Effects of short-range interactions on transport through quantum point contacts: A numerical approach

We study electronic transport through a quantum point contact, where the interaction between the electrons is approximated by a contact potential. Our numerical approach is based on the nonequilibrium Green-function technique which is evaluated at the Hartree-Fock level. We show that this approach allows us to reproduce relevant features of the so-called “0.7 anomaly” observed in the conductance at low temperatures, including the characteristic features in recent shot-noise measurements. This is consistent with a spin-splitting interpretation of the process, and indicates that the 0.7 anomaly should also be observable in transport experiments with ultracold fermionic atoms.

Figure 1

The geometry of the system. Each point corresponds to one site of the numerical grid; the grey points indicate the region where the interaction is gradually switched on and off. The leads are coupled to the left and to the right as indicated by the white bars.

Figure 2

(Color online) Total conductance (solid line) and the up (dashed) and down (dotted) contributions for different interaction constants $\gamma$. The coupling constant takes values $\gamma =3.7$ (black, left), $\gamma =4.1$ (red, center), and $\gamma =4.5$ (blue, right) from left to right in units of ${\hslash }^2∕\left(2m\right)$. The curves for $\gamma \ge 4.1$ have been horizontally offset for clarity.

Figure 3

(Color online) Lower panel: conductance curves for different values of the coupling constant [$\gamma$ is given in units of ${\hslash }^2∕\left(2m\right)$]. The derivative (in arbitrary units) of each curve is plotted straight above the particular graph. The dashed lines mark the conductance value of the “plateau” for the lowest value of $\gamma$, where a local minimum in $\partial G∕\partial \mu$ is visible. The different curves are offset horizontally.

Figure 4

(Color online) Energy levels $E_{\uparrow }$ (black) and $E_{\downarrow }$ (red) for $\gamma =4.5\times {\hslash }^2∕\left(2m\right)$ and $E_Z=0.0015E_1$. The dashed curve shows the chemical potential $\mu$.

Figure 5

(Color online) Conductance curves for $\gamma =4.5\times {\hslash }^2∕\left(2m\right)$ and different magnetic fields. The corresponding Zeeman energies vary from $0$ to $0.14E_1$ in steps of $0.012E_1$ from left to right. The curves are horizontally offset.

Figure 6

(Color online) Conductance in the zero-field case. The dashed lines are for $B=0$; there is no difference between the $\uparrow$ and $\downarrow$ contribution and the total conductance does not exhibit a 0.7 feature. The solid lines show the results for $B\to 0$ where the $\uparrow$ (red) and $\downarrow$ (green) contributions differ and the total conductance (bold blue line) has a shoulder at $G\approx 0.65G_0$.

Figure 7

(Color online) Noise factor for $\gamma =4.0\times {\hslash }^2∕\left(2m\right)$ and for different values of the magnetic field $E_Z∕E_1=0.0$, 0.0007, 0.006, 0.012, 0.018, 0.23 from top to bottom. The dashed line indicates the result for noninteracting electrons.

Figure 8

(Color online) The conductance contributions $G_{\uparrow }$ and $G_{\downarrow }$ for $\gamma =4.5\times {\hslash }^2∕\left(2m\right)$ and for different temperatures $k_{B}T=0$ (solid black line), $k_{B}T=0.029E_1$ (dashed red line), and $k_{B}T=0.058E_1$ (dotted blue line). The inset shows the corresponding total conductance $G=G_{\uparrow }+G_{\downarrow }$.

Figure 9

(Color online) Total conductance (solid line) and the up (dashed) and down (dotted) contributions for different interaction constants ${\gamma }_C$ calculated with full Coulomb interaction. The dimensionless coupling constant takes values ${\gamma }_C=0.18$ (black, left), ${\gamma }_C=0.20$ (red, center), and ${\gamma }_C=0.22$ (blue, right) from left to right. The curves for ${\gamma }_C\ge 0.20$ have been horizontally offset for clarity.

Figure 10

The Green function is constructed by coupling single slices starting from one of the leads (grey regions).