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The discovery of the quantum spin Hall effect led to the exploration of the electronic transport for spintronic devices. Here, we theoretically investigated the electronic conductance in large-gap realistic quantum spin Hall system, Pt$_2$HgSe$_3$ nanoribbons. By an ab initio approach, we found that the edge states present a penetration depth of about $0.9$\,{nm}, which is much smaller than those predicted in other 2D topological systems. Thus, suggesting that Pt$_2$HgSe$_3$ allows the exploitation of topological transport properties in narrow ribbons. Using non-equilibrium Green's functions calculations, we have examined the electron conductivity upon the presence of Se\,$\leftrightarrow$\,Hg antistructure defects randomly distributed in the Pt$_2$HgSe$_3$ scattering region. By considering scattering lengths up to $109$\,nm, we found localization lengths that can surpass $\mu$m sizes for narrow nanoribbons ($<9$\,nm). These findings can contribute to further understanding the behavior of topological insulators under realistic conditions and their integration within electronic, spintronic devices.

In recent years, synthesis and experimental research of fractalized materials has evolved in a paradigmatic crossover with topological phases of matter. We present here a theoretical investigation of the helical edge transport in Sierpinski carpets (SCs), combining the Bernevig-Hughes-Zhang (BHZ) model and the Landauer approach. Starting from a pristine two-dimensional topological insulator (2DTI), according to the BHZ model, our results reveal resonant transport modes when the SC fractal generation reaches the same scale as the space discretization; these modes are analyzed within a contour plot mapping of the local spin-polarized currents, shown spanned and assisted by inner-edge channels. From such a deeply fractalized SC building block, we introduce a rich tapestry formed by superior SC hierarchies, enlightening intricate patterns and unique fingerprints that offer valuable insights into how helical edge transport occurs in these fractal dimensions.

Spin-orbital textures in topological insulators due to the spin locking with the electron momentum, play an important role in spintronic phenomena that arise from the interplay between charge and spin degrees of freedom. We have explored interfaces between a ferromagnetic system (CrI$_3$) and a topological insulator (Bi$_2$Se$_3$) that allow the manipulation of spin-orbital textures. Within an {\it ab initio} approach we have extracted the spin-orbital-textures dependence of experimentally achievable interface designs. The presence of the ferromagnetic system introduces anisotropic transport of the electronic spin and charge. From a parameterized Hamiltonian model we capture the anisotropic backscattering behavior, showing its extension to other ferromagnetic/topological insulator interfaces. We verified that the van der Waals TI/MI interface is an excellent platform for controlling the spin degree of freedom arising from topological states, providing a rich family of unconventional spin texture configurations.

2D materials present an interesting platform for device designs. However, oxidation can drastically change the system's properties, which need to be accounted for. Through {\it ab initio} calculations, we investigated freestanding and SiC-supported As, Sb, and Bi mono-elemental layers. The oxidation process occurs through an O$_2$ spin-state transition, accounted for within the Landau-Zener transition. Additionally, we have investigated the oxidation barriers and the role of spin-orbit coupling. Our calculations pointed out that the presence of SiC substrate reduces the oxidation time scale compared to a freestanding monolayer. We have extracted the energy barrier transition, compatible with our spin-transition analysis. Besides, spin-orbit coupling is relevant to the oxidation mechanisms and alters time scales. The energy barriers decrease as the pnictogen changes from As to Sb to Bi for the freestanding systems, while for SiC-supported, they increase across the pnictogen family. Our computed energy barriers confirm the enhanced robustness against oxidation for the SiC-supported systems.

Currently, solid interfaces composed of two-dimensional materials (2D) in contact with metal surfaces (m-surf) have been the subject of intense research, where the borophene bilayer (BBL) has been considered a prominent material for the development of electronic devices based on 2D platforms. In this work, we present a theoretical study of the energetic, structural, and electronic properties of the BBL/m-surf interface, with m-surf = Ag, Au, and Al (111) surfaces, and the electronic transport properties of BBL channels connected to the BBL/m-surf top contacts. We find that the bottom-most BBL layer becomes metalized, due to the orbital hybridization with the metal surface states, resulting in BBL/m-surf ohmic contacts, meanwhile, the inner and top-most boron layers kept their semiconducting character. The net charge transfers reveal that BBL has become $n$-type ($p$-type) doped for m-surf = Ag, and Al (= Au). A thorough structural characterization of the BBL/m-surf interface, using a series of simulations of the X-ray photoelectron spectra, shows that the formation of BBL/m-surf interface is characterized by a redshift of the B-$1s$ spectra. Further electronic transport results revealed the emergence of a Schottky barrier between 0.1 and 0.2\,eV between the BBL/m-surf contact and the BBL channels. We believe that our findings are timely, bringing important contributions to the applicability of borophene bilayers for developing 2D electronic devices.

Two-dimensional arsenic allotropes have been grown on metallic surfaces, while topological properties have been theoretically described on strained structures. Here we experimentally grow arsenene by molecular beam epitaxy over the insulating SiC substrate. The arsenene presents a flat structure with a strain field that follows the SiC surface periodicity. Our ab initio simulations, based on the density functional theory, corroborate the experimental observation. The strained structure presents a new arsenene allotrope with a triangular structure, rather than the honeycomb previously predicted for other pnictogens. This strained structure presents a Peierls-like transition leading to an indirect gap semiconducting behavior.

Transition metal dichalcogenides have been the subject of numerous studies addressing technological applications and fundamental issues. Single-layer PtSe2 is a semiconductor with a trivial bandgap, in contrast, its counterpart with 25% of Se atoms substituted by Hg, Pt2HgSe3 (jacutingaite, a naturally occurring mineral), is a 2D topological insulator with a large bandgap. Based on ab-initio calculations, we investigate the energetic stability, and the topological transition in Pt(HgxSe1-x)2 as a function of alloy concentration, and the distribution of Hg atoms embedded in the PtSe2 host. Our findings reveal the dependence of the topological phase with respect to the alloy concentration and robustness with respect distribution of Hg. Through a combination of our ab-initio results and a defect wave function percolation model, we estimate the random alloy concentration threshold for the topological transition to be only 9%. Our results expand the possible search for non-trivial topological phases in random alloy systems.

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 non-trivial phase. Within an {\it 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 PtSe$_2$, to which 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.

Crystalline $\rm Bi_2Se_3$ is one of the most explored three-dimensional topological insulator, with a $0.3\;\rm eV$ energy gap making it promising for applications. Its amorphous counterpart could bring to light new possibilities for large scale synthesis and applications. Using ab initio molecular dynamics simulations, we have studied realistic amorphous $\rm Bi_2Se_3$ phases generated by different processes of melting, quenching, and annealing. Extensive structural and electronic characterizations show that the melting process induces an energy gap decrease ruled by growth of the defective local environments. This behavior dictates a weak stability of the topological phase to disorder, characterized by the spin Bott index. Interestingly, we identify the occurrence of topologically trivial surface states in amorphous $\rm Bi_2Se_3$ that show a strong resemblance with standard helical topological states. Our results and methods advance the search of topological phases in three-dimensional amorphous solids.

Understanding the role of microscopic attributes in nanocomposites allows for a controlled and, therefore, acceleration in experimental system designs. In this work, we extracted the relevant parameters controlling the graphene oxide binding strength to cellulose by combining first-principles calculations and machine learning algorithms. We were able to classify the systems among two classes with higher and lower binding energies, which are well defined based on the isolated graphene oxide features. By a theoretical X-ray photoelectron spectroscopy analysis, we show the extraction of these relevant features. Additionally, we demonstrate the possibilities of a refined control within a machine learning regression between the binding energy values and the system's characteristics. Our work presents a guiding map to the control graphene oxide/cellulose interaction.

Recently cycloarene has been experimentally obtained in a self-assembled structure, forming graphene-like monoatomic layered systems. Here, we establish the bandgap engineering/prediction in cycloarene assemblies within a combination of density functional theory and tight-binding Hamiltonians. Our results show a weak dependence of the gap with the assembly geometry, contrasting a strong dependence with the inter-molecule bond density. We derived a effective model that allows the interpretation of the arising energy gap for general particle-hole symmetric molecular arranges based on inter-molecular bond strength.

Material's geometrical structure is a fundamental part of their properties. The honeycomb geometry of graphene is responsible for the arising of its Dirac cone, while the kagome and Lieb lattice hosts flat bands and pseudospin-1 Dirac dispersion. These features seem to be particular for few 2D systems rather than a common occurrence. Given this correlation between structure and properties, exploring new geometries can lead to unexplored states and phenomena. Kepler is the pioneer of the mathematical tiling theory, describing ways of filing the euclidean plane with geometrical forms in its book {\it Harmonices Mundi}. In this letter, we characterize $1255$ lattices composed of the euclidean plane's k-uniform tiling, with its intrinsic properties unveiled - this class of arranged tiles present high-degeneracy points, exotic quasiparticles, and flat bands as a common feature. Here, we present aid for experimental interpretation and prediction of new 2D systems.

Jacutingate, a recently discovered Brazilian naturally occurring mineral, has shown to be the first experimental realization of the Kane-Mele topological model. In this letter we have unveiled a class of materials $M_2NX_3$ ($M$=Ni, Pt, Pd; $N$=Zn, Cd, Hg; and $X$=S, Se, Te), sharing jacutingaite's key features, i.e., high stability, and topological phase. By employing first-principles calculations we extensively characterize the energetic stability of this class while showing a common occurrence of the Kane-Mele topological phase. Here we found Pt-based materials surpassing jacutingaite's impressive topological gap and lower exfoliation barrier while retaining its stability.

The ability to construct 2D systems, beyond materials natural formation, enriches the search and control capability of new phenomena. For instance, the synthesis of topological lattices of vacancies on metal surfaces through scanning tunneling microscopy. In the present study we demonstrate that metal atoms encaged in silicate adlayer on silicon carbide is an interesting platform for lattices design, providing a ground to experimentally construct tight-binding models on an insulating substrate. Based on the density functional theory, we have characterized the energetic and the electronic properties of 2D metal lattices embedded in the silica adlayer. We show that the characteristic band structures of those lattices are ruled by surface states induced by the metal-$s$ orbitals coupled by the host-$p_{xy}$ states; giving rise to $sp_{xy}$ Dirac bands neatly lying within the energy gap of the semiconductor substrate.

A monolayer of CrI$_3$ is a two-dimensional crystal that in its equilibrium configuration is a ferromagnetic semiconductor, however, two coupled layers can be ferromagnetic or antiferromagnetic depending on the stacking. We study the magnetic phase diagram upon the strain of the antiferromagnetically coupled bilayer with C2/m symmetry. We found that strain may be an efficient tool to tune the magnetic phase of the structure. A tensile strain stabilizes the antiferromagnetic phase, while a compressive strain turns the system ferromagnetic. We understood that behavior by looking at the relative displacement between layers due to the strain. We also study the evolution of the magnetic anisotropy, the magnetic exchange coupling between Cr atoms, and how the Curie temperature is affected by the strain., Comment: 6 pages, 5 figures

Space group symmetries dictate the energy degeneracy of quasiparticles (e.g., electronic, photonic) in crystalline structures. For spinless systems, there can only be double or triple degeneracies protected by these symmetries, while other degeneracies are usually taken as \textit{accidental}. In this Letter we show that it is possible to design higher degeneracies exploring site permutation symmetries. These design principles are shown to be satisfied in previously studied lattices, and new structures are proposed with three, four and five degeneracy points for spinless systems. The results are general and apply to different quasiparticle models. Here, we focus on a tight-binding approach for the electronic case as a proof of principle. The resulting high-degeneracy points are protected by the site-permutation symmetries, yielding pseudospin-1 and -2 Dirac fermions. The strategy proposed here can be used to design lattices with high-degeneracy points in electronic (e.g. metal-organic frameworks), photonic, phononic, magnonic and cold-atom systems.

Materials with designed properties arises in a synergy between theoretical and experimental approaches. In this study we explore the set of Archimedean lattices forming a guidance to its electronic properties and topological phases. Within these lattices, rich electronic structure emerge forming type-I and II Dirac fermions, topological flat bands and high-degeneracy points with linear and flat dispersions. Employing a tight-binding model, with spin-orbit coupling, we characterize a quantum spin Hall (QSH) phase in all Archimedean lattices. Our discussion is validated within density functional theory calculations, where we show the characteristic bands of the studied lattices arising in 2D carbon allotropes.

We have studied how a generic bilayer kagome lattice behave upon layer rotation. We employed a Tight Binding model with one orbital per site and found (i) for low rotational angles, and at low energies, the same flat bands structure like in twisted bilayer graphene; though, for a larger value of the magic angle. Moreover, (ii) at high energies, due to the superstructure symmetry regions, we found the characteristics three band dispersion of the kagome lattice. In the latter, its band width decreases for lower angles confining them within a few meV. Therefore, we found in twisted kagome lattice the coexistence of two sets of flat bands in different energies and lying in different spatial regions of the bilayer system.

We investigate the layer localization control of two-dimensional states in multilayer metal-organic frameworks (MOFs). For finite stackings of (NiC4S4)3 MOFs, the weak van der Waals coupling between adjacent layers leads to a Fermi level dependent distribution of the electronic states in the monolayers. Such distribution is reflected in the topological edge states of multilayer nanoribbons. Moreover, by applying an external electric field, parallel to the stacking direction, the spacial localization of the electronic states can be controlled for a chosen Fermi energy. This localization behavior is studied comparing density functional theory calculations with a kagome lattice tight-binding model. Furthermore, for infinite stacked nanoribbons, a new V-gutter Dirac state is found in the side surfaces, which allows anisotropic current control by tuning the Fermi energy. Our results can be immediately extended to other kagome MOFs with eclipsed stackings, introducing a new degree of freedom (layer localization) to materials design.

The realization of the Quantum anomalous Hall effect (QAHE) in two dimensional (2D) metal organic frameworks (MOFs), (MC$_4$S$_4$)$_3$ with M = Mn, Fe, Co, Ru and Rh, has been investigated based on a combination of first-principles calculations and tight binding models. Our results for the magnetic anisotropy energy (MAE) reveal that the out-of-plane (in-plane) magnetization is favored for M = Mn, Fe, and Ru (Co, and Rh). Given the structural symmetry of (MC$_4$S$_4$)$_3$, the QAHE takes place only for M = Mn, Fe and Ru. Such a quantum anomalous Hall phase has been confirmed through the calculation of the Chern number, and examining the formation of topologically protected (metallic) edge states. Further electron ($n$-type) doping of the MOFs has been done in order to place the Fermi level within the non-trivial energy gap; where we find that in (RuC$_4$S$_4$)$_3$, in addition to the up-shift of the Fermi level, the MAE energy increases by 40\%. Finally, we show that in MOF/graphene (vdW) interfaces, the Fermi level tunning can be done with an external electric field, which controls the charge transfer at the MOF/graphene interface, giving rise to switchable topologically protected edge currents in MOFs.

We investigate the interplay between confinement and the fermion doubling problem in Dirac-like Hamiltonians. Individually, both features are well known. First, simple electrostatic gates do not confine electrons due to the Klein tunneling. Second, a typical lattice discretization of the first-order derivative $k \rightarrow -i\partial_x$ skips the central point and allow spurious low-energy, highly oscillating solutions known as fermion doublers. While a no-go theorem states that the doublers cannot be eliminated without artificially breaking a symmetry, here we show that the symmetry broken by the Wilson's mass approach is equivalent to the enforcement of hard-wall boundary conditions, thus making the no-go theorem irrelevant when confinement is foreseen. We illustrate our arguments by calculating the following: (i) the band structure and transport properties across thin films of the topological insulator Bi$_2$Se$_3$, for which we use ab-initio density functional theory calculations to justify the model; and (ii) the band structure of zigzag graphene nanoribbons., Comment: 10 pages, 9 figures

We have investigated the energetic stability and the electronic properties of metal-organic topological insulators bilayers (BLs), $(MC_4S_4)_3$-BL, with M=Ni and Pt, using first-principles calculations and tight-binding model. Our findings show that $(MC_4S_4)_3$-BL is an appealing platform to perform electronic band structure engineering, based on the topologically protected chiral edge states. The energetic stability of the BLs is ruled by van der Waals interactions; being the AA stacking the energetically most stable one. The electronic band structure is characterized by a combination of bonding and anti-bonding kagome band sets (KBSs), revealing that $(NiC_4S_4)_3$-BL presents a Z$_2$-metallic phase, whereas $(PtC_4S_4)_3$-BL may present both Z$_2$-metallic phase or quantum spin Hall phase. Those non-trivial topological states were confirmed by the formation of chiral edge states in $(MC_4S_4)_3$-BL nanoribbons. We show that the localization of the edge states can be controlled with a normal external electric field, breaking the mirror symmetry. Hence, the sign of electric field selects in which layer each set of edge states are located. Such a control on the (layer) localization, of the topological edge states, bring us an additional and interesting degree of freedom to control the transport properties in layered metal-organic topological insulator.

We have performed an ab initio investigation of the energetic stability, and the electronic properties of transition metals (TMs = Mn, Fe, Co, and Ru) adsorbed on graphene upon the presence of grain boundaries (GBs). Our results reveal an energetic preference for the TMs lying along the GB sites (TM/GB). Such an energetic preference has been strengthened by increasing the concentration of the TM adatoms; giving rise to TM nanolines on graphene ruled by GBs. Further diffusion barrier calculations for Fe adatoms support the formation of those TM nanolines. We find that the energy barriers parallel to the GBs are sligthly lower in comparision with those obtained for the defect free graphene; whereas, perpendicularly to the GBs the Fe adatoms face higher energy barriers. Fe and Co (Mn) nanolines are ferromagnetic (ferrimagnetic), in contrast the magnetic state of Ru nanolines is sensitive to the Ru/GB adsorption geometry. The electronic properties of those TM nanolines were characterized through extensive electronic band structure calculations. The formation of metallic nanolines is mediated by a strong hybridization between the TM and the graphene ($\pi$) orbitals along the GB sites. Due to the net magnetization of the TM nanolines, our band structure results indicate an anisotropic (spin-polarized) electronic current for some TM/GB systems.