Corner and edge states in topological Sierpinski Carpet systems.

Fractal lattices, with their self-similar and intricate structures, offer potential platforms for engineering physical properties on the nanoscale and also for realizing and manipulating high order topological insulator states in novel ways. Here we present a theoretical study on localized corner and edge states, emerging from topological phases in Sierpinski Carpet within a $\pi$-flux regime. A topological phase diagram is presented correlating the quadrupole moment with different hopping parameters. Particular localized states are identified following spatial signatures in distinct fractal generations. The specific geometry and scaling properties of the fractal systems can guide the supported topological states types and their associated functionalities. A conductive device is proposed by coupling identical Sierpinski Carpet units providing transport response through projected edge states which carry on the details of the system's topology. Our findings suggest that fractal lattices may also work as alternative routes to tune energy channels in different devices.

Quantum geometrical properties of topological materials.

The momentum space of topological insulators and topological superconductors is equipped with a quantum metric defined from the overlap of neighboring valence band states or quasihole states. We investigate the quantum geometrical properties of these materials within the framework of Dirac models and differential geometry. Their momentum space is found to be always a maximally symmetric space with a constant Ricci scalar, and the vacuum Einstein equation is satisfied in 3D with a finite cosmological constant. For linear Dirac models, several geometrical properties are found to be independent of the band gap, including a peculiar straight line geodesic, constant volume of the curved momentum space, and the exponential decay form of the nonlocal topological marker, indicating the peculiar yet universal quantum geometrical properties of these models.

DFT-1/2 method applied to 3D topological insulators.

In this paper, we present results and describe the methodology of application of DFT-1/2 method for five three-dimensional topological insulators materials that have been extensively studied in last years: Bi2Se3, Bi2Te3, Sb2Te3, CuTlSe2and CuTlS2. There are many differences between the results of simple DFT calculations and quasiparticle energy correction methods for these materials, especially for band dispersion in the character band inversion region. The DFT-1/2 leads to quite accurate results not only for band gaps, but also for the shape and atomic character of the bands in the neighborhood of the inversion region as well as the topological invariants, essential quantities to describe the topological properties of materials. The methodology is efficient and ease to apply for the different approaches used to obtain the topological invariantZ2, with the benefit of not increasing the computational cost in comparison with standard DFT, possibilitating its application for materials with a high number of atoms and complex systems.

Thermoelectric Transport in a Three-Dimensional HgTe Topological Insulator.

The thermoelectric response of 80 nm-thick strained HgTe films of a three-dimensional topological insulator (3D TI) has been studied experimentally. An ambipolar thermopower is observed where the Fermi energy moves from conducting to the valence bulk band. The comparison between theory and experiment shows that the thermopower is mostly due to the phonon drag contribution. In the region where the 2D Dirac electrons coexist with bulk hole states, the Seebeck coefficient is modified due to 2D electron-3D hole scattering.

At the Verge of Topology: Vacancy-Driven Quantum Spin Hall in Trivial Insulators.

Vacancies in materials structure─lowering its atomic density─take the system closer to the atomic limit, to which all systems are topologically trivial. Here we show a mechanism of mediated interaction between vacancies inducing a topologically nontrivial phase. Within an ab initio approach we explore topological transition dependence with the vacancy density in transition metal dichalcogenides. As a case of study, we focus on the PtSe2, for which the pristine form is a trivial semiconductor with an energy gap of 1.2 eV. The vacancies states lead to a large topological gap of 180 meV within the pristine system gap. We derive an effective model describing this topological phase in other transition metal dichalcogenide systems. The mechanism driving the topological phase allows the construction of backscattering protected metallic channels embedded in a semiconducting host.

Franckeite as an Exfoliable Naturally Occurring Topological Insulator.

Franckeite is a natural superlattice composed of two alternating layers of different composition which has shown potential for optoelectronic applications. In part, the interest in franckeite lies in its layered nature which makes it easy to exfoliate into very thin heterostructures. Not surprisingly, its chemical composition and lattice structure are so complex that franckeite has escaped screening protocols and high-throughput searches of materials with nontrivial topological properties. On the basis of density functional theory calculations, we predict a quantum phase transition originating from stoichiometric changes in one of franckeite composing layers (the quasihexagonal one). While for a large concentration of Sb, franckeite is a sequence of type-II semiconductor heterojunctions, for a large concentration of Sn, these turn into type-III, much alike InAs/GaSb artificial heterojunctions, and franckeite becomes a strong topological insulator. Transmission electron microscopy observations confirm that such a phase transition may actually occur in nature.

Toward Realistic Amorphous Topological Insulators.

The topological properties of materials are, until now, associated with the features of their crystalline structure, although translational symmetry is not an explicit requirement of the topological phases. Recent studies of hopping models on random lattices have demonstrated that amorphous model systems show a nontrivial topology. Using ab initio calculations, we show that two-dimensional amorphous materials can also display topological insulator properties. More specifically, we present a realistic state-of-the-art study of the electronic and transport properties of amorphous bismuthene systems, showing that these materials are topological insulators. These systems are characterized by the topological index [Formula: see text]2 = 1 and bulk-edge duality, and their linear conductance is quantized, [Formula: see text], for Fermi energies within the topological gap. Our study opens the path to the experimental and theoretical investigation of amorphous topological insulator materials.

Phase Separation of Dirac Electrons in Topological Insulators at the Spatial Limit.

In this work we present unique signatures manifested by the local electronic properties of the topological surface state in Bi2Te3 nanostructures as the spatial limit is approached. We concentrate on the pure nanoscale limit (nanoplatelets) with spatial electronic resolution down to 1 nm. The highlights include strong dependencies on nanoplatelet size: (1) observation of a phase separation of Dirac electrons whose length scale decreases as the spatial limit is approached, and (2) the evolution from heavily n-type to lightly n-type surface doping as nanoplatelet thickness increases. Our results show a new approach to tune the Dirac point together with reduction of electronic disorder in topological insulator (TI) nanostructured systems. We expect our work will provide a new route for application of these nanostructured Dirac systems in electronic devices.