Absence of Luttinger liquid behavior in Au-Ge wires: A high-resolution scanning tunneling microscopy and spectroscopy study

Abstract

Au-induced atomic wires on the Ge(001) surface were recently claimed to be an ideal 1D metal and their tunneling spectra were analyzed as the manifestation of a Tomonaga-Luttinger liquid (TLL) state. We reinvestigate this system for atomically well-ordered areas of the surface with high resolution scanning tunneling microscopy and spectroscopy (STS). The local density-of-states maps do not provide any evidence of a metallic 1D electron channel along the wires. Moreover, the atomically resolved tunneling spectra near the Fermi energy are dominated by local density-of-states features, deviating qualitatively from the power-law behavior. On the other hand, the defects strongly affect the tunneling spectra near the Fermi level. These results do not support the possibility of a TLL state for this system. An 1D metallic system with well-defined 1D bands and without defects are required for the STS study of a TLL state. DOI:PACS number(s): 71.10. Pm, 68.37.Ef, 73.20.Mf, 68.47.Fg Tomonaga-Luttinger liquid (TLL) is undoubtedly one of the most important theoretical models for interacting electrons in one dimension (1D) [1][2][3]. Over past decades, many efforts were made to experimentally observe a TLL state. The evidence for a TLL state has been accumulated in carbon nanotubes [4,5], strongly anisotropic bulk crystals [6][7][8], fractional-quantum-hall-effect edge states [9], and 1D electron gases of quantum wires [10].Along a largely different direction, the possibility of a TLL state was also discussed in metallic atomic wires selforganized on semiconductor surfaces, in particular, for Au-induced atomic wire arrays on vicinal silicon surfaces [11]. However, no clear indication of a TLL state has been identified for these systems so far [12][13][14][15]. As the most recent system in this line of researches, Au-induced atomic wires on the Ge(001) surface (hereafter, the Au-Ge wires) were suggested as an ideal 1D metallic system [16], with a clear signature of a TLL state in their scanning tunneling spectroscopy (STS) spectra [17]. However, not only the chemical composition and the atomic structure [18][19][20][21][22][23][24], but also their band structure is uncertain at present [25,26]. Most notably, a recent angle-resolved photoemission spectroscopy (ARPES) study, the first such study for a single domain surface, showed an anisotropic but 2D metallic band, which disperses more strongly in the direction perpendicular to the wire [27,28].This situation apparently and urgently requests the confirmation of the existence of a 1D metallic state itself in the Au-Ge wire and the TLL behavior of its tunneling spectra. We also note that while the importance of STS has been mentioned for a few 1D metallic systems [7,29], no detailed atomic scale investigation of STS spectra of a TLL system is available. For such an atomic scale study, a well ordered surface 1D metallic system would definitely be beneficial. Therefore, the Au-Ge wire could be an important model system to unveil a largely

Gold-induced nanowires on the Ge(100) surface yield a 2D and not a 1D electronic structure

“…nanowires would seem to mesh with the fact that these patches of high intensity in the low energy LDOS maps also run in the direction perpendicular to the nanowires. Similar results have been found by other groups [35], whereby straight differential conductance channels running along the nanowire direction were only observed for negative biases V b ≤-200 mV.…”

“…5 we show the spatial dependence of the LDOS for a straight and macroscopically defect/chain-end-free ∼20×20 nm 2 section of Au-induced nanowires. As reported in the literature [35,38], straight conduction channels can be observed along the nanowire direction in the troughs. These channels are most pronounced deeper in the occupied states, such as in panels e[f] for E=-0.5V[-0.8]V. For bias closer to the Fermi level, the existence of straight conduction channels becomes less and less clear.…”

“…This either/or situation essentially expresses the 2D nature of these low lying occupied states. Comparing to our ARPES data, we remark that the highest intensity in ARPES for the Au-induced electron pockets is close to 100 meV binding energy, and the fact that these electronic states disperse more rapidly perpendicular to the v The slight angle of the pearl-chain-like structures with respect to the direction normal to the nanowires is comparable to the angle the VW reconstruction has in this direction [35], suggesting a possible relation between this reconstruction and the enhanced LDOS patches. In addition, we note that the so-called bridge atoms, observed in the troughs in topographic images (see Fig.…”

“…the exact shape of this dip is by some measured to be particlehole symmetric around zero bias voltage [43] while in other data, such as that presented here and in Ref. 35, an symmetric dip is observed -i.e. there is no sign of p-h symmetry.…”

Correlated atomic wires on substrates. II. Application to Hubbard wires

“…The ground state in this case is a 1D conductor [2] with the low-energy properties of a Luttinger liquid [10]. We expect these systems to be quasi-1D conductors also for t ws = 0 and to yield information that could be relevant for understanding the numerous metallic atomic wires studied experimentally [15][16][17][18][19][20][21][22][23][24][25]. Figure 9 shows the variations of the charge distributions C(n) relative to half-filling as a function of the interaction U .…”