$. The width of the electrodes is $W=20a_0^{*}$, and the length of the computational area is $A=47a_0^{*}$ (see also Fig. 1). The successive curves have been shifted by $0.5G_0$. The conductance of the wire with $L=10a_0$ is decomposed into spin-up and spin-down contributions (dotted lines).

Figure 4

Conductance as a function of the gate voltage for QW’s with the width $S=5a_0^{*}$ and lengths $L=6a_0^{*}$ (wire A), $7a_0^{*}$ (wire B) and $8a_0^{*}$ (wire C) at the temperatures of $0\mathrm{K}$ (solid curve), $2\mathrm{K}$ (dashed curve), and $4\mathrm{K}$ (dotted curve).

Figure 5

Uppermost and middle panels: Conductances due to spin-up (dashed curves) and spin-down (solid curves) electrons as a function of the gate voltage and at temperatures of 0 and $2\mathrm{K}$. Lowest panel: LDOS corresponding to the QW region for the spin-up and spin-down states at the gate voltage of $14\mathrm{mV}$ and at the temperatures of $0\mathrm{K}$ (solid curve) and $2\mathrm{K}$ (dashed curve). The dotted line denotes the Fermi level. The results are for wire B with the length $L=7a_0^{*}$.

Figure 6

Differential conductance of wire B with the width $S=5a_0^{*}$ and length $L=7a_0^{*}$ as a function of the gate voltage and at zero temperature. Results for bias voltages of $0\mathrm{mV}$ (dotted curve), $0.23\mathrm{mV}$ (dashed curve), and $0.46\mathrm{mV}$ (solid curve) are given.