Ab initio study of the structural, electronic, magnetic, and optical properties of silicene nanoribbons

We present first-principles calculations of structural, electronic, magnetic, and optical properties of zigzag-oriented silicene nanoribbons, which, being endowed with spin-polarized edge states, are promising candidates as building blocks of future spintronic devices. The minimal width for a structurally stable planar structure having zigzag edges corresponds to a 4-chain ribbon, whose ground state presents antiferromagnetically coupled spin-polarized edges, and a lattice parameter along the nanoribbon axis contracted ($\sim 5\%$) with respect to the bulk value. Starting from the dependence of structural and electronic properties on the ribbon width, we present theoretical predictions for the optical spectra of narrow nanoribbons, in which excitonic effects are relevant due to the confinement in a quasi-one-dimensional structure. Especially for light polarized parallel to the ribbon axis, we find significant differences in the position of optical absorption peaks of ribbons with ferro- or antiferromagnetically coupled edges, showing that optical spectra can be used as a fingerprint of the magnetic coupling of electronic edge states.

Figure 1

Top and side views of reconstructed structures of 4-chain silicene nanoribbons having zigzag edges. The structure (b) has energy $28\mathrm{meV}{\AA }^{-1}$ lower than the structure (a). Edge atoms have a different color from the bulk ones to increase readability.

Figure 2

Left panel: Edge energy per atom in the edge chain for different width of the nanoribbon for antiferromagnetic (squares), ferromagnetic (circles), and nonmagnetic (diamonds) spin polarization at ribbon edges. Right panel: Lattice constant for different width of the nanoribbon for antiferromagnetic (squares), ferromagnetic (circles), and nonmagnetic (diamonds) spin polarization at ribbon edges. Lines are a guide to the eye.

Figure 3

Atomic buckling for different widths of the nanoribbon (see text). The error bars represent the standard error of the set of the distances of atoms along the (edge/central) chain from the $z=0$ plane. For a given number of chains, the values corresponding to different magnetic structures are slightly displaced along the horizontal axis to increase readability.

Figure 4

Electronic band structures of 4-chain zigzag silicene ribbon, for nonmagnetic, antiferromagnetic, and ferromagnetic configuration of spin density at the edges.

Figure 5

Optical response of the AFM 4-ZSiNR with electron-hole interaction (dashed area) in comparison with the spectra obtained at KS-RPA level (dashed line, from Ref. [25]) and QP-RPA level (blue line).

Figure 6

Left panel: Transitions which mainly contribute to the exciton peaks A and C (red) and B (blue) in Fig. 5. The electronic band structure is corrected with QP self-energies. Right panel: Spatial distribution of the electron for a hole (green dot) fixed at the edge of the ribbon for exciton peak A. The isosurface represents the 2% (top panel) and the 20% (bottom panel) of the maximum square modulus of the electron-hole wave function.

Figure 7

Optical response of the FM 4-ZSiNR with electron-hole interaction (dashed area) in comparison with the spectra obtained at KS-RPA level (dashed line, from Ref. [25]) and QP-RPA level (blue line). The Drude term has been included.

Figure 8

Optical response of the AFM 5-ZSiNR with electron-hole interaction (dashed area) in comparison with the spectra obtained at KS-RPA level (dashed line) and QP-RPA level (blue line).

Figure 9

Ferromagnetic edge states of 4-chain zigzag silicene nanoribbon. Panel (a): Detail of the band structure around the Fermi level. Panel (b): Projection in real space of the wave functions of the bands closest to the Fermi level. From left to right the wave functions reported in real space correspond to the $\mathrm{\Gamma }$ point, crossing point, and X point; the isovalue is set to $3\times {10}^{-3}{\text{(a.u.)}}^{-3}$. Panel (c): $\mathbf{k}$-resolved projected density of states. Blue and red lines indicate a greater localization on the edge and the center of the ribbon, respectively.

Figure 10

Band structure for AFM (left panel) and FM (right panel) magnetic configurations for 4-, 5-, 6-chain zigzag silicene nanoribbons (with the triangle-pentagon edge reconstruction).