We study theoretically two-dimensional single-crystalline sheets of semiconductors forming a honeycomb lattice with a period below 10 nm. These systems could combine the usual semiconductor properties with Dirac bands. Using atomistic tight-binding calculations, we show that both the atomic lattice and the overall geometry influence the band structure, revealing materials with unusual electronic properties. In rock-salt Pb-chalcogenides, the expected Dirac-type features are clouded by a complex band structure. However, in the case of zinc-blende Cd-chalcogenide semiconductors, the honeycomb nano-geometry leads to rich band structures including, in the conduction band, Dirac cones at two distinct energies and non-trivial flat bands, and, in the valence band, topological edge states. These edge states are present in several electronic gaps opened in the valence band by the spin-orbit coupling and the quantum confinement in the honeycomb geometry. The lowest Dirac conduction band has S-orbital character and is equivalent to the π − π ⋆ band of graphene but with renormalized couplings. The conduction bands higher in energy have no counterpart in graphene, they combine a Dirac cone and flat bands because of their P -orbital character. We show that the width of the Dirac bands varies between tens and hundreds of meV. These systems emerge as remarkable platforms for studying complex electronic phases starting from conventional semiconductors. Recent advancements in colloidal chemistry indicate that these materials can be synthesized from semiconductor nanocrystals.

The photoelectrochemical properties of electrodeposited Cu 2 O in aqueous solutions were investigated. The material showed long term stability under illumination at negative potentials. The diffusion length of electrons in the as-deposited material was of the order of 10-100 nm. We did not observe photocathodic reduction of water. The efficiencies for the reduction of oxygen and the methylviologen cation at these electrodes were surprisingly high. This suggests that, in conjunction with a suitable redox system, electrodeposited Cu 2 O could be a promising material as a p-type photoelectrode in an electrochemical photovoltaic cell.

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

Colloidal core-shell semiconductor nanocrystals form an important class of optoelectronic materials, in which the exciton wave functions can be tailored by the atomic configuration of the core, the interfacial layers, and the shell. Here, we provide a trustful 3D characterization at the atomic scale of a free-standing PbSe(core)-CdSe(shell) nanocrystal by combining electron microscopy and discrete tomography. Our results yield unique insights for understanding the process of cation exchange, which is widely employed in the synthesis of core-shell nanocrystals. The study that we present is generally applicable to the broad range of colloidal heteronanocrystals that currently emerge as a new class of materials with technological importance.

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