Current-induced spin polarization in chiral tellurium: A first-principles quantum transport study

Te is a naturally $p$-doped semiconductor with a chiral structure, where an electrical current causes the conduction electrons to become spin-polarized parallel to the transport direction. In this paper, we present a comprehensive theoretical study of this effect, named current-induced spin polarization (CISP), by employing density functional theory (DFT) combined with the nonequilibrium Green's function (NEGF) technique for quantum transport. CISP can be quantitatively described in terms of the nonequilibrium spin density, which we show to be localized around the atoms. We then compute the atomic magnetic moments as a function of doping and electronic temperature, obtaining results overall consistent with those of previous theoretical studies. Beyond that, our DFT + NEGF calculations show that CISP also leads to a spin current, which is found to be quite a large fraction of the charge current, indicating that Te can be an efficient material for spin transport. We further predict that the resistance along a ballistic Te wire changes when an external magnetic field is applied parallel or antiparallel to the direction of the charge current. The computed magnetoresistance ratio is, however, quite small ($\sim 0.025\%$). Finally, we conclude by arguing that CISP, as treated within the DFT + NEGF framework, coincides with the phenomenon called chiral-induced spin selectivity, recently reported in several nanojunctions.

Figure 1

Typical systems studied in the DFT + NEGF calculations. It is subdivided into a central region (C) and left (L) and right (R) leads. The gray spheres are the Te atoms. The arrows represent the current-induced magnetic moments. The orange “bubbles” mark the spin-$z$ density isosurface.

Figure 2

(a) Band structure of Te calculated by using Kohn-Sham DFT. (b) Zoom around the $H$ high-symmetry point in the Brillouin zone, showing the two topmost valence bands and the two lowest conduction bands. (c) Characteristic “camel-back” shape of the upper valence band with a local maximum along the $H\text{−}K$ line.

Figure 3

Spin density per unit cell, $S^z$, as a function of the hole concentration, $n_{\mathrm{h}}$. The results are for a charge current density, $j_z=100\mathrm{A}/{\mathrm{cm}}^2$, and an electronic temperature, $T=200$ K. The inset shows the same data, but with $n_{\mathrm{h}}$ plotted in logarithmic scale for a better display of the lowest doping region.

Figure 4

Spin density per unit cell, $S^z$, as a function of the electronic temperature, $T$. The results are for a charge current density, $j_z=100\mathrm{A}/{\mathrm{cm}}^2$, and two different hole concentrations, $n_{\mathrm{h}}=5\times {10}^{17}{\mathrm{cm}}^{-3}$ (black dots) and $5\times {10}^{18}{\mathrm{cm}}^{-3}$ (red dots).

Figure 5

Spin current density, $j_z^z$, as a function of the hole concentration, $n_{\mathrm{h}}$. The results are for a charge current density $j_z=100\mathrm{A}/{\mathrm{cm}}^2$ and an electronic temperature equal to 200 K. The inbox displays the ratio $\alpha =j_z^z/S^z$ as a function of the hole concentration.

Figure 6

Resistance variation $\mathrm{\Delta }R=R\left(\mathbf{B}\right)-R\left(0\right)$ as a function of the magnetic field parallel, $\mathbf{B}\parallel \mathbf{z}$, antiparallel, $\mathbf{B}\parallel -\mathbf{z}$, and perpendicular, $\mathbf{B}\perp \mathbf{z}$, to the charge transport direction and for a positive bias. The results are for $n_{\mathrm{h}}=5\times {10}^{17}{\mathrm{cm}}^{-3}$.

Figure 7

Resistance variation $\mathrm{\Delta }R$ as a function of the magnetic field angle $\theta$ in the $xz$ plane. The black and red curves are obtained for positive and negative bias voltages, respectively. The results are for $n_{\mathrm{h}}=5\times {10}^{17}{\mathrm{cm}}^{-3}$.

Figure 8

Effective current's spin polarization $P^z$ as a function of the magnetic field angle $\theta$ in the $xz$ plane. The results are for $5\times {10}^{17}{\mathrm{cm}}^{-3}$ and for the magnetic field modulus $B=9$ T.

Figure 9

MR ratio for $B=9$ T as a function of the hole concentration $n_{\mathrm{h}}$.