Ground state structure and conductivity of quantum wires of infinite length and finite width

We have studied the ground state structure of quantum strips within the local spin-density approximation, for a range of electronic densities between $\sim 5\times {10}^4$ and $2\times {10}^6{\mathrm{cm}}^{-1}$ and several strengths of the lateral confining potential. The results have been used to address the conductance $G$ of quantum strips. At low density, when only one subband is occupied, the system is fully polarized and $G$ takes a value close to $0.7(2e^2∕h)$, decreasing with increasing electron density in agreement with experiments. At higher densities the system becomes paramagnetic and $G$ takes a value near $(2e^2∕h)$, showing a similar decreasing behavior with increasing electron density. In both cases, the physical parameter that determines the value of the conductance is the ratio $K∕K_0$ of the compressibility of the system to the free one.

Figure 1

Energy per electron (meV, left scale) and magnetization (right scale) in the Hartree model for a parabolic confinement of ${\omega }_0=2\mathrm{meV}$ as a function of the linear density $\left({\mathrm{cm}}^{-1}\right)$. The regions separated by vertical lines correspond to the indicated number of occupied subbands. For one single occupied subband, the system is fully polarized.

Figure 2

Same as Fig. 1 for ${\omega }_0=4\mathrm{meV}$.

Figure 3

Same as Fig. 1 for ${\omega }_0=6\mathrm{meV}$.

Figure 4

Energy per electron (meV, bottom panel) and magnetization (top panel) in the exchange-correlation model for a parabolic confinement of ${\omega }_0=2\mathrm{meV}$ as a function of the linear density $\left({\mathrm{cm}}^{-1}\right)$. The regions separated by vertical lines correspond to the indicated number of occupied subbands. For one single occupied subband, the system is fully polarized.

Figure 5

Same as Fig. 4 for ${\omega }_0=4\mathrm{meV}$.

Figure 6

Same as Fig. 4 for ${\omega }_0=6\mathrm{meV}$.

Figure 7

Several density profiles of the 2D electronic density as a function of $x\left(\mathrm{nm}\right)$ for the Hartree model and a harmonic frequency ${\omega }_0=4\mathrm{meV}$ (left scale). Also shown is the local magnetization $\xi$ for the three-subband case (right scale). The values of the 1D electronic densities, which correspond to configurations with one, three, and six occupied subbands, are indicated.

Figure 8

Same as Fig. 7 for the exchange-correlation model.

Figure 9

Ratio $\gamma =\sqrt{K∕K_0}$ as a function of the linear density ${\rho }_1\left({\mathrm{cm}}^{-1}\right)$ for the exchange-correlation model and three values of the harmonic frequency ${\omega }_0$. The lines have been drawn to guide the eye.