Continuous crossover from two-dimensional to one-dimensional electronic properties for metallic silicide nanowires

In a joint experimental and theoretical study on metallic $\mathrm{Tb}{\mathrm{Si}}_2$ nanowires, we observe a continuous crossover from a two-dimensional (2D) to a quasi-one-dimensional (1D) electronic structure by reduction of the nanowire width. The nanowires were grown by self-organization on vicinal Si(111) substrates denoted by the Miller indices $\left(hhk\right)$. Their electronic structure was analyzed by angle-resolved photoemission spectroscopy (ARPES) and calculated using density functional theory (DFT). In ARPES, the $\mathrm{Tb}{\mathrm{Si}}_2$ nanowires show basically the 2D electronic structure of the $\mathrm{Tb}{\mathrm{Si}}_2$ film on planar Si(111) with an increasing momentum broadening for decreasing nanowire widths, consistent with Heisenberg's uncertainty principle. In contrast, DFT calculations predict a purely 1D electronic structure for $\mathrm{Tb}{\mathrm{Si}}_2$ nanowires. Unfolding this 1D electronic structure onto the Brillouin zone of the $\mathrm{Tb}{\mathrm{Si}}_2$ film leads to a Fermi surface appearing similar to the one of the 2D $\mathrm{Tb}{\mathrm{Si}}_2$ film, but with an additional 1D contribution from nanowire edges. Such an additional 1D signature is also observed in ARPES for narrow nanowires. These results indicate a continuous transition to a 1D electronic structure for decreasing nanowire widths.

Figure 1

(a) Overview STM image of the 2D $\mathrm{Tb}{\mathrm{Si}}_2$ film on planar Si(111) prepared by deposition of $1.5\mathrm{ML}$ and annealing at $500{}^{\circ }\mathrm{C}$ (sample voltage $V=-2.5\mathrm{V}$ and tunneling current $I=50\mathrm{pA}$). (b) Fermi surface of the 2D Tb disilicide nanostructure film ($1.0\mathrm{ML}$ Tb annealed at $500{}^{\circ }\mathrm{C}$). The dashed ellipses are matched to the contour of the horizontal electron pocket and overlayed on a nonhorizontal one in order to highlight their uniform appearances with hexagonal symmetry, while the different intensities are due to photoemission matrix element effects. (c) and (d) Structure model of the $\mathrm{Tb}{\mathrm{Si}}_2$ monolayer in (c) side view and (d) top view. Gray and green circles correspond to Si atoms. Yellow circles indicate Tb atoms. The red rhombus marks the $1\times 1$ unit cell of the $\mathrm{Tb}{\mathrm{Si}}_2$ monolayer.

Figure 2

(a)–(c) STM images of $\mathrm{Tb}{\mathrm{Si}}_2$ nanostructures. (a) Wide nanowires on Si(557) ($V=+1.5\mathrm{V}$, $I=100\mathrm{pA}$), (b) narrower nanowires on Si(557) ($V=-1.5\mathrm{V}$, $I=100\mathrm{pA}$), and (c) very nar- row nanowires on Si(335) ($V=-1.5\mathrm{V}$, $I=100\mathrm{pA}$). The nanostructures were prepared by deposition of (a) $1.3\mathrm{ML}$, (b) $0.7\mathrm{ML}$, and (c) $0.6\mathrm{ML}$ Tb and annealing at 450–$500{}^{\circ }\mathrm{C}$. (d)–(f) Fermi surfaces of $\mathrm{Tb}{\mathrm{Si}}_2$ nanostructure preparations similar to the ones shown in (a)–(c). The nanostructures were prepared by deposition of (d) $1.1\mathrm{ML}$ Tb on Si(557), (e) $0.7\mathrm{ML}$ Tb on Si(557), and (f) $0.7\mathrm{ML}$ Tb on Si(335) and annealing at $500{}^{\circ }\mathrm{C}$. In (d)–(f), the dashed ellipses are matched to the contour of one horizontal electron pocket and overlayed on a nonhorizontal one in order to highlight the different appearances. The arrows in (f) mark additional signals on the Fermi surface not observed for the other preparations.

Figure 3

(a) Contrast enhanced Fermi surface for the narrow nanowires already shown in Fig. 2. The red arrows mark the 1D signature. (b) Dispersion plot taken along the dashed line in (a). (c) Corresponding dispersion plot of the 2D film on Si(111) for comparison. In (b), the dispersion of the 1D signature is marked by red arrows. The strong signal observed in (b) for high binding energies ($E_{\mathrm{bin}}$) near zero momentum in the nanowire growth direction ($k_{\left[\overline{1}10\right]}=0$) originates from the Si bulk.

Figure 4

(a) Top view and (b) side view of a relaxed nanowire structure. (c) Corresponding electronic dispersion near the Fermi level and PDOS of the Tb atoms. In (a) and (b), gray and green circles indicate Si atoms while large yellow and small blue circles correspond to Tb and H atoms, respectively. The black arrow in (b) indicates an additional atom not present in the ideal $\mathrm{Tb}{\mathrm{Si}}_2$ structure. The periodicity of the supercell is marked in red. In (c), the gray shaded areas indicate the projected Si bulk band structure and green arrows mark bands of the nanowires corresponding to the electron pockets of the 2D film.

Figure 5

(a) Comparisons of the calculated band structure with ARPES data of $\mathrm{Tb}{\mathrm{Si}}_2$ nanowires averaged perpendicular to the nanowire direction. (b) Localization of the band marked by the left red arrow in (a) at the Fermi energy illustrated by the isosurface of its probability density shaded in red. (c) and (d) Calculated Fermi surface (c) before and (d) after unfolding the electronic structure onto the BZ of the $\mathrm{Tb}{\mathrm{Si}}_2$ film. The red arrows mark the linear Fermi contours of the edge state shown in (b).