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Incommensurate heterostructures of two-dimensional (2D) materials, despite their attractive electronic behaviour, are challenging to simulate because of the absence of translation symmetry. Experimental investigations of these structures often employ scanning tunneling microscopy (STM), however there is to date no comprehensive theory to simulate an STM image in such systems. In this paper, we present a geometry-based method to generate STM images in incommensurate van der Waals (vdW) heterostructures, which we call the moir\'e plane wave expansion model (MPWEM). We generate the STM images using a weighted sum of three image terms: the non-interacting STM images of (1) the substrate layer, (2) the adsorbate layer, and (3) a semi-empirical Fourier expansion of the moir\'e wavevectors obtained analytically which results from the interaction of (1) and (2). We illustrate and benchmark the model using selected vdW 2D systems composed of structurally and electronically distinct crystals, and show that the method reproduces experimental STM images down to angstrom-scale details. The MPWEM, thanks to its simplicity, can serve as an initial prediction tool prior to more computationally expensive calculations which are often limited by the number of atoms and the requirement of periodic supercells, and thus offers a promising class of computationally-friendly STM simulations, of high relevance in the growing field of twistronics., Comment: 12 pages, 5 figures (+ supplementary information)

We present a systematic investigation of the edge states of two-dimensional {\alpha}-bismuthene ({\alpha}-Bi) structures self-assembled on HOPG substrates, using scanning tunnelling microscopy and scanning tunnelling spectroscopy. The measurements are carried out for 3ML, 5ML and 7ML thick Bi structures. Our spectroscopy studies reveal clear features at the edges of the 5ML and 7ML thick structures, and the positions of the edge states (ESs) coincide with the topographical step edges. In contrast, in 3ML structures the ESs appear to be absent and instead new states are sometimes observed, far from the topographical edge. These states are associated with a moir\'e pattern and result from strain-induced modulation of the topology. Our observations demonstrate the impact on the edge states of coupling to adjacent structures., Comment: 17 pages, 6 figures

Two-dimensional (2D) Dirac-like electron gases have attracted tremendous research interest ever since the discovery of free-standing graphene. The linear energy dispersion and non-trivial Berry phase play the pivotal role in the remarkable electronic, optical, mechanical and chemical properties of 2D Dirac materials. The known 2D Dirac materials are gapless only within certain approximations, for example, in the absence of SOC. Here we report a route to establishing robust Dirac cones in 2D materials with nonsymmorphic crystal lattice. The nonsymmorphic symmetry enforces Dirac-like band dispersions around certain high-symmetry momenta in the presence of SOC. Through $\mu$-ARPES measurements we observe Dirac-like band dispersions in $\alpha$-bismuthene. The nonsymmorphic lattice symmetry is confirmed by $\mu$-LEED and STM. Our first-principles simulations and theoretical topological analysis demonstrate the correspondence between nonsymmorphic symmetry and Dirac states. This mechanism can be straightforwardly generalized to other nonsymmorphic materials. The results open the door for the search of symmetry enforced Dirac fermions in the vast uncharted world of nonsymmorphic 2D materials.

Van der Waals heterostructures have recently been identified as providing many opportunities to create new two-dimensional materials, and in particular to produce materials with topologically interesting states. Here we show that it is possible to create such heterostructures with multiple topological phases in a single nanoscale island. We discuss their growth within the framework of diffusion-limited aggregation, the formation of moir\'e patterns due to the differing crystallographies of the materials comprising the heterostructure, and the potential to engineer both the electronic structure as well as local variations of topological order. In particular we show that it is possible to build islands which include both the hexagonal $\beta$- and rectangular $\alpha$-forms of antimonene, on top of the topological insulator $\alpha$-bismuthene. This is the first experimental realisation of $\alpha$-antimonene, and we show that it is a topologically non-trivial material in the quantum spin Hall class., Comment: 6 pages, 3 figures, plus Supplementary material (9 pages, 6 figures)

Magnetic excitations of single atoms on surfaces have been widely studied experimentally in the past decade. Lately, systems with unprecedented magnetic stability started to emerge. Here, we present a general theoretical investigation of the stability of rare-earth magnetic atoms exposed to crystal or ligand fields of various symmetry and to exchange scattering with an electron bath. By analyzing the properties of the atomic wavefunction, we show that certain combinations of symmetry and total angular momentum are inherently stable against first or even higher order interactions with electrons. Further, we investigate the effect of an external magnetic field on the magnetic stability., Comment: 8 pages, 2 figures

Due to underlying symmetries the ground states of magnetic adatoms may be highly stable, which opens perspectives for application as single-atom memory. A specific example is a single holmium atom (with $J=8$) on a platinum (111) surface for which exceptionally long lifetimes were observed in recent scanning tunneling microscopy studies. For control and read-out the atom must be coupled to electronic contacts. Hence the spin dynamics of the system is governed by a quantum master equation. Our analysis shows that in general it cannot be reduced to a classical master equation in the basis of the unperturbed crystal-field Hamiltonian. Rather, depending on parameters and control fields, "environment induced superselection" principles choose the appropriate set of basis states, which in turn determines the specific relaxation channels and lifetimes. Our simulations suggest that in ideal situations the lifetimes should be even longer than observed in the experiment. We, therefore, investigate the influence of various perturbations. We also study the initialization process of the state of the Ho atom by applied voltage pulses and conclude that fast, high fidelity preparation, on a $100\,\text{ns}$ timescale, should be possible., Comment: 14 pages, 11 figures

Inelastic tunneling spectroscopy of Pb islands on Cu(111) obtained by scanning tunneling microscopy below 1K provides a direct access to the local Eliashberg function of the islands with high energy resolution. The Eliashberg function describes the electron-phonon interaction causing conventional superconductivity. The measured Eliashberg function strongly depends on the local thickness of the Pb nanostructures and shows a sharp maximum when quantum well states of the Pb islands come close to the Fermi energy. Ab initio calculations reveal that this is related to enhanced electron-phonon coupling at these thicknesses., Comment: 5 pages, 4 figures