Long-period surface structure stabilized by Fermi surface nesting: $\mathrm{Cu}\left(001\right)\text{−}(\sqrt{20}\times \sqrt{20})R26.6°\text{−}\mathrm{In}$

We have studied the atomic and electronic structure of the $\mathrm{Cu}\left(001\right)\text{−}(\sqrt{20}\times \sqrt{20})R26.6°\text{−}\mathrm{In}$ surface, which undergoes a reversible transition to a $p(2\times 2)$ phase at high temperature. Low temperature scanning-tunneling microscopy indicates a $p(2\times 2)$ structure modulated at the $(\sqrt{20}\times \sqrt{20})$ periodicity. Angle-resolved photoelectron spectroscopy shows a surface resonance exhibiting gap opening and backfolding along a $(\sqrt{20}\times \sqrt{20})$ zone boundary. We suggest that the $(\sqrt{20}\times \sqrt{20})$ structure is stabilized due to the Fermi surface nesting accompanying a surface charge density wave.

Figure 1

LEED pattern for the $(\sqrt{20}\times \sqrt{20})R26.6°\text{−}\mathrm{In}$ surface at the primary energy of (a) $90\mathrm{eV}$, and (b) $60\mathrm{eV}$. (c) Schematics of the LEED pattern. Solid and open circles represent diffraction spots due to $(1\times 1)$ and $\sqrt{20}$ periodicities, respectively. Dotted circles represent the area observed in (a) and (b).

Figure 2

(a) STM image for the $(\sqrt{20}\times \sqrt{20})R26.6°$ phase ($V_s=-7\mathrm{mV}$, $I_t=1\mathrm{nA}$, $150\times 150{\mathrm{\AA }}^2$), and (b) zoomed-up image ($V_s=-7\mathrm{mV}$, $I_t=10\mathrm{nA}$, $30\times 30{\mathrm{\AA }}^2$). The solid and broken lines represent unit cells of $(\sqrt{20}\times \sqrt{20})R26.6°$ and $p(2\times 2)$, respectively. (c) Fourier transform of the STM image shown in (a).

Figure 3

(Color online) (a) Schematic drawing of the In-induced surface resonance bands on Cu(001). $S_1$ and $S_2$ denote surface resonance bands originating from In-Cu interface. (b) Electronic band map along $\overline{\Gamma }\text{−}\overline{X}$. $B$ denotes the bulk Cu $4sp$ band. (b) Electronic band map along $\overline{\Gamma }\text{−}\overline{M}$. The photoemission intensity is normalized to the Fermi distribution function.

Figure 4

(a) The minimum binding energy of the $S_1$ band as a function of the angle from the [100] azimuth. The arrows (b)–(e) in the right panel indicate the paths along which the band maps shown in (b)–(e) are measured. The circles indicate the Fermi wave vectors along $\overline{\Gamma }\text{−}\overline{M}$ and $\overline{\Gamma }\text{−}\overline{X}$. (b)–(e) Electronic band maps taken at azimuthal angles indicated in (a) as a function of the momentum components along $\overline{\Gamma }\text{−}\overline{M}$, $k_x$. The photoemission intensity is normalized to the Fermi distribution function.

Figure 5

(Color online) The $k$ points where the $S_1$ band is backfolded (triangles) and reciprocal lattices: thick and thin solid (black) lines indicate SBZ and reciprocal lattice, respectively, of $(1\times 1)$; dotted (blue) and dashed (red) lines indicate reciprocal lattices for two equiprobable $\sqrt{20}$ structures rotated by 53.1° from each other. The reciprocal lattice points are indicated by ${\overline{\Gamma }}_{nm}$ for $(1\times 1)$ and ${\overline{\Gamma }}_{n^{\prime }{m}^{\prime }}^{\prime }$ and ${\overline{\Gamma }}_{n^{″}{m}^{″}}^{″}$ for two $\sqrt{20}$ structures, where $n$, $m$, $n^{\prime }$, $m^{\prime }$, $n^{″}$, and $m^{″}$ denote integers. Circles indicate the $k$ positions where the $S_1$ and $S_2$ bands cross $E_{\mathrm{F}}$. A gray (blue) solid line indicates SBZ boundary created by ${\Gamma }_{43}^{\prime }$ and ${\Gamma }_{05}^{″}$.