High-symmetry Points Research Articles

Lattice dynamics in the double-helix antiferromagnet FeP

We present a comprehensive investigation of lattice dynamics in the double-helix antiferromagnet FeP by means of high-resolution time-of-flight neutron spectroscopy and ab-initio calculations. Phonons can hybridize with the magnetic excitations in noncollinear magnets to significantly influence their properties. We observed a rich spectrum of phonon excitations, which extends up to $\sim$50 meV. We performed detailed analysis of the observed and calculated spectra for all high-symmetry points and high-symmetry directions of the Brillouin zone. We show that the DFT calculations quantitatively capture the essential features of the observed phonons, including both dispersions and scattering intensities. By making use of the detailed intensity comparison between the theory and the data, we were able to identify displacement vectors for the majority of the observed modes. The overall excellent agreement between the DFT predictions and the experimental results breaks down for the lowest mode at the $Y$-point, whose energy is lower than calculated by $\sim$13%. The present study provides vital information on the lattice dynamics in FeP and demonstrates applicability of the DFT to novel pressure-induced phenomena in related materials, such as MnP and CrAs.

Peierls versus Holstein models for describing electron-phonon coupling in perovskites

We use the Momentum Average approximation together with perturbative approaches, in the appropriate limits, to study the single polaron physics on a perovskite lattice inspired by BaBiO3. We investigate electron-phonon coupling of the Peierls type whereby the motion of ions modulates the values of the hopping integrals between sites, and show that it cannot be mapped onto the simpler one-band Holstein model in the whole parameter space. This is because the dispersion of the Peierls polaron has sharp transitions where the ground-state momentum jumps between high-symmetry points in the Brillouin zone, whereas the Holstein polaron always has the same ground-state momentum. These results imply that careful consideration is required to choose the appropriate model for carrier-lattice coupling in such complex lattices.

Edge mode manipulation through commensurate multifrequency driving

We explore the impact of commensurate multifrequency driving protocols on the stability of topological edge modes in topological 1D systems of spinless fermions. Using Floquet theory, we show that all the topological phase transitions can be mapped to their single-frequency counterparts in terms of effective driving parameters. This drastic simplification can be explained by considering the gap closures in the quasienergy dispersion. These gap closures are pinned to high-symmetry points, where all the effective Floquet Hamiltonians collapse to the same form. While for all protocols all topological phase transitions coincide, the gap size and the number of edge modes in the quasienergy spectra vary considerably depending on the chosen driving pattern. This gives rise to a full range of edge states with different degrees of localization, from highly localized to completely delocalized. Switching between different driving protocols then suggests a dynamical control of the localization and stability of topological edge modes, with possible applications in quantum computation. We illustrate our findings on three paradigmatic fermionic systems -- namely the Kitaev chain, the Su-Schrieffer-Heeger model, and the Creutz ladder, and demonstrate how to control the localization length of the corresponding edge states.

Band structure and absorption spectra of NH4XI3 (X = Pb, Mg) based hybrid Perovskite for UV ray protector and electrochromic materials applications

Modeling Perovskite materials and tuning their properties by monovalent or divalent cations substitution produce several choice Perovskite compounds, studied extensively to improve the power conversion efficiency, reduce toxicity, and enhance stability. We modeled NH4PbI3 and NH4MgI3 from the parent compound CH3NH3PbI3, by replacing the monovalent CH3NH3+ with NH4+ and the divalent Pb atom with Mg. In this study, the electronic band structure, as well as the electronic bandgaps, were calculated using the Perdew-Burke-Enzenhoff (PBE) and Perdew-Burke-Enzenhoff for solid (PBEsol) exchange-correlation functionals of the Density-functional Theory (DFT) and GW quasiparticle method of the Many-Body Perturbation Theory (MBPT). Similarly, we used Time-Dependent Density Functional Perturbation Theory (TDDFPT) and the solution of the Bethe-Salpeter equation (BSE) of the Many-Body Perturbation Theory to determine the real and imaginary dielectric tensors with and without spin-orbit coupling (SOC). Direct bandgaps at R high symmetry point were reported for NH4PbI3, while NH4MgI3 showed indirect bandgaps at Γ→R high symmetry points with lower bandgaps compared to NH4PbI3. The projected density of state around the Fermi level reveals that the iodine (I) p orbital is most responsible for the valence band in both NH4PbI3 and NH4MgI3, while the Lead (Pb) p orbital and the Magnesium (Mg) s orbitals, show the most prominent contribution to the Conduction bands. Similar Optical spectra were achieved with BSE-SOC, TDDFPT, and TDDFPT-SOC for NH4PbI3 without the absorption onsets, while NH4PbI3 predicts higher values of absorbance and absorption coefficient compared to NH4MgI3 which predict lower reflectivity and higher transmittance. Both compounds show maximum absorption coefficient in the order of 105 in the ultraviolet region like CH3NH3PbI3 and silicon. Therefore, we suggest that NH4PbI3 will be useful as solar cell absorber and UV ray protector, while NH4MgI3 would have more applications in the production of electrochromic materials.

Topological phase transition and conductance in topological crystalline insulator with honeycomb lattice

Topological crystalline insulators (TCI) represent a new state of quantum matter which is topologically protected by crystalline symmetry. We construct a minimal tight-binding model for 2D thin TCI films with C 3 -symmetry honeycomb lattice. Four Dirac cones are observed at the high-symmetry points K, K′ and Γ points, considering the basic term spin-orbit interaction. By introducing the mass term, Dirac gaps can be opened to trigger the topological phase transition. We then numerically investigate the band structure, conductance and local density of state of the TCI films consisting of zigzag and armchair nanoribbons. The results indicate that there is a one-to-one correspondence between gapless topological edge states and nonzero mirror-Chern number. Finally, we apply an external electric field perpendicular to the TCI films, which breaks mirror symmetry. As a result, the nontrivial edge modes are destroyed, and the conductance is turned off by the electric field.

Metalated Graphyne-Based Networks as Two-Dimensional Materials: Crystallization, Topological Defects, Delocalized Electronic States, and Site-Specific Doping.

Graphyne-based two-dimensional (2D) carbon allotropes feature extraordinary physical properties; however, their synthesis as crystalline single-layered materials has remained challenging. We report on the fabrication of large-area organometallic Ag-bis-acetylide networks and their structural and electronic properties on Ag(111) using low-temperature scanning tunneling microscopy combined with density functional theory (DFT) calculations. The metalated graphyne-based networks are robust at room temperature and assembled in a bottom-up approach via surface-assisted dehalogenative homocoupling of terminal alkynyl bromides. Large-area networks of several hundred nanometers with topological defects at domain boundaries are obtained due to the Ag-acetylide bonds' reversible nature. The thermodynamically controlled growth mechanism is explained through the direct observation of intermediates, which differ on Ag(111) and Au(111). Scanning tunneling spectroscopy resolved unoccupied states delocalized across the network. The energy of these states can be shifted locally by the attachment of a different number of Br atoms within the network. DFT revealed that free-standing metal-bis-acetylide networks are semimetals with a linear band dispersion around several high-symmetry points, which suggest the presence of Weyl points. These results demonstrate that the organometallic Ag-bis-acetylide networks feature the typical 2D material properties, which make them of great interest for fundamental studies and electronic materials in devices.

Three-orbital continuous model for 1H -type metallic transition metal dichalcogenide monolayers

We theoretically investigate the electronic states in monolayer $\mathrm{Nb}{\mathrm{Se}}_{2}$ and develop continuous models to describe these states in Fermi pockets. In $1H$-type metallic transition metal dichalcogenides (TMDCs), the Fermi surface consists of three pockets enclosing the $\mathrm{\ensuremath{\Gamma}},$ $K,$ and ${K}^{\ensuremath{'}}$ points. We reveal that the conventional effective model used for semiconducting TMDCs is not sufficient to describe the electronic states in metallic TMDCs and thus introduce a scheme to construct the effective model from the first-principle results. All models can be represented by a $3\ifmmode\times\else\texttimes\fi{}3$ Hamiltonian and well reproduce electronic states around the Fermi energy in terms of the orbital composition and the phase factor. We also show that the $p$ orbitals in chalcogen atoms, which are ignored in the conventional $2\ifmmode\times\else\texttimes\fi{}2$ model, play a crucial role in metallic TMDCs. Although the aim of these models is to reproduce electronic states, they can well describe states near the high-symmetry points and the profile of Berry curvature in wave-vector space. The continuous model can be a handleable tool to describe the electronic states and to analyze the transport phenomena in metallic TMDCs.

Radial Spin Texture of the Weyl Fermions in Chiral Tellurium.

Trigonal tellurium, a small-gap semiconductor with pronounced magneto-electric and magneto-optical responses, is among the simplest realizations of a chiral crystal. We have studied by spin- and angle-resolved photoelectron spectroscopy its unconventional electronic structure and unique spin texture. We identify Kramers-Weyl, composite, and accordionlike Weyl fermions, so far only predicted by theory, and show that the spin polarization is parallel to the wave vector along the lines in k space connecting high-symmetry points. Our results clarify the symmetries that enforce such spin texture in a chiral crystal, thus bringing new insight in the formation of a spin vectorial field more complex than the previously proposed hedgehog configuration. Our findings thus pave the way to a classification scheme for these exotic spin textures and their search in chiral crystals.

Scaling behavior in a multicritical one-dimensional topological insulator

A class of Aubry-Andr\'e-Harper models of spin-orbit coupled electrons exhibits a topological phase diagram where two regions belonging to the same phase are split up by a multicritical point. The critical lines which meet at this point each defines a topological quantum phase transition with a second-order nonanalyticity of the ground-state energy, accompanied by a linear closing of the spectral gap with respect to the control parameter; except at the multicritical point which supports fourth-order transitions with parabolic gap-closing. Here both types of criticality are characterized through a scaling analysis of the curvature function defined from the topological invariant of the model. We extract the critical exponents of the diverging curvature function at the non-high symmetry points in the Brillouin zone where the gap closes, and also apply a renormalization group approach to the flattening curvature function at high symmetry points. We also derive a basis-independent correlation function between Wannier states to characterize the transition. Intriguingly, we find that the critical exponents and scaling law defined with respect to the spectral gap remain the same regardless of the order of the transition.

Topological electronic properties of silicon

The central role that materials play in human history is exemplified by the three-age division of prehistory into the stone, bronze, and iron ages. References to our present time as the information age or silicon age epitomizes the important role that this semiconducting material came to play in the development of computers and devices that permeate our daily lives. Here we show that the electronic states in silicon have nontrivial topological structures that are captured by a network of Berry flux lines that link at points of high symmetry in the Brillouin zone. This complex network has ice-nodal points where fluxes satisfy ice rules, making silicon a "nodal-chain insulator". Fixing the longitudinal momentum parallel to such flux lines yields a two-dimensional Dirac Hamiltonian for the transverse degrees of freedom. This complex Berry-flux network implies a topologically stable two-fold degeneracy along the X-W direction in all of silicon bands, a fact that is supported by crystal symmetry arguments as well as direct inspection of the vast literature on silicon band structures. Similarly to nodal-chain semimetals, we find drumhead-like states in the regions that are delimited by the projections of the bulk Berry flux network on the surface Brillouin zone.

Glide-symmetric topological crystalline insulator phase in a nonprimitive lattice

We study the topological crystalline insulator phase protected by the glide symmetry, which is characterized by the Z2 topological number. In the present paper, we derive a formula for the Z2 topological invariant protected by glide symmetry in a nonprimitive lattice, from that in a primitive lattice. We establish a formula for the glide-Z2 invariant for the space group No. 9 with glide symmetry in the base-centered lattice, by folding the Brillouin zone into that of the primitive lattice where the formula for the glide-Z2 invariant is known. The formula is written in terms of integrals of the Berry curvatures and Berry phases in the k-space. We also derive a formula of the glide-Z2 invariantwhen the inversion symmetry is added, and the space group becomes No. 15. This reduces the formula into the Fu-Kane-like formula, expressed in terms of the irreducible representations at high-symmetry points in $k$ space. We also construct these topological invariants by the layer-construction approach, and the results completely agree with those from the k-space approach.

Viscous Maxwell-Chern-Simons theory for topological electromagnetic phases of matter

We present the fundamental model of a topological electromagnetic phase of matter: viscous Maxwell-Chern-Simons theory. Our model applies to a quantum Hall fluids with viscosity. We solve both continuum and lattice regularized systems to demonstrate that this is the minimal (exactly solvable) gauge theory with a nontrivial photonic Chern number ($C\neq 0$) for electromagnetic waves coupled to a quantum Hall fluid. The interplay of symmetry and topology is also captured by the spin-1 representations of a photonic skyrmion at high-symmetry points in the Brillouin zone. To rigorously analyze the topological physics, we introduce the viscous Maxwell-Chern-Simons Lagrangian and derive the equations of motion, as well as the boundary conditions, from the principle of least action. We discover topologically-protected chiral (unidirectional) edge states which minimize the surface variation and correspond to massless photonic excitations costing an infinitesimal amount of energy. Physically, our predicted electromagnetic phases are connected to a dynamical photonic mass in the integer quantum Hall fluid. This arises from viscous (nonlocal) Hall conductivity and we identify the nonlocal Chern-Simons coupling with the Hall viscosity. The electromagnetic phase is topologically nontrivial $C\neq 0$ when the Hall viscosity inhibits the total bulk Hall response. Our work bridges the gap between electromagnetic and condensed matter topological physics while also demonstrating the central role of spin-1 quantization in nontrivial photonic phases.

First principle calculation of mechanical stability, opto-electronic and thermo-electric properties of TaIrGe1-xSnx(0 ≤ x ≤ 1) Half-Heusler alloy

In this study, the structural, elastic, opto-electronic and thermo-electric properties of TaIrGe1-xSnx (x = 0, 0.25, 0.50, 0.75 and 1) Half-Heusler alloy are predicted. The full potential-linearized augmented plane wave (FP-LAPW) method is used within density functional theory (DFT). The structural properties such as the equilibrium lattice parameters, bulk modulus and its pressure derivative are investigated using the PBEsol-GGA approximation, as well as elastic constants. Elastic constants obey the mechanical condition stability. The energy band structure of TaIrGe1-xSnx (x = 0, 0.25, 0.50, 0.75 and 1) alloy is computed along the high symmetry points and results show the indirect nature of the band gap, with smaller difference of energy from direct band gap nature. Thermoelectric properties of half-Heusler compounds TaIrGe1-xSnx (x = 0, 0.25, 0.50, 0.75 and 1) has been computed using semi-classical Boltzmann transport theory, TaIrGe0.5Sn0.5 has a higher value of Figure of merit with low thermal conductivity as compared to other concentrations. Our results show that TaIrGe1-xSnx (x = 0, 0.25, 0.50, 0.75 and 1) alloy can be applied as an important opto-electronics and thermoelectric material in the future.

GW study of pressure-induced topological insulator transition in group-IV tellurides

We calculate the electronic structure of the narrow gap semiconductors PbTe, SnTe and GeTe in the cubic phase using density functional theory (DFT) and the $G_0W_0$ method. Within DFT, we show that the band ordering obtained with a conventional semilocal exchange-correlation approximation is correct for SnTe and GeTe but wrong for PbTe. The correct band ordering at the high-symmetry point L is recovered adding $G_0W_0$ quasiparticle corrections. However, one-shot $G_0W_0$ produces artifacts in the band structure due to the wrong orbital character of the DFT single-particle states at the band edges close to L. We show that in order to correct these artifacts it is enough to consider the off-diagonal elements of the $G_0W_0$ self-energy corresponding to these states. We also investigate the pressure dependence of the band gap for these materials and the possibility of a transition from a trivial to a non-trivial topology of the band structure. For PbTe, we predict the band crossover and topological transition to occur at around 4.8 GPa. For GeTe, we estimate the topological transition to occur at 1.9 GPa in the constrained cubic phase, a pressure lower than the one of the structural phase transition from rombohedral to cubic. SnTe is a crystalline topological insulator at ambient pressure, and the transition into a trivial topology would take place under a volume expansion of approximately $10\%$.

Exploring the structural stability order and electronic properties of transition metal M@Ge12 (M = Co, Pd, Tc, and Zr) doped germanium cage clusters–A density functional simulation

In the present report, the structural stability order and electronic properties of the transition metal M@Ge12 (M = Co, Pd, Tc, and Zr) doped germanium cage has been carried out at B3LYP/LANL2DZ ECP level by using spin polarized density functional theory. Initially, we selected five lowest energy structure of neutral TM doped Ge12 cluster with high symmetry point like D6h-symmetric hexagonal prism (HP), the D6d-symmetric hexagonal anti-prism (HAP), D2d-symmetric bi-capped pentagonal prism (BPP), perfect icosahedrons (Ih) and Fullerene type structures. Further, we discussed the electronic origin of stability as well as electronic properties by calculating binding energy, HOMO-LUMO gap, charge transfer mechanism and density of states. We indentified that the Pd, Tc, and Zr encapsulated Ge12 cage with hexagonal prism [HP] structures are minimum energy structures while Co@Ge12 cage prefer HAP structure. The magnitudes of binding energy of the clusters indicate that the doping of 4d transition metal gives most stable structure rather than 3d transition metal Co atom. The large HOMO-LUMO gap and natural bond orbital analysis explain the stability of these clusters using closed shell electronic configuration and the contribution of π and σ bond. Charge transfer mechanism shows that the Tc, Pd and Zr atoms play role as an electron donor in the system whereas Co inclined to accept the electrons. The importances of “d” orbital in localized electrons near the Fermi level are also explained through partial density of states.

Corner states and topological transitions in two-dimensional higher-order topological sonic crystals with inversion symmetry

Macroscopic two-dimensional sonic crystals with inversion symmetry are studied to reveal higher-order topological physics in classical wave systems. By tuning a single geometry parameter, the band topology of the bulk and the edges can be controlled simultaneously. The bulk band gap forms an acoustic analog of topological crystalline insulators with edge states which are gapped due to symmetry reduction on the edges. In the presence of mirror symmetry, the band topology of the edge states can be characterized by the Zak phase, illustrating the band topology in a hierarchy of dimensions, which is at the heart of higher-order topology. Moreover, the edge band gap can be closed without closing the bulk band gap, revealing an independent topological transition on the edges. The rich topological transitions in both bulk and edges can be well-described by the symmetry eigenvalues at the high-symmetry points in the bulk and surface Brillouin zones. We further analyze the higher-order topology in the shrunken sonic crystals where slightly different physics but richer corner and edge phenomena are revealed. In these systems, the rich, multidimensional topological transitions can be exploited for topological transfer among zero-, one- and two- dimensional acoustic modes by controlling the geometry.

Electronic and optical properties of graphene/molybdenite bilayer composite

Since its discovery, graphene has been the object of study for several and manifold applications, ranging from photocatalysis to mechanics and electronics of materials. However, the use of pure graphene in certain opto- and microelectronic applications is sometimes limited because of its zero band gap. Among the different methods to widen the band gap, in the present work the attention is focused on the so-called van der Waals composites (or heterostructures, or heterojunctions), namely the stacking of two monolayers of different materials that are held together by weak van der Waals interactions. An interesting composite is the graphene/molybdenite (MoS2) heterostructure, where the second material is a bidimensional semiconductor characterized by strong in-plane covalent bonds and weak out-of-plane interactions, which means that it is possible to exfoliate MoS2 into monolayers of atomic thickness. Also, from the crystallographic point of view, both graphene and the monolayer of molybdenite (MoS2-1H) have a 2D hexagonal lattice and their stacking could be structurally favourable. In this work, the electronic band structure and density of states, complex dielectric function and optical properties of the stacked van der Waals bilayer heterojunction graphene/MoS2-1H were calculated and compared to both the single monolayers of graphene and molybdenite, to understand how the interaction between the two materials may alter the above cited properties. The analysis of the band structure in this van der Waals composite clearly showed a small direct band gap related to the transition π→π∗ (ca. 2.5 meV) in correspondence of the high symmetry point K. The heterojunction showed also, as expected, some important variations in the complex dielectric function and related properties in the visible-light spectral region. The results obtained in the present work could be of use for future development and applications of this kind and similar 2D composite materials with tailored electronic and optical properties.

Peculiar symmetry-protected electronic dispersions in two-dimensional materials

Symmetry indicates that low energy spectra of materials could be richer than well-known Dirac, semi-Dirac, or quadratic, hosting some unusual quasiparticles. Performing the systematic study of exact forms of low energy effective Hamiltonians and dispersions in high-symmetry points with fourfold degeneracy of bands, we found new, previously unreported dispersion, which we named poppy flower (PF) after its shape. This massless fermion exists in non-magnetic two-dimensional (2D) crystals with spin–orbit coupling (SOC), which are invariant under one of the proposed ten noncentrosymmetric layer groups. We suggest real three-dimensional (3D) layered materials suitable for exfoliation, having layers that belong to these symmetry groups as candidates for realization of PF fermions. In 2D systems without spin–orbit interaction, fortune teller (FT)-like fermions were theoretically predicted, and afterward experimentally verified in the electronic structure of surface layer of silicon. Herein, we show that such fermions can also be hosted in 2D crystals with SOC, invariant under additional two noncentrosymmetric layer groups. This prediction is confirmed by density functional based calculation: layered BiIO4, which has been synthesized already as a 3D crystal, exfoliates to stable monolayer with symmetry pb21a, and FT fermion is observed in the band structure. Analytically calculated density of states (DOS) of the PF shows semimetallic characteristic, in contrast to metallic nature of FT having non-zero DOS at the bands contact energy. We indicate possibilities for symmetry breaking patterns which correspond to the robustness of the proposed dispersions as well as to the transition from Dirac centrosymmetric semimetal to PF.

First‐principles study of f‐orbital‐dependent band topology of topological rare earth hexaborides

AbstractThe rare earth hexaboride (RE)B6 series of compounds (RE = Ce, Pr, Nd, Pm, Sm, Eu, Gd) was investigated using the first‐principles approach for exploring new topological insulators. The calculated structural, electronic, and magnetic properties of the materials are discussed in detail. To account for better f‐electron correlation, the Hubbard correction was also tested to correct the Kondo states. The lattice appeared contracted for materials from CeB6 to GdB6, and charge is transferred from RE to boron. The inspection of band structure points to spd hybridization between RE‐5d and B‐2s, 2p states at Fermi level. The application of spin‐orbit coupling revealed the conversion in the parity, and an odd number of Dirac cones is found at Γ and X points without Kondo mechanism. PrB6, GdB6, and PmB6 revealed a dispersive conic region near the Fermi level at high symmetry points, which enclosed Kramer's degenerate points with surface states of opposite parity. These materials prove to be a strong topological Kondo insulator with an SmB6‐like cubic structure without involvement of f‐orbitals in the formation of a Dirac cone. The Hubbard U parameter determined from atomic calculation of RE f‐orbital, apart from the few cases when f‐states remain close to the Fermi level, revealed that the band structures are semimetallic in most cases.

Neurocomputing approach to predict 2D ferromagnetic lattices by spin dynamics

An artificial neural networks modeling, based on spin dynamics, has been proposed to predict the 2D ferromagnetic crystals. The purpose is to establish an artificial neural network model (ANNM), which is able to predict the ordered magnetic surfaces. In crystal surfaces, Wood’s notation is used to describe different configurations. From the magnons dispersion curves and group velocity data of 2D spins crystallographic waveguide, we deduce the data used as an up input–output set to feed the ANNM. The input data are being given by the magnons modes over high symmetry points, or, by the group velocity of the magnon modes. However, the basis vectors of matrix notation and the rotation angle that aligns the unit cell of the reconstructed surface are giving the output data. The proposed neurocomputing model was capable of predicting the 2D crystals for the possible arrangements that the surface might take. In addition, the magnon excitations data were a useful approach for building a neural model which was able to predict and classify the magnetic surfaces of the crystals.