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One dimensional (1D) electronic system is a versatile platform hosting novel physics, such as charge density wave, Su-Schrieffer-Heeger (SSH) topological state and solitons, Tomonaga-Luttinger Liquid etc. Here, we systematically study the surface electronic properties on layered composition-tunable compounds Nb2n+1SinTe4n+2 (n = 1–5), which is predicted to be a nodal-line semimetal when n = 1 (Nb3SiTe6). Via scanning tunneling microscopy/spectroscopy, we observe 1D chains formed on the surface of the compounds. We uncover that with the increasing of n, the distance between the chains becomes larger, and the 1D electronic state is developed in the compounds with n ≥ 3. Our first-principle calculations reveal that the nodal-line in Nb3SiTe6 and the 1D electronic state in the crystals with higher n in fact arise from the same bands, which are protected by the same nonsymmorphic symmetry. Furthermore, we can understand the evolution of the electronic states on these series of compounds with such complicated structures and compositions based on a simple SSH type picture. Our experiment demonstrates a tunable and unidirectional 1D electronic system, which offers a concrete platform for the exploration of intriguing 1D electron physics and will enrich the opportunity for future condensed matter physics, material science and nanotechnology researches.

The interplay between time-reversal symmetry (TRS) and band topology plays a crucial role in topological states of quantum matter. In time-reversal-invariant (TRI) systems, the inversion of spin-degenerate bands with opposite parity leads to nontrivial topological states, such as topological insulators and Dirac semimetals. When the TRS is broken, the exchange field induces spin splitting of the bands. The inversion of a pair of spin-splitting subbands can generate more exotic topological states, such as quantum anomalous Hall insulators and magnetic Weyl semimetals. So far, such topological phase transitions driven by the TRS breaking have not been visualized. In this work, using angle-resolved photoemission spectroscopy, we have demonstrated that the TRS breaking induces a band inversion of a pair of spin-splitting subbands at the TRI points of Brillouin zone in EuB$_6$, when a long-range ferromagnetic order is developed. The dramatic changes in the electronic structure result in a topological phase transition from a TRI ordinary insulator state to a TRS-broken topological semimetal (TSM) state. Remarkably, the magnetic TSM state has an ideal electronic structure, in which the band crossings are located at the Fermi level without any interference from other bands. Our findings not only reveal the topological phase transition driven by the TRS breaking, but also provide an excellent platform to explore novel physical behavior in the magnetic topological states of quantum matter., Comment: 22 pages, 7 figures, accepted by Phys. Rev. X

Co3Sn2S2 is a recently identified magnetic Weyl semimetal in Shandite compounds. Upon cooling, Co3Sn2S2 undergoes a ferromagnetic transition with c-axis polarized moments (∼0.3 µB/Co) around TC = 175 K, followed by another magnetic anomaly around TA ≈ 140 K. A large intrinsic anomalous Hall effect is observed in the magnetic state below TC with a maximum of anomalous Hall angle near TA. Here, we report an elastic neutron scattering on the crystalline lattice of Co3Sn2S2 in a magnetic field up to 10 T. A strongly anisotropic magnetoelastic response is observed-while only a slight enhancement of the Bragg peaks is observed when B//c. The in-plane magnetic field (B//ab) dramatically suppresses the Bragg peak intensity probably by tilting the moments and lattice toward the external field direction. The in-plane magnetoelastic response commences from TC, and as it is further strengthened below TA, it becomes nonmonotonic against the field between TA and TC because of the competition from another in-plane magnetic order. These results suggest that a magnetic field can be employed to tune the Co3Sn2S2 lattice and its related topological states.