Spin depolarization in quantum wires polarized spontaneously in zero magnetic field

The conditions for a spontaneous spin polarization in a quantum wire positioned in a zero magnetic field are analyzed under weak population of one-dimensional (1D) subbands, which gives rise to the efficient quenching of the kinetic energy by the exchange energy of carriers. The critical linear concentration of carriers above which the quasi-one-dimensional gas undergoes a complete spin depolarization is determined by the Hartree-Fock approximation. The dependence of the critical linear concentration on the carrier’s concentration is defined to reveal the interplay of the spin depolarization with the evolution of the “$0.7(2e^2∕h)$” feature in the quantum conductance staircase from the $e^2∕h$ to $\left(3∕2\right)(e^2∕h)$ values. This dependence is used to study the effect of the hole concentration on the $0.7(2e^2∕h)$ feature in the quantum conductance staircase of the quantum wire prepared inside the $p$-type silicon quantum well using the split-gate technique. The 1D channel is demonstrated to be spin-polarized at the linear concentration of holes lower than the critical linear concentration, because the $0.7(2e^2∕h)$ feature is close to the value of $0.5(2e^2∕h)$ that indicates the spin degeneracy lifting for the first step of the quantum conductance staircase. The $0.7(2e^2∕h)$ feature is found to take, however, its normal magnitude when the linear concentration of holes attains the critical value corresponding to the spin depolarization. The variations in the height of the $0.7(2e^2∕h)$ feature observed in the hole quantum conductance staircase that is revealed by the p-type silicon quantum wire seem to be related to the evidences of the quantum conductance staircase obtained by varying the concentration of electrons in the 1D channel prepared inside the $\mathrm{GaAs}\text{−}\mathrm{AlGaAs}$ heterojunction [K. S. Pyshkin, C. J. B. Ford, R. H. Harrell, M. Pepper, E. H. Linfield, and D. A. Ritchie, Phys. Rev. B 62, 15842 (2000)].

Figure 1

Dependence of the critical linear concentration corresponding to a complete spin depolarization of the quasi-1D electron gas in a quantum wire connecting 2D reservoirs in a $\mathrm{GaAs}∕\mathrm{GaAlAs}$ QW on the concentration of electrons; $R=100\mathrm{nm},$ $d=20\mathrm{nm}$. Circles indicate the height of the $0.7(2e^2∕h)$ feature determined in the studies of the 1D channels prepared by split-gate method in $\mathrm{GaAs}∕\mathrm{GaAlAs}$ QWs (Refs. 1, 7, 8, 9).

Figure 2

Schematic diagram of the device that demonstrates a perspective view of the $p$-type silicon quantum well located between the $\delta$ barriers heavily doped with boron on the $n$-type $\mathrm{Si}\left(100\right)$ substrate as well as the top gate and the depletion regions created by split-gate method, which indicate a $D$ channel connecting two 2D reservoirs.

Figure 3

The quantum conductance staircase of the silicon quantum wire as a function of the sheet density of holes that was tuned controllably by biasing the top gate, which fulfills the application of the $p^{+}\text{−}n$ bias voltage to the $p$-type silicon quantum well on the $n$-type $\mathrm{Si}\left(100\right)$ surface. The $p^{+}\text{−}n$ bias voltage is varied from the forward branch to the reverse branch between $+110\mathrm{mV}$ and $-120\mathrm{mV}$, which establishes the range of the magnitude of $p_{2\mathrm{D}}$ from $5\times {10}^{12}{\mathrm{m}}^{-2}$ to $9\times {10}^{13}{\mathrm{m}}^{-2}$ provided that zero $p^{+}\text{−}n$ bias voltage results in the value of $p_{2\mathrm{D}}$ equal to $4\times {10}^{13}{\mathrm{m}}^{-2}$.

Figure 4

Dependence of the critical linear concentration corresponding to a complete spin depolarization of the quasi-1D hole gas in a quantum wire connecting 2D reservoirs in a silicon quantum well on the concentration of holes; $R=2\mathrm{nm},$ $d=2\mathrm{nm}$. Circles indicate the values of the height of the $0.7(2e^2∕h)$ feature that are shown in Fig. 1.