Controlling the Topology of Fermi Surfaces in Metal Nanofilms

The properties of metal crystals are governed by the electrons of the highest occupied states at the Fermi level and determined by Fermi surfaces, the Fermi energy contours in momentum space. Topological regulation of the Fermi surface has been an important issue in synthesizing functional materials, which we found to be realized at room temperature in nanometer-thick films. Reducing the thickness of a metal thin film down to its electron wavelength scale induces the quantum size effect and the electronic system changes from three to two-dimensional, transforming the Fermi surface topology. Such an ultrathin film further changes its topology through one-dimensional (1D) structural deformation of the film when it is grown on a 1D substrate. In particular, when the interface has 1D metallic bands, the system is additionally stabilized by forming an electron energy gap by hybridization between 1D states of the film and substrate.

Figure 1

In-plane ($k_x$, $k_y$) photoemission intensity map at the Fermi level for (a) 1.4-nm (6 ML) thick Ag(111) film on Si(111)-($7\times 7$), (b) 1.4-nm (6 ML) thick, and (c) 0.7-nm (3 ML) thick Ag films on Si(111)-($4\times 1$)-In, measured at $h\nu =50\mathrm{eV}$ at room temperature. The difference is due to the change of an atomic layer at the interface between the metal film and semiconductor substrate. The brightness is proportional to the intensity of photoemission.

Figure 2

(a)–(c) Photoemission intensity maps in Fig. 1, superimposed by white traces of observed contours for the QWS subbands. In (b) and (c), the unperturbed Fermi surfaces of the films without 1D modulation are shown in red (dark gray). The unit cell is shown as a rectangle in (c).

Figure 3

2D intensity maps of 19.9 keV x ray in reciprocal space ($H$, $K=1.33$, $L$). The data in (a) and (b) are experimental results obtained at room temperature on (a) 6-ML thick and (b) 3-ML thick Ag films on Si(111)-($4\times 1$)-In, while those in (c) and (d) are simulations of a 6-ML thick fcc-Ag(111) film with and without stacking faults, respectively. The red arrows point to the same diffraction spots found in (a) and (c). The reciprocal lattice units (r.l.u.) are defined by the fundamental length of the Si(111)-($1\times 1$) reciprocal vector. $H$ and $L$ are along $x$ and $z$ directions, respectively. $K$ is along the $⟨112⟩$ symmetry axis, which is rotated by 30° by the $y$ direction.

Figure 4

(a–f) Photoemission band diagrams of (a)–(c) 6-ML thick, and (d)–(f) 3-ML thick Ag films on Si(111)-($4\times 1$)-In along the $k_y$ axis at the selected $k_x$ points and at the $\overline{M}-\overline{K}$ line. The $k_{F,y}$ points of the 1D Fermi lines of the intensity maps in Figs. 2, 3 are indicated by arrows. (g)–(i) Schematic diagrams for modeling 1D band dispersion curves for the (g) 3-ML thick Ag film, (h) Si(111)-($4\times 1$)-In substrate, and (i) 1D modulated $\mathrm{Ag}(111)/\mathrm{Si}(111)\mathrm{\text{−}}(4\times 1)-\mathrm{In}$ system.