Magnetic Dirac fermions and Chern insulator supported on pristine silicon surface

Emergence of ferromagnetism in nonmagnetic semiconductors is strongly desirable, especially in topological materials because of the possibility of achieving the quantum anomalous Hall effect. Based on first-principles calculations, we propose that for Si thin film grown on metal substrate, the pristine Si(111)-$\sqrt{3}\times \sqrt{3}$ surface with a spontaneous weak reconstruction has a strong tendency toward ferromagnetism and nontrivial topological properties, characterized by spin-polarized Dirac-fermion surface states. In contrast to conventional routes relying on introduction of alien charge carriers or specially patterned substrates, the spontaneous magnetic order and spin-orbit coupling on the pristine silicon surface together give rise to the quantized anomalous Hall effect with a finite Chern number $\mathcal{C}=-1$. This work suggests opportunities in silicon-based spintronics and quantum computing free from alien dopants or proximity effects.

Figure 1

Top view (a) and side view (b) of Si-$\sqrt{3}$ surface. The green, red, and orange balls, respectively, denote three types of silicon atoms: $\mathrm{S}{\mathrm{i}}_{\mathrm{A}}$ (highest), $\mathrm{S}{\mathrm{i}}_{\mathrm{B}}$ (lower), $\mathrm{S}{\mathrm{i}}_{\mathrm{C}}$ (lowest) on the surface layer. Yellow spheres are the bulk Si atoms. The bottom Si layer is saturated by H atoms. (c) Schematic diagram of spin-polarized Dirac cones around the Fermi level in the first Brillouin zone.

Figure 2

Band structures for the Si-$\sqrt{3}$ surface in the NM (a) and FM phase (c). The shadow regions are the bulk states and the flat band from $\mathrm{S}{\mathrm{i}}_{\mathrm{A}}$ atoms. The yellow, red, and blue lines are the Dirac bands from the states of $\mathrm{S}{\mathrm{i}}_{\mathrm{B}}$ atoms. (b, d) The corresponding DOS for the Si thin films. The yellow, red, and blue regions correspond to the projected DOS on $\mathrm{S}{\mathrm{i}}_{\mathrm{B}}$ atoms. (e, f) Top and side view of the spin density distribution at the isosurface level of $0.002{\mathrm{e}}^{-}\AA {}^{-3}$.

Figure 3

(a) Energy band structure for the Si-$\sqrt{3}$ surface calculated by DFT (green dashed line) and fitted by a Wannier basis set (red line). (b) The Berry curvature for the valence bands below the Fermi level along the high-symmetry direction. (c) The 2D distribution of Berry curvature for the occupied bands in momentum space. (d) The energy dependence of the first Chern number around the quantized conductance plateau.

Figure 4

(a) Schematic illustration of the quantum anomalous Hall conductivity ${\sigma }_{xy}^H$. The spin-polarized Hall currents along two edges are shown by blue and red color. (b) The tight-binding band structure for a Si-$\sqrt{3}$ nanoribbon with a width of 200 zigzag Si chains. The quantized edge states are shown by red lines. (c) Atomic structure and spin distribution of five-layer Si(111) films with $\sqrt{3}$ surface on Ag(111) substrate. The lattice constant of the supercell is 11.56 Å. The spin density distribution at the isosurface level of $0.002{\mathrm{e}}^{-}\AA {}^{-3}$ is shown. (d) Projected band structure on the topmost Si atomic layer for the five-layer Si(111) films on silver substrate. The red and blue dots represent spin-majority and spin-minority Dirac states from $\mathrm{S}{\mathrm{i}}_{\mathrm{B}}$ atoms, respectively. The sizes of dots denote the weight of contribution.