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Soliton molecules, bound states of two solitons, can be important for the informatics using solitons and the quest for exotic particles in a wide range of physical systems from unconventional superconductors to nuclear matter and Higgs field, but have been observed only in temporal dimension for classical wave optical systems. Here, we identify a topological soliton molecule formed spatially in an electronic system, a quasi 1D charge density wave of indium atomic wires. This system is composed of two coupled Peierls chains, which are endowed with a Z$_4$ topology and three distinct, right-chiral, left-chiral, and non-chiral, solitons. Our scanning tunneling microscopy measurements identify a bound state of right- and left-chiral solitons with distinct in-gap states and net zero phase shift. Our density functional theory calculations reveal the attractive interaction of these solitons and the hybridization of their electronic states. This result initiates the study of the interaction between solitons in electronic systems, which can provide novel manybody electronic states and extra data-handling capacity beyond the given soliton topology.

Localized modes in one dimensional topological systems, such as Majonara modes in topological superconductors, are promising platforms for robust information processing. In one dimensional topological insulators, mobile topological solitons are expected but have not been fully realized yet. We discover fractionalized phase defects moving along trimer silicon atomic chains formed along step edges of a vicinal silicon surface. Tunneling microscopy identifies local defects with phase shifts of 2{\pi}/3 and 4{\pi}/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 {\pm}2e/3 and {\pm}4e/3. An individual soliton can be created and annihilated at a desired location by current pulse from the probe tip. Mobile and manipulatable topological solitons discovered here provide a new platform of robustly-protected informatics with extraordinary functionalities., Comment: 18 pages, 4 figures

We investigate in atomic scale the electronic phase separation occurring in the well known quasi 1D charge-density wave (CDW) phase of the In atomic wire array on a Si(111) surface. The characteristic atomic scale defects, originated from excess In atoms, are found to be actively involved in the formation of the phase boundary between the metallic and the CDW phases by extensive analysis of scanning tunneling microscopy images at various temperatures. These particular defects flip the phase of the quasi 1D CDW to impose strong local constraints in the CDW correlation. We show that such local constraints and the substantial interwire CDW interaction induce local condensates of CDW and the phase separation between the metallic and the CDW phases. This work unveils the atomistic origin of the electronic phase separation, highlighting the importance of atomic scale structures of defects and their collective interaction in electronically inhomogeneous materials.

We demonstrate the existence of atomically-sized topological solitons in a quasi one-dimensional charge density wave system: indium atomic wires on Si(111). Performing joint scanning tunneling microscopy and density-functional calculations, we show that the Si(111)-(8x2)In surface features two conceptually different types of abrupt phase flip structures. One is caused by In adatoms and is, hence, non-solitonic in nature. The other one is an abrupt left-chiral soliton.

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 1${T}$-TaS$_{2}$ featuring Mott-insulating ground state, charge-density-wave, spin frustration and emerging superconductivity together. We investigated local electronic states of Se-substituted 1${T}$-TaS$_{2}$ 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 (E$_{F}$), 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.

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.