Fermi gas behavior of a one-dimensional metallic band of Pt-induced nanowires on Ge(001)

We have investigated the electronic band structure of Pt-induced nanowires on Ge(001) [Pt/Ge(001) NWs] by angle-resolved photoelectron spectroscopy at 6 K. Single-domain samples of Pt/Ge(001) NWs were prepared on vicinal Ge(001) substrates. One of the bands disperses only in the nanowire direction, and its Fermi surface consists of strictly straight lines, indicating that it is an ideal one-dimensional metallic state. An energy distribution curve of the one-dimensional band is explained by a Fermi-Dirac-type spectral shape, which is against both a Luttinger liquid and Peierls instability schemes.

Figure 1

(a) Top view of the surface structure model of Pt/Ge(001) NWs proposed by RHEPD.[21] Dashed rectangle represents a $p(4\times 2)$ unit cell of the HT phase. (b) Side views of the structure model of Pt/Ge(001) NWs, where the structural models of the HT and LT phases are shown in the upper and lower panels, respectively.

Figure 2

(a), (b) LEED patterns of Pt/Ge(001) NWs on vicinal (a) and flat (b) Ge(001) substrates at RT. The primary electron energy was set to 128 eV. An arrow in (a) represents the miscut direction of the vicinal surface. The unit cell of each domain is presented with solid and dashed rectangles in the images. (c) Large-scale STM image ($400\times 400$ nm${}^2$) of Pt/Ge(001) NWs on the vicinal Ge(001) substrate. Most of wide terraces are covered by the nanowires parallel to the step edges. The areas surrounded by bold lines (green) represent minority domains. (d) Magnified STM image ($130\times 130$ nm${}^2$). The protrusions (white) correspond to the Ge dimers in the topmost layer. In both images, the bias voltage is 1.5 V and the tunneling current 0.5 nA.

Figure 3

(a) Constant energy ARPES map at $E_{\mathrm{F}}$ of Pt/Ge(001) NWs with the single-domain surface formed on the vicinal Ge(001) substrate. The photoelectron intensity is represented by color scale. Thin solid and dashed lines denote the boundaries of the SBZs of $p(4\times 4)$ and $p(4\times 2)$, respectively. (b) Peak position plots from the MDCs at $E_{\mathrm{F}}$ in the third SBZ. Circles and squares correspond to the $S_1$ and $S_2$ bands, respectively. Lines $l_1$-$l_4$ represent the wave vector cuts of ARPES images shown in Figs. 4a, 4b, 4c, 4d, respectively.

Figure 4

(a)–(d) ARPES images taken along thin solid (green) lines, $l_1$–$l_4$, shown in Fig. 3b, where $l_1$, $l_2$, $l_3$, and $l_4$ correspond to $k_{\mathrm{y}}$ $=$ 0.60, 0.64, 0.69, 0.78 Å${}^{-1}$ on the $\overline{\Gamma }\overline{J^{\prime }}$ axis, respectively. Dashed curves in (d) represent the band structures of $S_1$ and $S_2$, which were fitted to the data.[24] (e) Schematic drawing of the $S_1$ and $S_2$ bands. (f) (Top) The integrated EDC of $S_1$ near $E_{\mathrm{F}}$. A thin solid parallelogram shown in (d) represents an extracted $E$-$k_{\mathrm{x}}$ plane to obtain an EDC for a $k_{\mathrm{y}}$ slice. The EDC with the $E$-$k_{\mathrm{x}}$ plane is integrated over $k_{\mathrm{y}}$ in the SBZ. (Bottom) The Fermi edge (red circles) taken from Ta foil. Solid curves represent fitting results with the Fermi distribution function and polynomial background.