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

Strain Solitons in an Epitaxially Strained van der Waals-like Material

Strain solitons are quasi-dislocations that form in van der Waals materials to relieve the energy associated with lattice or rotational mismatch. Novel electronic properties of strain solitons were predicted and observed. To date, strain solitons have been observed only in exfoliated crystals or mechanically strained crystals. The lack of a scalable approach toward the generation of strain solitons poses a significant challenge in the study of and use of their properties. Here, we report the formation of strain solitons with epitaxial growth of bismuth on InSb(111)B by molecular beam epitaxy. The morphology of the strain solitons for films of varying thickness is characterized with scanning tunneling microscopy, and the local strain state is determined from atomic resolution images. Bending in the solitons is attributed to interactions with the interface, and large angle bending is associated with edge dislocations. Our results enable the scalable generation of strain solitons.

Topological magnetoelectric response in ferromagnetic axion insulators

The topological magnetoelectric effect (TME) is a hallmark response of the topological field theory, which provides a paradigm shift in the study of emergent topological phenomena. However, its direct observation is yet to be realized due to the demanding magnetic configuration required to gap all surface states. Here, we theoretically propose that axion insulators with a simple ferromagnetic configuration, such as the MnBi2Te4/(Bi2Te3)n family, provide an ideal playground to realize the TME. In the designed triangular prism geometry, all the surface states are magnetically gapped. Under a vertical electric field, the surface Hall currents give rise to a nearly half-quantized orbital moment, accompanied by a gapless chiral hinge mode circulating in parallel. Thus, the orbital magnetization from the two topological origins can be easily distinguished by reversing the electric field. Our work paves the way for direct observation of the TME in realistic axion-insulator materials.

Emergence of quasi-1D spin-polarized states in ultrathin Bi films on InAs(111)A for spintronics applications

The discovery, characterization, and control of heavy-fermion low-dimensional materials are central to nanoscience since quantum phenomena acquire an exotic and highly tunable character. In this work, through a variety of comprehensive experimental and theoretical techniques, it was observed and predicted that the synthesis of ultrathin Bi films on the InAs(111)A surface produces quasi-one-dimensional spin-polarized states, providing a platform for the realization of a unique spin-transport regime in the system. Scanning tunneling microscopy and low-energy electron diffraction measurements revealed that the InAs(111)A substrate facilitates the formation of the Bi-dimer phase of 2√3 × 3 periodicity with an admixture of the Bi-bilayer phase under submonolayer Bi deposition. X-ray photoelectron spectroscopy (XPS) measurements have shown the chemical stability of the Bi-induced phases, while spin and angle resolved photoemission spectroscopy (SARPES) observations combined with state-of-the-art DFT calculations have revealed that the electronic spectrum of the Bi-dimer phase holds a quasi-1D hole-like spin-split state at the Fermi level with advanced spin texture, whereas the Bi-bilayer phase demonstrates metallic states with large Rashba spin-splitting. The band structure of the Bi/InAs(111)A interface is discovered to hold great potential as a high-performance spintronics material fabricated in the ultimate two-dimensional limit.

Moiré Pattern Formation in Epitaxial Growth on a Covalent Substrate: Sb on InSb(111)A

Structural moiré superstructures arising from two competing lattices may lead to unexpected electronic behavior. Sb is predicted to show thickness-dependent topological properties, providing potential applications for low-energy-consuming electronic devices. Here we successfully synthesize ultrathin Sb films on semi-insulating InSb(111)A. Despite the covalent nature of the substrate, which has dangling bonds on the surface, we prove by scanning transmission electron microscopy that the first layer of Sb atoms grows in an unstrained manner. Rather than compensating for the lattice mismatch of -6.4% by structural modifications, the Sb films form a pronounced moiré pattern as we evidence by scanning tunneling microscopy. Our model calculations assign the moiré pattern to a periodic surface corrugation. In agreement with theoretical predictions, irrespective of the moiré modulation, the topological surface state known on a thick Sb film is experimentally confirmed to persist down to small film thicknesses, and the Dirac point shifts toward lower binding energies with a decrease in Sb thickness.

A 2D Bismuth-Induced Honeycomb Surface Structure on GaAs(111)

Two-dimensional (2D) topological insulators have fascinating physical properties which are promising for applications within spintronics. In order to realize spintronic devices working at room temperature, materials with a large nontrivial gap are needed. Bismuthene, a 2D layer of Bi atoms in a honeycomb structure, has recently attracted strong attention because of its record-large nontrivial gap, which is due to the strong spin-orbit coupling of Bi and the unusually strong interaction of the Bi atoms with the surface atoms of the substrate underneath. It would be a significant step forward to be able to form 2D materials with properties such as bismuthene on semiconductors such as GaAs, which has a band gap size relevant for electronics and a direct band gap for optical applications. Here, we present the successful formation of a 2D Bi honeycomb structure on GaAs, which fulfills these conditions. Bi atoms have been incorporated into a clean GaAs(111) surface, with As termination, based on Bi deposition under optimized growth conditions. Low-temperature scanning tunneling microscopy and spectroscopy (LT-STM/S) demonstrates a well-ordered large-scale honeycomb structure, consisting of Bi atoms in a √3 × √3 30° reconstruction on GaAs(111). X-ray photoelectron spectroscopy shows that the Bi atoms of the honeycomb structure only bond to the underlying As atoms. This is supported by calculations based on density functional theory that confirm the honeycomb structure with a large Bi-As binding energy and predict Bi-induced electronic bands within the GaAs band gap that open up a gap of nontrivial topological nature. STS results support the existence of Bi-induced states within the GaAs band gap. The GaAs:Bi honeycomb layer found here has a similar structure as previously published bismuthene on SiC or on Ag, though with a significantly larger lattice constant and only weak Bi-Bi bonding. It can therefore be considered as an extreme case of bismuthene, which is fundamentally interesting. Furthermore, it has the same exciting electronic properties, opening a large nontrivial gap, which is the requirement for room-temperature spintronic applications, and it is directly integrated in GaAs, a direct band gap semiconductor with a large range of (opto)electronic devices.

Fractals via Controlled Fisher Iterated Function System

This paper explores the generalization of the fixed-point theorem for Fisher contraction on controlled metric space. The controlled metric space and Fisher contractions are playing a very crucial role in this research. The Fisher contraction on the controlled metric space is used in this paper to generate a new type of fractal set called controlled Fisher fractals (CF-Fractals) by constructing a system named the controlled Fisher iterated function system (CF-IFS). Furthermore, the interesting results and consequences of the controlled Fisher iterated function system and controlled Fisher fractals are demonstrated. In addition, the collage theorem on controlled Fisher fractals is established as well. The newly developing IFS and fractal set in the controlled metric space can provide the novel directions in the fractal theory.

Growth mechanism and self-polarization of bilayer InSb (111) on Bi (001) substrate

Polarity introduced by inversion symmetry broken along <111> direction has strong impacts on the physical properties and morphological characteristics of III-V component nanostructure. Take III-V component semiconductor InSb as an example, we systematically investigate the growth sequence and morphology evolution of InSb (111) on Bi (001) substrate from adatoms to bilayers. We discovered and verified that the presence of amorphous-like morphology of monolayer InSb was attributed to the strong interaction between mix-polarity InSb and Bi substrate. Further, our comprehensive energy investigations of bilayer InSb reveal that an amorphous first layer will be crystallized and polarized driven by the low surface energy of the reconstructed second layers. Phase diagrams were developed to describe the ongoing polarization process of bilayer InSb under various chemical environments as a function of deposition time. The growth mechanism and polarity phase diagram of bilayer InSb on Bi substrate may advance the progress of polarity controllable growth of low-dimensional InSb nanostructure as well as other polar III-V compound semiconductors.

Fractal photonic topological insulators

Topological insulators constitute a novel state of matter with scatter-free edge states surrounding an insulating bulk. Conventional wisdom regards the insulating bulk as essential, since the invariants describing the topological properties of the system are defined therein. Here, we study fractal topological insulators based on exact fractals comprised exclusively of edge sites. We present experimental proof that, despite the lack of bulk bands, photonic lattices of helical waveguides support topologically protected chiral edge states. We show that light transport in our topological fractal system features increased velocities compared to the corresponding honeycomb lattice. By going beyond the confines of the bulk-boundary correspondence, our findings pave the way toward an expanded perception of topological insulators and open a new chapter of topological fractals.