High-symmetry Points Research Articles

Structural, electronic and thermoelectric properties of monolayer TiSe2.

In this work the first-principles calculations of the structural, electronic and thermoelectric properties of monolayer TiSe2 are presented. The optimized lattice parameter of monolayer TiSe2 shows excellent agreement with the experimental value. The computed band structure and density of states calculations predict metallic nature of monolayer TiSe2 with overlapping of 0.44eV between the lowest conduction band and top valance band at high symmetry point M. The position of pseudogap formed by Ti-3d orbitals near the Fermi level confirms the mechanical stability of monolayer TiSe2. Due to the influence of positive strain (tensile strain), the Ti-Se bond length increases and the layer height decreases. The applied tensile strain changes the metallic nature of TiSe2 into a semiconductor with opening of bandgap. It has also been observed that the positions of conduction band minima and valance band maxima change with strain. The charge analysis shows that charge transfer from Ti to Se atom increases when tensile strain is applied, while an opposite trend is observed with compression. The computed thermoelectric coefficientsi.e. Seeback coefficient, power factor and figure of merit are in good agreement with the experimental data.The temperature dependence of these coefficientsis also reported. The density functional theory based calculations are reported employing the PBE-GGA ansatz using the plane wave-pseudopotential method embodied in the Quantum ESPRESSO package. The self-consistent field calculations are performed over a dense Monkhorst-Pack net of 12 × 12 × 1k-points. The energy convergence criteria for the self-consistent field calculation were set to 10-6 Ry/atom with a cutoff energy of 90 Ry. The thermoelectric properties are computed by combining the band structure calculations with the Boltzmann transport equation using Boltztrap2 peckage.

Nodal phases in non-Hermitian wallpaper crystals

Symmetry and non-Hermiticity play pivotal roles in photonic lattices. While symmetries, such as parity-time (PT) symmetry, have attracted ample attention, more intricate crystalline symmetries have been neglected in comparison. Here, we investigate the impact of the 17 wallpaper space groups of two-dimensional crystals on non-Hermitian band structures. We show that the non-trivial space group representations enforce degeneracies at high symmetry points and dictate their dispersion away from these points. In combination with either T or PT, the symmorphic p4 mm symmetry and the non-symmorphic p2mg, p2gg, and p4gm symmetries protect exceptional chains intersecting at the pertinent high symmetry points.

Influcence of external electric field and B/N doping on the band gap of stanene

Stanene possesses excellent properties, including an extremely high charge carrier density, massless Dirac fermions, and high thermal conductivity. Moreover, it exhibits band inversion phenomena, being made a candidate for a topological insulator. Topological insulators can generate dissipationless electric currents under certain conditions, showing great application potentials. However, the presence of a Dirac cone in the band structure of stanene at the high-symmetry point <i>K</i> in the Brillouin zone, resulting in a zero band gap, significantly limits its applications in the semiconductor field. This study adopts the method of doping B/N elements in stanene and applying an electric field perpendicular to the stanene to open the band gap at the <i>K</i> point. The effects of doping and the intensity of the applied electric field on the structural and electronic properties of stanene are investigated. The results reveal that both doping B elements and applying a vertical electric field can open the band gap at the <i>K</i> point while preserving the topological properties of stanene. Additionally, there is a positive correlation between the applied vertical electric field intensity and the band gap at the <i>K</i> point. Simultaneously doping B elements and applying a vertical electric field can increase the band gap at the <i>K</i> point, reaching 0.092 eV when the electric field intensity is 0.5 V/Å. After doping N elements, stanene is transformed into an indirect band gap semiconductor with a band gap of 0.183 eV. Applying a vertical electric field cannot change the structure of N-doped stanene, and the intensity of the applied vertical electric field is negatively correlated with the band gap at the <i>K</i> point. When the electric field intensity is 0.5 V/Å, the band gap at the <i>K</i> point decreases to 0.153 eV.

Prediction of a two-dimensional high Curie temperature Weyl nodal line kagome semimetal.

Kagome lattices may have numerous exotic physical properties, such as stable ferromagnetism and topological states. Herein, combining the particle swarm structure search method with first-principles calculations, we identify a two-dimensional (2D) kagome Mo2Se3 crystal structure with space group P6/mmm. The results show that 2D kagome Mo2Se3 is a 100% spin-polarized topological nodal line semimetal and exhibits excellent ambient stability. The band crossing points form two nodal loops around the high-symmetry points Γ and K. On the other hand, Mo2Se3 shows intrinsic ferromagnetism with a large magnetic moment of 3.05 μB per Mo atom and magnetic anisotropy energy (MAE) of 4.78 meV. Monte Carlo simulations estimate that Mo2Se3 possesses a high Curie temperature of about 673 K. In addition, its ferromagnetic ground state can be well preserved under external strain, and the MAE can be improved by increasing the strain. More importantly, the position of each nodal line can be adjusted to the Fermi level through hole doping. This multifunctional 2D magnetic material that combines spin and topology has great potential in the field of nanoscale spintronic devices.

First-principles study of electronic, optical, and thermoelectric properties of KMCuS3 (M = Th and Sm) quaternary chalcogenides.

Copper-based quaternary chalcogenides are considered as intriguing material systems in terms of their remarkable optoelectronic and thermoelectric properties. Here we investigated the light interaction and electronic transport properties of novel KMCuS3 (M = Th, Sm) materials. Advanced computations based on density functional theory were used for these calculations. The PBE-GGA scheme predicted band gaps for the KSmCuS3 and KmThCuS3 were 0.61, and 2.03 eV, respectively. While the TB-mBJ computed band gap values for KSmCuS3 and KThCuS3 were 0.91, and 2.39 eV, respectively. A direct band gap nature for both materials was confirmed by identifying the CBM and VBM at the same high symmetry gamma point. The Cu-d, Sm-f, Th-f, and S-p orbitals unified to form the valence band region at the BZ high symmetry point, while the Th-d and Sm-d orbitals formed the conduction band region. Furthermore, linear optical properties such as complex dielectric function components, along with other important optical parameters were computed and explained for possible employment in optoelectronic devices. The considerable thermoelectric characteristics were also predicted, and the incredible outcomes were described, implying that these compounds have potential for thermoelectric applications.

Mechanism of Negative Thermal Expansion in Monoclinic Cu2P2O7 from First Principles.

Negative thermal expansion (NTE) materials generally have high-symmetry space groups, large average atomic volumes, and corner-sharing octahedral and tetrahedral coordination structures. By contrast, monoclinic α-Cu2P2O7, which has a small average atomic volume and edge-sharing structure, has been reported to exhibit NTE, the detailed mechanism of which is unclear. In this study, we investigate the A2B2O7 polymorphs and analyze the NTE behavior of α-Cu2P2O7 using first-principles lattice-dynamics calculations. From the polymorphism investigation in 20 A2B2O7 compounds using 6 representative crystal structures, small A and B cationic radii are found to stabilize the α-Cu2P2O7-type structure. We then analyze the NTE behavior of α-Cu2P2O7 using quasi-harmonic approximation. Our calculated thermal expansion coefficients and anisotropic atomic displacement parameters were in good agreement with those of the experimental reports at low temperatures. From the mode-Grüneisen parameter distribution plotted over the entire first-Brillouin zone, we found that the phonon contributing most significantly to NTE emerges not into the special points but between them. In this phonon mode, the O connecting two PO4 tetrahedra rotates, and the Cu and O vibrate perpendicular to the bottom of the CuO5 pyramidal unit, which folds the ac lattice plane. This vibration behavior can explain the experimentally reported anisotropic NTE behavior of α-Cu2P2O7. Our results demonstrate that the most negative mode-Grüneisen parameter contributing to NTE behavior is not always located on high-symmetry special points, indicating the importance of lattice vibration analyses for the entire first-Brillouin zone.

Intrinsically large effective mass and multi-valley band characteristics of n-type Bi2[sbnd]Bi2Te3 superlattice-like films

Thermoelectric superlattices are expected to decouple the strong correlation between various thermoelectric parameters, and are an important strategy for excellent thermoelectric performances. The superlattices of (Bi2)m(Bi2Te3)n homologous series are well-known for low lattice thermal conductivity and intriguing topological surface states. However, the impacts of electronic structure on the thermoelectric performance were still not well-understood in (Bi2)m(Bi2Te3)n. To cope with this issue, Bi2Bi2Te3 superlattice-like films with adjustable Bi2/(Bi2+Bi2Te3) molar ratio (R) were successfully fabricated by the molecular beam epitaxy technique. Angle-resolved photoemission spectroscopy measurements combined with theoretical calculations revealed the conduction band evolution from single-valley to multi-valley as R ≥ 0.30, leading to intrinsically high carrier effective mass and improved thermoelectric power factor. Also, the superlattice film (R = 0.46) with the structure close to Bi4Te3 possesses the topological surface state feature around the high symmetry point. As a result of the high effective mass of 3.9 m0 and very high electron density of 2.31 × 1021 cm−3, the film with R = 0.46 acquired the highest power factor of 1.49 mW·m−1·K−2 at 420 K, outperforming that of other (Bi2)m(Bi2Te3)n superlattices. This work lays an essential foundation on understanding the electronic structure and further improving thermoelectric performances of (Bi2)m(Bi2Te3)n homologous series.

Genuine Dirac Half-Metals in Two-Dimensions.

When spin-orbit coupling (SOC) is absent, all proposed half-metals with twofold degenerate nodal points at the K (or K') point in 2D materials are classified as "Dirac half-metals" owing to the way graphene is utilized in the earliest studies. Actually, each band crossing point at the K or K' point is described by a 2D Weyl Hamiltonian with definite chirality; hence, it should be a Weyl point. To the best of its knowledge, there have not yet been any reports of a genuine (i.e., fourfold degenerate) 2D Dirac point half-metal. In this work, using first-principles calculations, it proposes for the first time that the 2D d0 -type ferromagnet Mg4 N4 is a genuine 2D Dirac half-metal candidate with a fourfold degenerate Dirac point at the S high-symmetry point, intrinsic magnetism, a high Curie temperature, 100% spin polarization, topology robust under the SOC and uniaxial and biaxial strains, and spin-polarized edge states. This work can serve as a starting point for future predictions of intrinsically magnetic materials with genuine 2D Dirac points, which will aid the frontier of topo-spintronics research in 2Dsystems.

The effect of non-metals (O, F) dopant on the electronic structure, Dirac cone, and optical characteristics of graphene sheets applicable for gas sensing

In order to gain a systematic comprehension of the impacts of low-level defects in graphene, ab-initio calculations were performed on monolayer graphene sheets to examine how oxygen and fluorine substitutional impurities affect their energetic stability, electronic and optical characteristics. The optimal configurations, structural stability, electronic band structures, spatial charge density, and optical spectra of graphene single-layer materials doped with oxygen and fluorine atoms are investigated. The fluorine-doped graphene, therefore, showed a lower formation energy than its oxygen-doped counterpart. Additionally, F-doped graphene shows a higher charge density around the fluorine atom than O-doped graphene. Based on band structure analysis, the lower conduction bands of graphene sheets shift below the Fermi state (EF) when two O or F impurities are substituted into it. With two O/F impurity atoms doped into graphene, the conduction states are farther displaced below the EF, resulting in n-type behavior. Consequently, altering graphene structure via an O/F-substituting scheme results from the disruption of the Dirac cone near EF, which has become flat along the high symmetry point (K-point) in the Brillouin zone. Furthermore, the substitution of graphene sheets via O or F impurities exhibit markedly modified optical spectra and refractive indices at low photon energies. As a result, with one or two O/F impurity elements inserted into graphene sheets, the reflectivity and optical conductivity spectra differ at the lowest electromagnetic radiation ranges. Additionally, the electron energy loss functions as well as X-ray absorption spectra of clean and doped graphene monolayers revealed spectral variations at a moderate energy span. These investigations surmise that novel chemical modifications to graphene sheets doped with light non-metallic elements (O/F) may offer the opportunity to tailor their optical characteristics in the infrared spectrum, which may be beneficial in sensor and electrocatalyst uses.

2D ZrS2: An experimentally realizable monolayer with multiple linear Weyl point phonons

In recent years, there has been a great deal of interest in predicting Weyl physics in phonons due to the unique properties of topological phonons. In this study, we postulate that ZrS2 is a candidate material with multiple Linear Weyl point (LWP) phonons at the K (or K') high-symmetry point in its phonon curves. The existence of an opposite quantized Berry phase at the K and K' valleys determines the topologically nontrivial nature of these LWPs. Fascinatingly, the nonzero quantized Berry phase at the two valleys produced phononic edge states on the (100) surface. On the one hand, our research emphasizes for the first time the topological phononic properties of 2D ZrS2. On the other hand, note that 2D ZrS2 is an experimentally feasible material, making it a concrete material platform for investigating and confirming the predicted topological physics.

Angle-resolved photoemission study of NbGeSb with non-symmorphic symmetry

We investigate the electronic structure of NbGeSb with non-symmorphic symmetry. We employ angle-resolved photoemission spectroscopy (ARPES) to observe and identify the bulk and surface states over the Brillouin zone. By utilizing high-energy photons, we identify the bulk Fermi surface and bulk nodal line along the direction X–R, while the Fermi surface of the surface state is observed by using low-energy photons. We observe the splitting of surface bands away from the high-symmetry point X¯ . The density functional theory calculations on bulk and 1 to 5-layer slab models, as well as spin textures of NbGeSb, verify that the band splitting could be attributed to the Rashba-like spin–orbit coupling caused by space-inversion-symmetry breaking at the surface. These splitted surface bands cross with each other, forming two-dimensional Weyl-like crossings that are protected by mirror symmetry. Our findings provide insights into the two-dimensional topological and symmetry-protected band inversion of surface states.

Strain engineering of magnetic exchange and topological magnons in chromium trihalides from first-principles

Recent experiments evidence the direct observation of spin waves in chromium trihalides and the presence of a gap at the Dirac points of the magnon dispersion in bulk CrI3. However, the topological origin of this feature remains unclear and its emergence at the 2D limit has not yet been proven experimentally. Herein, we perform a fully self-consistent ab initio analysis to deeply understand magnetic exchange of chromium trihalides in the 2D limit. We compute the orbital dependent magnetic interactions and Curie temperatures under applied biaxial strain. Our results confirm the existence of a gap around the K high-symmetry point in the linear magnon dispersion of CrI3, which originates as a direct consequence of intralayer Dzyaloshinskii–Moriya (DM) interaction. In addition, our orbital resolved analysis reveals the microscopic mechanisms that can be exploited using strain engineering to increase the strength of the DM interaction and thus control the topological gap width in CrI3. This paves the way to the further development of this family of materials as building-blocks for topological magnonics at the limit of miniaturization.

Investigation on prospective thermoelectrics — cubic Nd-doped LMO and rhombohedral Cu4Mn2Te4 materials — first principles approach

Structural, electronic, magnetic and optical properties of Cu4Mn2Te4 have been reported earlier by the authors, and here, the transport properties of the same are discussed along with the band structure investigation of the neodymium-doped cubic material LMO (LiMn2O4), namely LiMn[Formula: see text]Nd[Formula: see text]O4 compound, under spin polarized schemes through the First Principles calculations. The Full Potential-Linearized Augumented Plane Wave Method (FP-LAPW) method is adopted to investigate the electronic structures based on the framework of Density Functional Theory (DFT). Exchange potentials are treated using the Generalized Gradient Approximations (GGA). Cohesive energy calculations reveal that the ferromagnetic phase of LiMn[Formula: see text]Nd[Formula: see text]O4 and the antiferromagnetic phase of Cu4Mn2Te4 exhibits a stable phase. Of these, FM-LiMn[Formula: see text]Nd[Formula: see text]O4 shows a semi-metallic-like behavior in spin-up channel and metallic behavior in spin-down channel whereas antiferromagnetic Cu4Mn2Te4 exhibits a band gap in both spin-up and spin-down channels. Dirac points are identified at −0.0625[Formula: see text]eV in the band structure plot of FM-LiMn[Formula: see text]Nd[Formula: see text]O4 at its high symmetry points [Formula: see text] and W which is an indication of high electron mobility at ambient condition. The presence of flat and dispersive bands around the Fermi energy level is an indication of high thermopower, and it is present in both the compounds FM-LiMn[Formula: see text]Nd[Formula: see text]O4 and AFM-Cu4Mn2Te4. From the present computations, at 300[Formula: see text]K, a power factor range of ([Formula: see text] scaled by relaxation time in [Formula: see text]W/msK2) [Formula: see text] and [Formula: see text] is obtained for ferromagnetic LiMn[Formula: see text]Nd[Formula: see text]O4 compounds at up and down spins, respectively. A typical power factor ([Formula: see text]Wm[Formula: see text]s[Formula: see text]K[Formula: see text]) of [Formula: see text] and [Formula: see text] is obtained for antiferromagnetic Cu4Mn2Te4 at 325[Formula: see text]K required for good thermoelectric performance.

Phase-change in topological chiral phononic crystal for directional coupling switch

Recently, acoustic valley Hall topological insulators have become a cutting-edge area of acoustic physics, where the topological phase transition in phononic crystals shows the presence of band inversion through the Dirac point in the momentum space. We developed a 2D hexagonal lattice chiral phononic crystal using reconfigurable construction by extending one side of the original rectangular rods. When the variation of the side length was from left to right, the topological phase transition is triggered by reopening the Dirac degeneracies beyond high-symmetry points in the first Brillouin zone. We numerically showed valley edge state’s propagation through the interface bent toward distinct chiral topological phononic crystals. Moreover, we assembled 2 × 2 cross-waveguides with a defect cavity based on double heterostructure interfaces. The simulated results verify that the phase change is achieved by the directional coupling switching. This research possibly paves the way for exploiting valley edge states to design the complex acoustic waveguide.

Local symmetry groups for arbitrary wavevectors

We present an algorithm for the determination of the local symmetry group for arbitrary k-points in 3D Brillouin zones. First, we test our implementation against tabulated results available for standard high-symmetry points (given by universal fractional coordinates). Then, to showcase the general applicability of our methodology, we produce the irreducible representations for the ‘non-universal high-symmetry’ points, first reported by Setyawan and Curtarolo (2010 Comput. Mater. Sci. 49 299). The present method can be regarded as a first step for the determination of elementary band decompositions and symmetry-enforced constraints in crystalline topological materials.

Effects of vacancy defects on vibrational properties of Ni–Al

The phonon spectra of Ni, Al, and NiAl, as well as their electronic characteristics, are investigated using density functional theory and density functional perturbation theory. Our research on phonon dispersion has concentrated on every high symmetry point of NiAl, both with and without defects. The phonon gap of NiAl is measured to be 1.78 THz between the lowest value of the optical branch and the top bound of the acoustic branch. The NiAl supercell with a center Al vacancy was built to investigate the effects of defects on its vibrational characteristics. The phonon gap of a NiAl crystal at the center of the Brillouin zone with no defect is calculated to be 1.06 THz. This value of the phonon gap is affected by the Al vacancy defect and decreases by 7.67%. The development of phonon spectrum is investigated using electronic structure and properties. The majority of free electrons accumulated at the Fermi level contribute to promoting the vibration. The importance of a heavier element in a compound has also been explored in terms of gap tuning. Reduced thermal conductivity by narrowing the gap between optical and acoustic modes raises the figure of merit (zT) value, which improves the thermoelectric energy conversion efficiency.

Monolayer TiC—A high-performance Dirac anode with ultralow diffusion barriers and high energy densities for Li-ion and Na-ion batteries

Two-dimensional Dirac materials have stimulated substantial research interest as binder-free anodes in metal-ion batteries, owing to their ultrahigh electronic conductivity, large specific area, and higher energy density. Here, using first-principles density functional theory calculations, we have investigated the feasibility of monolayer TiC as a potential anode material for Li/Na-ion batteries. The results indicate that monolayer TiC exhibits excellent dynamical and thermal stability. The electronic structure of monolayer TiC shows semimetallic characteristics with a Dirac cone at the M high symmetry point and the formation of Ti or C vacancies transforms the Dirac cone into a nodal loop or a nodal surface, respectively. Thus, monolayer TiC possesses superior electrical conductivity, which can be further enhanced by the formation of Ti or C vacancies in the material. Furthermore, the calculated adsorption energy values of -0.85 and -0.46 eV for Li-ion and Na-ion, respectively, indicate that Li/Na atom adsorption over monolayer TiC is a favorable process. The density of states plots show that after the adsorption of a single Li/Na atom, monolayer TiC maintains its metallic state, which is advantageous for the diffusion of stored electrons. Most remarkably, monolayer TiC exhibits energy densities of 2684 and 2015 mWh/g for Li and Na, respectively, which are significantly higher than commercial graphite and most other 2D anode materials. The fully loaded TiC anode exhibits excellent cycle stability with volume expansions as low as 0.13 and 0.11%, for Li and Na, respectively. Furthermore, an ultrafast diffusivity with low energy barriers of 0.02 and 0.10 eV is found in monolayer TiC for Li-ion and Na-ion, respectively, which suggests that it has an excellent charge/discharge capability. These exceptional properties make monolayer TiC an excellent candidate as an anode material for Li-ion and Na-ion batteries. Finally, SiC(111) has been proposed as a candidate substrate for monolayer TiC due to its minimal lattice mismatch.

Bandgaps of long-period polytypes of IV, IV-IV, and III-V semiconductors estimated with an Ising-type additivity model.

We apply an Ising-type model to estimate the bandgaps of the polytypes of group IV elements (C, Si, and Ge) and binary compounds of groups: IV-IV (SiC, GeC, and GeSi), and III-V (nitride, phosphide, and arsenide of B, Al, and Ga). The models use reference bandgaps of the simplest polytypes comprising 2-6 bilayers calculated with the hybrid density functional approximation, HSE06. We report four models capable of estimating bandgaps of nine polytypes containing 7 and 8 bilayers with an average error of ≲0.05eV. We apply the best model with an error of <0.04 eV to predict the bandgaps of 497 polytypes with up to 15 bilayers in the unit cell, providing a comprehensive view of the variation in the electronic structure with the degree of hexagonality of the crystal structure. Within our enumeration, we identify four rhombohedral polytypes of SiC-9R, 12R, 15R(1), and 15R(2)-and perform detailed stability and band structure analysis. Of these, 15R(1) that has not been experimentally characterized has the widest bandgap (>3.4 eV); phonon analysis and cohesive energy reveal 15R(1)-SiC to be metastable. Additionally, we model the energies of valence and conduction bands of the rhombohedral SiC phases at the high-symmetry points of the Brillouin zone and predict band structure characteristics around the Fermi level. The models presented in this study may aid in identifying polytypic phases suitable for various applications, such as the design of wide-gap materials, that are relevant to high-voltage applications. In particular, the method holds promise for forecasting electronic properties of long-period and ultra-long-period polytypes for which accurate first-principles modeling is computationally challenging.

Twisted-bilayer FeSe and the Fe-based superlattices

We derive BM-like continuum models for the bands of superlattice heterostructures formed out of Fe-chalcogenide monolayers: (I) a single monolayer experiencing an external periodic potential, and (II) twisted bilayers with long-range moire tunneling. A symmetry derivation for the inter-layer moire tunnelling is provided for both the \GammaΓ and MM high-symmetry points. In this paper, we focus on moire bands formed from hole-band maxima centered on \GammaΓ, and show the possibility of moire bands with C=0C=0 or ±1±1 topological quantum numbers without breaking time-reversal symmetry. In the C=0C=0 region for \theta→0θ→0 (and similarly in the limit of large superlattice period for I), the system becomes a square lattice of 2D harmonic oscillators. We fit our model to FeSe and argue that it is a viable platform for the simulation of the square Hubbard model with tunable interaction strength.

Research on bending vibration characteristics of phononic crystal plates based on Mindlin’s piezoelectric plate theory

Based on Mindlin’s theory and the plane wave expansion method, the formulas are proposed for the governing equations and dispersion relations of bending waves in piezoelectric phononic crystal plates. The shear correction factors can be obtained through transcendental equations based on forced vibrations of the plate. The plates are made of inclusions of different shapes and lattice types, finding that the inclusion shape dramatically affects the mid-to-high frequency band gaps. Piezoelectric materials exhibit distinct eigenfrequencies at the high-symmetry point Γ at low frequencies. Thickness affects the band gap width differently than in two-dimensional models, and cuts influence band gap width significantly.