Quantum simulators are an essential tool for understanding complex quantum materials. Platforms based on ultracold atoms in optical lattices and photonic devices led the field so far, but electronic quantum simulators are proving to be equally relevant. Simulating topological states of matter is one of the holy grails in the field. Here, we experimentally realize a higher-order electronic topological insulator (HOTI). Specifically, we create a dimerized Kagome lattice by manipulating carbon-monoxide (CO) molecules on a Cu(111) surface using a scanning tunneling microscope (STM). We engineer alternating weak and strong bonds to show that a topological state emerges at the corner of the non-trivial configuration, while it is absent in the trivial one. Contrarily to conventional topological insulators (TIs), the topological state has two dimensions less than the bulk, denoting a HOTI. The corner mode is protected by a generalized chiral symmetry, which leads to a particular robustness against perturbations. Our

Artificial electronic lattices, created atom by atom in a scanning tunneling microscope, have emerged as a highly tunable platform to realize and characterize the lowest-energy bands of novel lattice geometries. Here, we show that artificial electronic lattices can be tailored to exhibit higherenergy bands. We study p-like bands in four-fold and three-fold rotationally symmetric lattices. In addition, we show how an anisotropic design can be used to lift the degeneracy between px-and py-like bands. The experimental measurements are corroborated by muffin-tin and tight-binding calculations. The approach to engineer higher-energy electronic bands in artificial quantum systems introduced here enables the realization of complex band structures from the bottom up.

Theory anticipates that the in-plane p x , p y orbitals in a honeycomb lattice lead to potentially useful quantum electronic phases. So far, p orbital bands were only realized for cold atoms in optical lattices and for light and exciton-polaritons in photonic crystals. For electrons, in-plane p orbital physics is difficult to access since natural electronic honeycomb lattices, such as graphene and silicene, show strong s–p hybridization. Here, we report on electronic honeycomb lattices prepared on a Cu(111) surface in a scanning tunneling microscope that, by design, show (nearly) pure orbital bands, including the p orbital flat band and Dirac cone.

The boundary states of topological insulators are thought not to depend on the precise atomic structure of the boundary. A recent theoretical study showed that, for topological crystalline insulators with given bond strengths, topological states should only emerge for certain edge geometries. We experimentally probe this effect by creating artificial Kekulé lattices with different atomically well-defined edge geometries and hopping ratios in a scanning tunneling microscope. Topological edge modes are found to only appear for specific combinations of edge geometry and hopping ratio.

We use computer simulations to study the phase behaviour for hard, right rhombic prisms as a function of the angle of their rhombic face (the "slant" angle). More specifically, using a combination of event-driven molecular dynamics simulations, Monte Carlo simulations, and free-energy calculations, we determine and characterize the equilibrium phases formed by these particles for various slant angles and densities. Surprisingly, we find that the equilibrium crystal structure for a large range of slant angles and densities is the simple cubic crystal-despite the fact that the particles do not have cubic symmetry. Moreover, we find that the equilibrium vacancy concentration in this simple cubic phase is extremely high and depends only on the packing fraction and not the particle shape. At higher densities, a rhombic crystal appears as the equilibrium phase. We summarize the phase behaviour of this system by drawing a phase diagram in the slant angle-packing fraction plane.

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