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

Localized modes in one-dimensional (1D) topological systems, such as Majonara modes in topological superconductors, are promising candidates for robust information processing. While theory predicts mobile integer and fractional topological solitons in 1D topological insulators, experiments so far have unveiled immobile, integer solitons only. Here we observe fractionalized phase defects moving along trimer silicon atomic chains formed along step edges of a vicinal silicon surface. By means of tunnelling microscopy, we identify local defects with phase shifts of 2π/3 and 4π/3 with their electronic states within the band gap and with their motions activated above 100 K. Theoretical calculations reveal the topological soliton origin of the phase defects with fractional charges of ±2e/3 and ±4e/3. Additionally, we create and annihilate individual solitons at desired locations by current pulses from the probe tip. Mobile and manipulable topological solitons may serve as robust, topologically protected information carriers in future information technology.

We investigated the atomic scale electronic phase separation emerging from a quasi-1D charge-density-wave (CDW) state of the In atomic wire array on a Si(111) surface. Spatial variations of the CDW gap and amplitude are quantified for various interfaces of metallic and insulating CDW domains by scanning tunneling microscopy and spectroscopy (STS). The strong anisotropy in the metal−insulator junctions is revealed with an order of magnitude difference in the interwire and intrawire junction lengths of 0.4 and 7 nm, respectively. The intrawire junction length is reduced dramatically by an atomic scale impurity, indicating the tunability of the metal−insulator junction in an atomic scale. Density functional theory calculations disclose the dynamical nature of the intrawire junction formation and tunability.

The competition, coexistence and cooperation of various orders in low-dimensional materials like spin, charge, topological orders and charge-density-wave has been one of the most intriguing issues in condensed matter physics. In particular, layered transition metal dichalcogenides provide an ideal platform for studying such an interplay with a notable case of 1T -TaS2 featuring Mottinsulating ground state, charge-density-wave, spin frustration and emerging superconductivity together. We investigated local electronic states of Se-substituted 1T -TaS2 by scanning tunneling microscopy/spectroscopy (STM/STS), where superconductivity emerges from the unique Mott-CDW state. Spatially resolved STS measurements reveal that an apparent V-shape pseudogap forms at the Fermi Level (EF ), with the origin of the electronic states splitting and transformation from the Mott states, and the CDW gaps are largely preserved. The formation of the pseudogap has little correlation to the variation of local Se concentration, but appears to be a global characteristics. Furthermore, the correlation length of local density of states (LDOS) diverges at the Fermi energy and decays rapidly at high energies. The spatial correlation shows a power-law decay close to the Fermi energy. Our statistics analysis of the LDOS indicates that our system exhibits weak multifractal behavior of the wave functions. These findings strongly support a correlated metallic state induced by disorder in our system, which provides an new insight into the novel mechanism of emerging superconductivity in the two-dimensional correlated electronic systems.In low-dimensional electronic systems, the interplay between electron correlation, superconductivity and charge density wave (CDW) or spin density wave has attracted great research interests. Outstanding examples are the unconventional superconductivity in cuprate [1, 2] and pnictide [3-5] materials. Another notable case is the layered transition-metal dichalcogenides (TMDs), which provides an ideal platform for investigating the interplay between the