Topological edge and corner states in Bi fractals on InSb

Topological materials hosting metallic edges characterized by integer quantized conductivity in an insulating bulk have revolutionized our understanding of transport in matter. The topological protection of these edge states is based on symmetries and dimensionality. However, only integer-dimensional models have been classified, and the interplay of topology and fractals, which may have a non-integer dimension, remained largely unexplored. Quantum fractals have recently been engineered in metamaterials, but up to present no topological states were unveiled in fractals realized in real materials. Here, we show theoretically and experimentally that topological edge and corner modes arise in fractals formed upon depositing thin layers of bismuth on an indium antimonide substrate. Scanning tunneling microscopy reveals the appearance of (nearly) zero-energy modes at the corners of Sierpi\'nski triangles, as well as the formation of outer and inner edge modes at higher energies. Unexpectedly, a robust and sharp depleted mode appears at the outer and inner edges of the samples at negative bias voltages. The experimental findings are corroborated by theoretical calculations in the framework of a continuum muffin-tin and a lattice tight-binding model. The stability of the topological features to the introduction of a Rashba spin-orbit coupling and disorder is discussed. This work opens the perspective to novel electronics in real materials at non-integer dimensions with robust and protected topological states.Comment: Main manuscript 14 pages, supplementary material 34 page

On the wake flow of asymmetrically beveled trailing edges

Trailing edge and wake flows are of interest for a wide range of applications. Small changes in the design of asymmetrically beveled or semi-rounded trailing edges can result in significant difference in flow features which are relevant for the aerodynamic performance, flow-induced structural vibration and aerodynamically generated sound. The present study describes in detail the flow field characteristics around a family of asymmetrically beveled trailing edges with an enclosed trailing-edge angle of 25 ∘ and variable radius of curvature R. The flow fields over the beveled trailing edges are described using data obtained by particle image velocimetry (PIV) experiments. The flow topology for different trailing edges was found to be strongly dependent on the radius of curvature R, with flow separation occurring further downstream as R increases. This variation in the location of flow separation influences the aerodynamic force coefficients, which were evaluated from the PIV data using a control volume approach. Two-point correlations of the in-plane velocity components are considered to assess the structure in the flow field. The analysis shows large-scale coherent motions in the far wake, which are associated with vortex shedding. The wake thickness parameter yf is confirmed as an appropriate length scale to characterize this large-scale roll-up motion in the wake. The development in the very near wake was found to be critically dependent on R. In addition, high-speed PIV measurements provide insight into the spectral characteristics of the turbulent fluctuations. Based on the time-resolved flow field data, the frequency range associated with the shedding of coherent vortex pairs in the wake is identified. By means of time-correlation of the velocity components, turbulent structures are found to convect from the attached or separated shear layers without distinct separation point into the wake.Wind Energ

Topological edge and corner states in Bi fractals on InSb

Topological materials hosting metallic edges characterized by integer quantized conductivity in an insulating bulk have revolutionized our understanding of transport in matter. The topological protection of these edge states is based on symmetries and dimensionality. However, only integer-dimensional models have been classified, and the interplay of topology and fractals, which may have a non-integer dimension, remained largely unexplored. Quantum fractals have recently been engineered in metamaterials, but up to present no topological states were unveiled in fractals realized in real materials. Here, we show theoretically and experimentally that topological edge and corner modes arise in fractals formed upon depositing thin layers of bismuth on an indium antimonide substrate. Scanning tunneling microscopy reveals the appearance of (nearly) zero-energy modes at the corners of Sierpi\'nski triangles, as well as the formation of outer and inner edge modes at higher energies. Unexpectedly, a robust and sharp depleted mode appears at the outer and inner edges of the samples at negative bias voltages. The experimental findings are corroborated by theoretical calculations in the framework of a continuum muffin-tin and a lattice tight-binding model. The stability of the topological features to the introduction of a Rashba spin-orbit coupling and disorder is discussed. This work opens the perspective to novel electronics in real materials at non-integer dimensions with robust and protected topological states

Precise Control of π-electron Magnetism in Metal-free Porphyrins

The porphyrin marcocycle can stabilize a set of magnetic metal ions, thus introducing localized net spins near the center. However, it remains illusive but most desirable to introduce delocalized spins in porphyrins with wide implications, for example, for building correlated quantum spins. Here, we demonstrate that metal-free porphyrins host delocalized π-electron magnetism as revealed by scanning probe microscopy and different level of theory calculations. Our results demonstrate that engineering of π-electron topologies introduces spin polarized singlet state and delocalized net spins in metal-free porphyrins. In addition, the π-electron magnetism can be switched on/off via STM manipulation by tunning the interfacial charge transfer. Our results provide an effective way to precisely control the π-electron magnetism in metal-free porphyrins, which can be further extended to design new magnetic functionalities of porphyrin-based architectures

Interface-enhanced superconductivity in monolayer 1T′-MoTe2 on SrTiO3(001)

Abstract Introducing superconductivity into two-dimensional (2D) films with nontrivial topology has been intensively pursued as one of the feasible scenarios to realize 1D topological superconductor. Prevailing endeavors mostly exploit the external gating or proximity effect of a traditional superconductor, by which the critical temperatures ( T c $T_{\mathrm{c}}$ ) are limited to several Kelvin range. Here, we report on the discovery of interface-enhanced superconductivity in monolayer 1T′-MoTe2 film. A thermally driven phase transition from Mo6Te6 nanowires to 1T′-MoTe2 films, grown on SrTiO3(001) surface by the molecular beam epitaxial methods, is demonstrated. A combined study of scanning tunneling microscopy/spectroscopy, electrical transport and magnetization measurements indicates the T c $T_{\mathrm{c}}$ of MoTe2 film is around 30 K, two orders of magnitude larger than its 3D counterpart crystal. This study shows that interfacial engineering is an efficient way to tune monolayer 1T′-MoTe2 film into superconducting states, and thus may pave the way toward higher- T c $T_{\mathrm{c}}$ 1D intrinsic topological superconductivity

Sierpiński Structure and Electronic Topology in Bi Thin Films on InSb(111)B Surfaces

Deposition of Bi on InSb(111)B reveals a striking Sierpiński-triangle (ST)-like structure in Bi thin films. Such a fractal geometric topology is further shown to turn off the intrinsic electronic topology in a thin film. Relaxation of a huge misfit strain of about 30% to 40% between Bi adlayer and substrate is revealed to drive the ST-like island formation. A Frenkel-Kontrova model is developed to illustrate the enhanced strain relief in the ST islands offsetting the additional step energy cost. Besides a sufficiently large tensile strain, forming ST-like structures also requires larger adlayer-substrate and intra-adlayer elastic stiffnesses, and weaker intra-adlayer interatomic interactions.</p