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The discovery of topologically non-trivial electronic systems has opened a new age in condensed matter research. From topological insulators to topological superconductors and Weyl semimetals, it is now understood that some of the most remarkable and robust phases in electronic systems (e.g., Quantum Hall or Anomalous Quantum Hall) are the result of topological protection. These powerful ideas have recently begun to be explored also in bosonic systems. Topologically protected acoustic, mechanical, and optical edge states have been demonstrated in a number of systems that recreate the requisite topological conditions. Such states that propagate without backscattering could find important applications in communications and energy technologies. In this work we demonstrate the mechanical analogue of a topologically bound state, a different class of non-propagating protected state that cannot be destroyed by local perturbations. These are well known in electronic systems, such as Majorana bound states in topological superconductors, but remain largely unexplored in a bosonic setting. We implement topological binding by creating a Kekul\'e distortion vortex on a two-dimensional mechanical honeycomb superlattice.

We report the finding of the analogous valley Hall effect in phononic systems arising from mirror symmetry breaking, in addition to spatial inversion symmetry breaking. We study topological phases of plates and spring-mass models in Kagome and modified Kagome arrangements. By breaking the inversion symmetry it is well known that a defined valley Chern number arises. We also show that effectively, breaking the mirror symmetry leads to the same topological invariant. Based on the bulk-edge correspondence principle, protected edge states appear at interfaces between two lattices of different valley Chern numbers. By means a plane wave expansion method and the multiple scattering theory for periodic and finite systems respectively, we computed the Berry curvature, the band inversion, mode shapes and edge modes in plate systems. We also find that appropriate multi-point excitations in finite system gives rise to propagating waves along a one-way path only.

In this paper we study Maxwell lattices with non-rectilinear constraints, where the elastic energy is determined by the collective motion of three or more particles, in contrast to a rectilinear spring whose elastic energy only relies on the displacement of two particles attached to the two ends of the spring. Utilizing polygon-shaped constraints, we found that the Maxwell counting argument and the topological construction, based on the compatibility matrix and the equilibrium matrix, can be generalized in our models, and our elastic systems follow the same topological classification. In addition, we also found that non-rectilinear constraints offers a natural pass towards topological states with higher topological indices and multiple edge states, which can be achieved even for a simple unit cell with one degree of freedom per unit cell without enlarging the unit cell in the bulk or at the edge., Comment: 10 pages, 19 figures

The angle resolved photoemission spectroscopy lineshapes of quasi one-dimensional (1d) Li0.9Mo6O17 display both agreement with and departures from the one-band Tomonaga-Luttinger model. We show that the departures can be understood by explicitly accounting for the four modes arising from the two quasi-1d bands known to cross the Fermi energy. The key assumption is that the antisymmetric charge mode is gapped with a magnitude near the temperature (T) of a mysterious 25K powerlaw resistivity upturn. The gap is consistent with the lack of a charge or spin density wave accompanying the upturn, is able to control the upturn T, and prevents crossover to a Fermi liquid (FL) down to the superconducting transition at 1.9K., Comment: 5 pages 4 figures

Superconductivity in the quasi-one-dimensional material Li$_{0.9}$Mo$_6$O$_{17}$ is analyzed based on a multiorbital extended Hubbard model. We found strong charge fluctuations at two different momenta ${\bf Q_1}$ and ${\bf Q_2}$ giving rise to two different charge ordered phases. Evaluating the superconducting vertex, we found superconductivity near strong charge fluctuations at ${\bf Q_1}$. The order parameter has the p-wave symmetry with nodes on the Fermi surface. The metallic state displays a characteristic charge collective mode ${\bf Q_1}$ due to nesting and for on-site Hubbard repulsion sufficiently large, a charge critical mode ${\bf Q_2}$ driven by Coulomb repulsion, which softens at the proximity to the transition. The results are quite robust for different coupling parametrizations. A phase diagram discussing the relevance of the model to the physics of the material is proposed.