Twelve multicomponent spinels, comprised of (Mg, Cr, Mn, Co, Fe, Ni, Cu, and/or Zn)${\left(\mathrm{Cr},\mathrm{Fe},\mathrm{or}\mathrm{Al}\right)}_2{\mathrm{O}}_4$, were prepared using solid state synthesis methods, resulting in nine homogenous, single phase samples with a $Fm-3m$ structure, and three samples with multiple phases. Using dc magnetometry in conjunction with x-ray diffraction, scanning electron microscopy with energy dispersive x-ray spectroscopy, and x-ray absorption spectroscopy, the effects of multicomponent material design on the structural, magnetic, and chemical properties are explored. The ferritic spinel high-entropy oxide (HEO) samples show high-temperature ferrimagnetic transitions and both ferritic and chromium-based HEO spinel samples show evidence of low-temperature antiferromagnetic ordering. Blocking temperatures are evident in some samples and magnetic transition temperatures are reported. Constituent valence states and temperature dependent valence is described for the example case of $\left(\mathrm{M}{\mathrm{g}}_{0.2}\mathrm{F}{\mathrm{e}}_{0.2}\mathrm{C}{\mathrm{o}}_{0.2}\mathrm{N}{\mathrm{i}}_{0.2}\mathrm{C}{\mathrm{u}}_{0.2}\right)\mathrm{C}{\mathrm{r}}_2{\mathrm{O}}_4$, including the unexpected presence of $\mathrm{C}{\mathrm{r}}^{4+}$, indicating a 2–4 type spinel configuration. Valence trends for two ferritic HEO spinels are also discussed. Some of these compositions are synthesized for the first time and this work provides an investigation into the magnetic properties of the novel class of cubic spinel multicomponent oxides showing interesting behavior that warrants further investigation.

When it comes to providing the unusual combination of optical transparency, $p$-type conductivity, and relatively high mobility, ${\mathrm{Sn}}^{2+}$-based oxides are promising candidates. Epitaxial films of the simplest ${\mathrm{Sn}}^{2+}$ oxide, SnO, are grown in an adsorption-controlled regime at $380{}^{\circ }\mathrm{C}$ on ${\mathrm{Al}}_2{\mathrm{O}}_3$ substrates by molecular-beam epitaxy, where the excess volatile ${\mathrm{SnO}}_x$ desorbs from the film surface. A commensurately strained monolayer and an accompanying van der Waals gap is observed near the substrate interface, promoting layers with high structural perfection notwithstanding a large epitaxial lattice mismatch ($-12\%$). The unintentionally doped films exhibit $p$-type conductivity with carrier concentration $2.5\times {10}^{16}{\mathrm{cm}}^{-3}$ and mobility $2.4{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ at room temperature. Additional physical properties are measured and linked to the ${\mathrm{Sn}}^{2+}$ valence state and corresponding lone-pair charge-density distribution.

Rapid decline in fossil fuel energy necessitates the immediate need for renewable energy resources. Here, we report a previously unexplored class of nitrides ${\mathrm{AMN}}_2$ (A=Na, K, Rb, Cs, M=V, Nb, Ta) keeping renewable energy applications in mind. Using a detailed structure and stability analysis using first principles simulation, we discovered twelve such compounds (few of which were already synthesized before), which are chemically, mechanically, and dynamically stable. These twelve compounds were then evaluated for their suitability for three renewable energy applications: (i) photovoltaics, (ii) water splitting, and (iii) thermoelectrics. Careful analysis of electronic structure reveals high optical transition strength resulting in a sharp rise in absorption. This in turn yields high short circuit current and hence excellent solar efficiency for a few compounds namely ${\mathrm{CsVN}}_2$ and ${\mathrm{RbVN}}_2$. Along with excellent absorption quality, some compounds show favorable band edge positions compared to water redox levels and hence are promising as photoelectrodes in photo(electro)chemical water splitting devices. Mixture of flat and dispersive bands in the band structure yields both high Seebeck and electrical conductivity, thus an excellent power factor for six compounds. Simulated lattice thermal conductivity shows moderate to ultralow values and thus the possibility of achieving a high thermoelectric figure of merit (ZT), even at lower temperatures. From the experimental perspective, we discuss the possible challenges that may arise while utilizing these compounds for the desired applications and suggest possible pathways to overcome them. We believe such theoretical prediction of promising materials is extremely useful for new materials discovery and anticipate rapid response from the experimental community.

Native point defect doping via thermal treatment is an easy and promising method to tune the electrical transport properties of semiconductors made for renewable-energy conversion. In this study, we investigate the vacancy doping of the lowly toxic semiconductor $\mathrm{B}{\mathrm{i}}_2{\mathrm{S}}_3$ using electrical conductivity as well as thermoelectric power measurements. We enhance the electrical conductivity of bismuth sulfide nanoparticle layers by more than four orders of magnitude by a stepwise thermal treatment in a moderate temperature range (300–480 K). Via thermoelectric power measurements we attribute this enhancement to an increase in charge-carrier mobility by two orders of magnitude and to an increase in charge-carrier density by more than two orders of magnitude. We find that the energetic position of the electron-doping sulfur vacancies of bismuth sulfide nanoparticles is significantly shallower than previously reported for bulk material. Subsequently, we implement $\mathrm{B}{\mathrm{i}}_2{\mathrm{S}}_3$ nanoparticles doped with sulfur vacancies by thermal annealing in photovoltaic devices using P3HT as an electron donor molecule. We find that annealing up to 383 K yields the best compromise between improving charge-carrier transport and increasing defect densities.

We analyze the optical properties of zincblende gallium-nitride in the infrared and ultraviolet spectral range ($\approx 27\mathrm{meV}–6.5\mathrm{eV}$) experimentally by spectroscopic ellipsometry and provide a quantitative description of these results by $\mathbf{k}·\mathbf{p}$ perturbation theory. Free-electron concentrations above ${10}^{20}{\mathrm{cm}}^{-3}$ are achieved by introducing germanium as a donor. We determine the dielectric function as well as band filling effects like the Burstein-Moss shift and band gap renormalization. The Kane model for the band structure of semiconductors near the $\mathrm{\Gamma }$-point allows to calculate the effective electron mass and to determine the nonparabolicity of the conduction band. At the same time, these results can be used to derive the free-electron concentration all-optically. The combination of Kane's model, Burstein-Moss shift, and band-gap renormalization can be used to expertly describe the measured transition energies up to $\approx 3.7\mathrm{eV}$ dependent on the carrier concentration, yielding an averaged hole mass of $\approx 0.61{\mathrm{m}}_{\mathrm{e}}$ for the contributing valence bands.

The superconductor ${\mathrm{Sn}}_{1-x}{\mathrm{In}}_x\mathrm{Te}$ is derived from the topological crystalline insulator SnTe and is a candidate topological superconductor. So far, high-quality thin films of this material have not been available, even though such samples would be useful for addressing the nature of its superconductivity. Here we report the successful molecular beam epitaxy growth of superconducting ${\mathrm{Sn}}_{1-x}{\mathrm{In}}_x\mathrm{Te}$ films by using ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ as a buffer layer. The data obtained from tunnel junctions made on such films show the appearance of two superconducting gaps, which points to the coexistence of bulk and surface superconductivity. Given the spin-momentum locking of the surface states, the surface superconductivity is expected to be topological with an effective $p$-wave character. Since the topological surface states of SnTe consist of four Dirac cones, this platform offers an interesting playground for studying topological surface superconductivity with additional degrees of freedom.

A structural transition in an $AB{\mathrm{O}}_3$ perovskite thin film involving the change of the $B{\mathrm{O}}_6$ octahedral rotation pattern can be hidden under the global lattice symmetry imposed by the substrate and often easily overlooked. We carried out high-resolution x-ray diffraction experiments to investigate the structures of epitaxial ${\mathrm{Ca}}_{0.5}{\mathrm{Sr}}_{0.5}{\mathrm{IrO}}_3$ (CSIO) perovskite iridate films grown on ${\mathrm{SrTiO}}_3$ (STO) and ${\mathrm{GdScO}}_3$ (GSO) substrates in detail. Although the CSIO/STO film layer displays a global tetragonal lattice symmetry evidenced by the reciprocal space mapping, synchrotron x-ray data indicate that its room-temperature structure is monoclinic due to Glazer's $a^{+}{a}^{-}{c}^{-}$-type rotation of the ${\mathrm{IrO}}_6$ octahedra. In order to accommodate the lower-symmetry structure under the global tetragonal symmetry, the film breaks into four twinned domains, resulting in the splitting of the (half-integer, 0, integer) superlattice reflections. Surprisingly, the splitting of these superlattice reflections decrease with increasing temperature, eventually disappearing at $T_S=510\left(5\right)\mathrm{K}$, which signals a structural transition to an orthorhombic phase with $a^{+}{a}^{-}{c}^0$ octahedral rotation. In contrast, the CSIO/GSO film displays a stable monoclinic symmetry with $a^{+}{b}^{-}{c}^{-}$ octahedral rotation, showing no structural instability caused by the substrate up to 520 K. Our study illustrates the importance of the symmetry in addition to the lattice mismatch of the substrate in determining the structure of epitaxial thin films.

Halide perovskites constitute a chemically diverse class of crystals with great promise as photovoltaic absorber materials, featuring band gaps between about 1 and 3.5 eV depending on composition. Their diversity calls for a general computational approach to predicting their band gaps. However, such an approach is still lacking. Here, we use density functional theory (DFT) and ab initio many-body perturbation theory within the $\mathit{GW}$ approximation to compute the quasiparticle or fundamental band gap of a set of ten representative halide perovskites: ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$ (${\mathrm{MAPbI}}_3$), ${\mathrm{MAPbBr}}_3, {\mathrm{CsSnBr}}_3$, (${\mathrm{MA})}_2{\mathrm{BiTlBr}}_6, {\mathrm{Cs}}_2{\mathrm{TlAgBr}}_6, {\mathrm{Cs}}_2{\mathrm{TlAgCl}}_6, {\mathrm{Cs}}_2{\mathrm{BiAgBr}}_6, {\mathrm{Cs}}_2{\mathrm{InAgCl}}_6, {\mathrm{Cs}}_2{\mathrm{SnBr}}_6$, and ${\mathrm{Cs}}_2{\mathrm{Au}}_2{\mathrm{I}}_6$. Comparing with recent measurements, we find that a standard generalized gradient exchange-correlation functional can significantly underestimate the experimental band gaps of these perovskites, particularly in cases with strong spin-orbit coupling (SOC) and highly dispersive band edges, to a degree that varies with composition. We show that these nonsystematic errors are inherited by one-shot $G_0{W}_0$ and eigenvalue self-consistent ${\mathrm{GW}}_0$ calculations, demonstrating that semilocal DFT starting points are insufficient for ${\mathrm{MAPbI}}_3, {\mathrm{MAPbBr}}_3, {\mathrm{CsSnBr}}_3$, (${\mathrm{MA})}_2{\mathrm{BiTlBr}}_6, {\mathrm{Cs}}_2{\mathrm{TlAgBr}}_6$, and ${\mathrm{Cs}}_2{\mathrm{TlAgCl}}_6$. On the other hand, we find that DFT with hybrid functionals leads to an improved starting point and ${GW}_0$ results in better agreement with experiment for these perovskites. Our results suggest that ${GW}_0$ with hybrid functional-based starting points are promising for predicting band gaps of systems with large SOC and dispersive bands in this technologically important class of semiconducting crystals.

The $\mathrm{N}{\mathrm{i}}_2\mathrm{MnSn}$-derived $\mathrm{N}{\mathrm{i}}_{50-x}\mathrm{C}{\mathrm{o}}_x\mathrm{M}{\mathrm{n}}_{25+y}\mathrm{S}{\mathrm{n}}_{25-y}$ alloys are premier examples of a class of off-stoichiometric Heusler alloys recently discovered to exhibit attractive magnetic properties in tandem with extraordinarily reversible martensitic phase transformations. Multiferroicity, magnetic phase competition and separation, field-induced martensitic transformations, magnetic shape memory behavior, and sizable magneto-, elasto-, and barocaloric effects result, generating substantial interest and application potential. In this work we expand on a prior small-angle neutron scattering (SANS) study at a single composition $\left(\mathrm{N}{\mathrm{i}}_{44}\mathrm{C}{\mathrm{o}}_6\mathrm{M}{\mathrm{n}}_{40}\mathrm{S}{\mathrm{n}}_{10}\right)$ by exploring all three main regions of the recently established $\mathrm{N}{\mathrm{i}}_{50-x}\mathrm{C}{\mathrm{o}}_x\mathrm{M}{\mathrm{n}}_{40}\mathrm{S}{\mathrm{n}}_{10}$ phase diagram, i.e., at the representative $y=15$ composition. Wide temperature and scattering wave-vector range $\left(20-500\mathrm{K},0.004-0.2{\AA }^{-1}\right)$ SANS data on $x=2$, 6, and 14 polycrystals provide a detailed picture of the evolution in magnetic order and inhomogeneity. Consistent with recent studies with a variety of techniques, phase separation into short-range coexisting ferromagnetic and antiferromagnetic regions is deduced below the martensitic transformation at $x=2$ and 6, with average ferromagnetic cluster spacing of ∼13 nm. Remarkably, at $x=14$, where the martensitic transformation is suppressed and ferromagnetic austenite is stabilized to low temperatures, nanoscopic magnetic inhomogeneity nevertheless persists. Distinct ferromagnetic clusters (∼36-nm average spacing) in a ferromagnetic matrix are observed at intermediate temperatures, homogenizing into a uniform long-range ordered ferromagnet only at low temperatures. This unusual ferromagnet cluster/ferromagnet matrix inhomogeneity, as well as $x$-dependent subtleties of the superparamagnetic freezing of ferromagnetic clusters, are discussed in light of ${}^{55}\mathrm{Mn}$ nuclear magnetic resonance data, and the recent observation of annealing-induced core/shell nanoprecipitates. The origins of nanoscale magnetic inhomogeneity are discussed in terms of statistical variations in local composition and structure, tendency to chemical phase separation, and other forms of disorder.

Using Landau-Ginzburg-Devonshire theory and effective medium approximation, we analytically calculate typical dependences of the pyroelectric and electrocaloric coefficients on external electric field, temperature, and radius of spherical single-domain ferroelectric nanoparticles. The considered physical model corresponds to the nanocomposite with a small fraction of ferroelectric nanoparticles. Within the framework of the analytical model, we establish how the size changes determine the temperature and field behavior of pyroelectric and electrocaloric coefficients on the example of $\mathrm{BaTi}{\mathrm{O}}_3$ nanoparticles covered by a semiconducting shell and placed in a dielectric polymer. We show that by changing the particle size one can induce maxima of the pyroelectric coefficient and electrocaloric temperature variation, control their width and height. Obtained analytical expressions allow selecting the interval of particle sizes, voltage, and/or temperature for which the pyroelectric energy conversion and electrocaloric coefficient are optimal for applications. The observed size effect opens the possibility to control pyroelectric and electrocaloric properties of ferroelectric nanocomposites that can be important for their advanced applications in energy convertors and cooling systems.

Silver is an extremely appealing metal for plasmonics due to its very low optical losses in the visible and near-ultraviolet range and its relatively low reactivity. Within the emerging field of thermoplasmonics, where light-metal interactions are exploited to generate heat on the nanometric scale, knowledge of temperature-dependent complex permittivities of plasmonic materials is indispensable. We extracted the temperature-dependent complex permittivity of silver ${\varepsilon }_{Ag}$ by spectroscopic ellipsometry under high-vacuum conditions. For rising $T$, we observed an increase of the free-electron contribution to the imaginary part of the permittivity $\text{Im}\left[{\varepsilon }_{Ag}\right]$ and a temperature-dependent absorption band splitting off the interband absorption edge in the 320–360-nm range. Around 340 nm the relative increase of $\text{Im}\left[{\varepsilon }_{Ag}\right]$ at 600 K with respect to its room-temperature value is around 500%. In order to understand the implications of this behavior on silver thermoplasmonics, we computed the temperature-dependent extinction efficiency of oblate Ag ellipsoids with localized plasmon resonance within the 320–360-nm range. We predict that dramatic damping of the plasmon resonance occurs for increasing temperature, possibly leading to intriguing self-limiting effects in Ag thermoplasmonics.

Two-dimensional (2D) materials have attracted a great deal of attention because they exhibit intriguing physical and chemical properties with great potential applications in electronic and optoelectronic devices, and even energy conversion. Due to the high anisotropy and unique crystal structure of layered materials, the properties can be effectively tuned by simply reducing dimensions to 2D. In this work, a unique 2D semiconductor, namely, monolayered SbAs, with high stability and indirect band gap, is predicted on the basis of first-principles calculations together with cluster expansion and Monte Carlo simulations. Interestingly, although the bulk antimony arsenide compound SbAs is known to exhibit semimetallic behavior, our calculations find that it is transformed into a direct semiconductor with a band gap of 1.28 eV when thinned down to a single atomic layer. The monolayer with antisite defects is transformed from indirect into a direct band-gap semiconductor. Such dramatic changes in the electronic structure could pave the way for SbAs to play a role in electronic device applications. Moreover, we find that the interlayer interactions in SbAs lead to a higher exfoliation energy than typical transition metal dichalcogenides such as $\mathrm{Mo}{\mathrm{S}}_2$, and hence we suggest that chemical deposition methods might be better than mechanical exfoliation methods for obtaining monolayer samples.

We demonstrate how exchange hardening can arise in a chemically disordered solid solution from a first-principles statistical mechanics approach. A general mixed-basis chemical and magnetic cluster expansion has been developed, and applied to the ${\mathrm{Mn}}_{1-x}{\mathrm{Fe}}_x{\mathrm{Ru}}_2\mathrm{Sn}$ Heusler alloy system; single-phase solid solutions between antiferromagnetic ${\mathrm{MnRu}}_2\mathrm{Sn}$ and ferromagnetic ${\mathrm{FeRu}}_2\mathrm{Sn}$ with disorder on the Mn/Fe sublattice that exhibit unexpected exchange hardening. Monte Carlo simulations applied to the cluster expansion are able to reproduce the experimentally measured magnetic transition temperatures and the bulk magnetization as a function of composition. The magnetic ordering around a site is shown to be dependent not only on bulk composition, but also on the identity of the site and the local composition around that site. The simulations predict that local antiferromagnetic orderings form inside a bulk ferromagnetic region at intermediate compositions that drives the exchange hardening. Furthermore, the antiferromagnetic regions disorder at a lower temperature than the ferromagnetic regions, providing an atomistic explanation for the experimentally observed decrease in exchange hardening with increasing temperature. These effects occur on a length scale too small to be resolved with previously used characterization techniques.

Neutron diffraction studies on epitaxially strained orthorhombic (010) oriented $\mathrm{TbMn}{\mathrm{O}}_3$ thin films verify a theoretical prediction of an unusual magnetic phase with coexisting incommensurate and a commensurate order. Magnetic field dependent measurements of the $\left(0q1\right)$ and $\left(01+q1\right)$ Bragg reflections confirm that the magnetic intensity corresponding to an incommensurate $q$ value has contributions from magnetic domains with both incommensurate and commensurate order. The ratio between the population of domains with commensurate and incommensurate order can be tuned by the magnetic field. In addition, the incommensurate order shows strong evidence of supporting the predicted $ab$ cycloidal spin structure.

The kink-pair activation enthalpy is a fundamental parameter in the theory of plasticity of body-centered cubic (bcc) metals. It controls the thermally activated motion of screw dislocation at low and intermediate temperatures. While direct atomistic calculations of kink pairs on screw dislocations have reached a high degree of accuracy, they can only be practically performed using semiempirical interatomic force fields, as electronic structure methods have not yet reached the level of efficiency needed to capture the system sizes required to model kink-pair structures. In this context, an alternative approach based on standard three-dimensional elastic models, which are efficient but lack atomic-level information, coupled to a substrate potential that represents the underlying lattice, has been widely applied over the past few years. This class of methods, known as ‘line-on-substrate’ (LOS) models, uses the substrate potential to calculate the lattice contribution to the kink-pair energies. In this work, we introduce the stress dependence of the substrate potential into LOS models to evaluate its impact on kink-pair energies. In addition, we include asymmetric dislocation core energies as an extra descriptor of the dislocation character. This asymmetry is also elevated to the continuum level by adding core energies to the general LOS formulation and used to explain potential energy differences known to exist between left and right kinks in bcc metals. More importantly, by matching the total LOS energies to previously calculated atomistic energies of kink-pair configurations, we issue a rule to establish the value of the so-called core width in nonsingular elasticity theories and reduce its arbitrariness as a mathematical construct.

Core-electron x-ray photoelectron spectroscopy is a powerful technique for studying the electronic structure and chemical composition of molecules, solids, and surfaces, but the interpretation of measured spectra and the assignment of peaks to atoms in specific chemical environments is often challenging. Here, we address this problem and demonstrate that accurate absolute core-electron binding energies can be obtained from the total energy difference of the ground state and a state with an explicit core hole when exchange and correlation effects are described by the strongly constrained and appropriately normed metageneralized gradient approximation and relativistic effects are included self-consistently even for light elements. We carry out calculations for molecules, solids, and surface species and find excellent agreement with available experimental measurements. For example, we find a mean absolute error of only 0.16 eV for a reference set of 103 molecular core-electron binding energies.

Hole-doped perovskite bismuthates such as ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{BiO}}_3$ and ${\mathrm{Sr}}_{1-x}{\mathrm{K}}_x{\mathrm{BiO}}_3$ are well-known bismuth-based oxide high-transition-temperature superconductors. Reported thin bismuthate films show relatively low quality, likely due to their large lattice mismatch with the substrate and a low sticking coefficient of Bi at high temperatures. Here, we report the successful epitaxial thin film growth of the parent compound strontium bismuthate ${\mathrm{SrBiO}}_3$ on SrO-terminated ${\mathrm{SrTiO}}_3$ (001) substrates by molecular beam epitaxy. Two different growth methods, high-temperature codeposition or recrystallization cycles of low-temperature deposition plus high-temperature annealing, are developed to improve the epitaxial growth. ${\mathrm{SrBiO}}_3$ has a pseudocubic lattice constant $\approx 4.25$ Å and an $\approx 8.8\%$ lattice mismatch on ${\mathrm{SrTiO}}_3$ substrate, leading to a large strain in the first few unit cells. Films thicker than 6 unit cells prepared by both methods are fully relaxed to bulk lattice constant and have similar quality. Compared to high-temperature codeposition, the recrystallization method can produce higher quality 1- to 6-unit cell films that are coherently or partially strained. Photoemission experiments reveal the bonding and antibonding states close to the Fermi level due to Bi and O hybridization, in good agreement with density functional theory calculations. This work provides general guidance to the synthesis of high-quality perovskite bismuthate films.

Small polarons (SPs) are known to exist in most important transition metal oxides; however, the nature of small polaron formation remains enigmatic, and a fundamental understanding of how SPs impact the intrinsic electronic structure and optical properties of these materials is largely lacking. In this work, we employ first-principles calculations to investigate SP formation in ${\mathrm{Co}}_{\text{3}}{\mathrm{O}}_{\text{4}}$, a highly promising material for a wide range of emerging energy applications, and we resolve the conflicting findings that have been reported on the electronic structure of the system. We confirm that the intrinsic band gap of ${\mathrm{Co}}_{\text{3}}{\mathrm{O}}_{\text{4}}$ is 1.6 eV, and we show that the formation of small hole polarons significantly influences the optical absorption spectra, leading to a 0.8 eV transition that is often misinterpreted as the band edge that defines the fundamental gap. In addition, we discuss how uniaxial strain can be utilized to probe the Jahn-Teller distortion of SP states and, in turn, effect their optical transitions. Beyond ${\mathrm{Co}}_{\text{3}}{\mathrm{O}}_{\text{4}}$, our study suggests a general roadmap for establishing a first-principles computational approach that can simultaneously achieve an accurate description of SP states, electronic band structure, and optical transitions of polaronic magnetic oxides.

Epitaxial SnTe (111) is grown by molecular-beam epitaxy on $\mathrm{B}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_3$ substrates. Structural evaluation indicates that SnTe deviates from cubic due to in-plane compressive strain, which induces significant changes in the electronic band structure. More specifically, a pair of gapless crossings between the two uppermost valence bands occurs in $k$ space along the out-of-plane ΓZ direction of the Brillouin zone, associated with a band inversion, thus defining topological three-dimensional Dirac nodes. Combined first-principles calculations and angle-resolved photoelectron spectroscopy reveal an overtilted Dirac cone indicating that the crossing is a topological type-III Dirac node at the borders between type-I and type-II Dirac nodes.