One-Dimensional Plasmon in an Atomic-Scale Metal Wire

Abstract

We have measured one-dimensional (1D) plasmons in an atom wire array on the Si(557)-Au surface by inelastic scattering of a highly collimated slow electron beam. The angular dependence of the excitation energy clearly indicates the strong 1D confinement and free propagation of the plasma wave along the wire. The observed plasmon dispersion is explained very well by a quantum-mechanical scheme which takes into account dynamic exchange-correlation effects, interwire interactions, and spin-orbit splitting of the 1D bands. Although the qualitative feature of the plasmon dispersion is reminiscent of that of a highdensity free-electron gas, we detected the substantial influence of electron correlation due to strong 1D confinement. DOI: 10.1103/PhysRevLett.97.116802 PACS numbers: 73.20.Mf, 71.45.Gm, 72.15.Nj, 73.63.Nm One-dimensional electron systems (1DESs) such as metallic atom wires are expected to sustain a unique collective charge-density excitation which can be called onedimensional (1D) plasmon, or wire plasmon. This excitation mode propagates only along the wire and strongly reflects the confined nature of the electron motion. Such a dimensionality effect will show up clearly in the energy dispersion and the linewidth of a plasmon. For example, 3D-type plasmons (bulk and surface plasmons) have finite energies at q 0 (q denotes momentum) [1], but the energies of 1D and 2D plasmons vanish at q 0 [2,3], since the restoring force for charge-density waves in low dimension vanishes in the long-wavelength limit. However, in spite of its broad interest, experimental observation of a plasmon in an atomic-scale metal wire has been lacking so far and its details remain unexplored.Recently, Au-induced 1D chain structures on stepped Si(111) surfaces were found to comprise 1DESs with metallic electron densities [4 -9]. Among them, Au-Si atom wires formed on the Si(557) surface possess two proximal and deep (1 eV) electron pockets [5][6][7][8][9] and can be regarded as an ideal 1D metal. This system has been providing many intriguing topics such as spin-charge separation in a Tomonaga-Luttinger liquid, lattice distortion by Peierls instability, etc., which originate from the restricted 1D motion of electrons [4 -8]. Moreover, a recent theoretical study by ab initio calculation has proposed a large spinorbit (SO) splitting in the 1D electronic band which results from the strong Au 6p character of this 1D band [10].In this Letter, we report the electron-energy-loss spectroscopy (EELS) of the plasmon in such a model 1D system on the Si(557) surface. The measured plasmon clearly shows strong one-dimensional and metallic characteristics which are expected from a 1D electron gas. We analyzed the observed plasmon dispersion by a quantummechanical scheme including the effects of dynamic exchange correlation (XC), interwire interactions, and SO splitting of the 1D bands. These results demonstrate that, although the Fermi velocity of the 1DES is very high, suggesting its free-electron nature, the dynamic electron correlation effect...

Plasmons in nanoscale and atomic-scale systems

“…As mentioned in section 2, the thinnest media known to support plasmon so far are Au atomic wires self-assembled on a stepped silicon surface [46,47]. The same type of plasmons was recently found in some other atomic-wire systems [79][80][81][82], and two-dimensional plasmon (sheet plasmon) was also reported [39][40][41][42].…”

“…As shown in figure 4, the dispersion curve resembles that of the 1D plasmon but its origin is rather different [16,17,46,47]. The linear dispersion is a consequence of the redshift from the 2D plasmon at larger wavenumbers owing to the increased dynamical screening from the metallic substrate [49].…”

“…This sound-wave-like dispersion was introduced in the early theory of 1D electron systems by Tomonaga in 1950 [43] and some further theoretical works were subsequently carried out [44,45]. Even for a metallic atomic wire as thin as 0.3 nm, this mode can be detected by EELS [46,47]. The atomic structure of a self-assembled chain of gold atoms is shown on the left of figure 3, and EELS spectra taken at different values of momentum q (along the chains) are presented on the right.…”

“…Dashed line shows an early dispersion prediction obtained in a simplified 1D calculation [48]. The shape of the dispersion curve is similar to that of the 1D plasmon but its origin is different [16,17,46,47]. Right: imaginary part of induced charge-density distribution (red solid line) corresponding to the acoustic surface plasmon in direction perpendicular to the Be(0001) surface (ab initio calculation).…”

Plasmonics in atomically thin materials

“…In a separate effort, atomic self-assembly has been used to produce monoatomic gold wires [56], which were later shown to sustain extremely confined plasmons [57]. Similar low-dimensional plasmons have been experimentally characterized using electron spectroscopy in ultrathin indium [58] and silicide [59] wires, as well as in few-atomic-layer silver films [60] and monolayer DySi 2 [61].…”