Ab Initio Band Structure Research Articles

Symmetry-enforced topological band crossings in orthorhombic crystals: Classification and materials discovery

We identify all symmetry-enforced band crossings in nonmagnetic orthorhombic crystals with and without spin-orbit coupling and discuss their topological properties. We find that orthorhombic crystals can host a large number of different band degeneracies, including movable Weyl and Dirac points with hourglass dispersions, fourfold double Weyl points, Weyl and Dirac nodal lines, almost movable nodal lines, nodal chains, and topological nodal planes. Interestingly, spin-orbit coupled materials in the space groups 18, 36, 44, 45, and 46 can have band pairs with only two Weyl points in the entire Brillouin zone. This results in a simpler connectivity of the Fermi arcs and more pronounced topological responses than in materials with four or more Weyl points. In addition, we show that the symmetries of the space groups 56, 61, and 62 enforce nontrivial weak $\mathbb{Z}_2$ topology in materials with strong spin-orbit coupling, leading to helical surface states. With these classification results in hand, we perform extensive database searches for orthorhombic materials crystallizing in the relevant space groups. We find that Sr$_2$Bi$_3$ and Ir$_2$Si have bands crossing the Fermi energy with a symmetry-enforced nontrivial $\mathbb{Z}_2$ invariant, CuIrB possesses nodal chains near the Fermi energy, Pd$_7$Se$_4$ and Ag$_2$Se exhibit fourfold double Weyl points, the latter one even in the absence of spin-orbit coupling, whereas the fourfold degeneracies in AuTlSb are made up from intersecting nodal lines. For each of these examples we compute the ab-initio band structures, discuss their topologies, and for some cases also calculate the surface states.

Time evolution of energies and populations in germanium perturbed by a near-infrared pulse on the atto-second scale

Implementing time-resolved spectroscopy is one of the challenging topics in solid-state physics: indeed, it can be a crucial step to unveil the early time dynamics of fundamental processes in systems such as semiconductors, metals, superconductors and topological materials. Then, it is essential to build theoretical tools in order to understand the experimental results and what actually happens in solid-state systems on a new and finer timescale: the atto-second one. Accordingly, we have developed a theoretical–numerical tool in order to study the time evolution of the electronic populations on the atto-second scale in materials perturbed by a laser pulse. After finding the ab-initio band structure of the material, we compute the maximally-localized Wannier functions and obtain the hopping terms. Then, we study the effect of the laser pulse using the Peierls substitution method and obtain the equation of motion for the electronic populations. Finally, we obtain a dynamical DOS of the system and the corresponding dynamical electronic populations. In this work, as a relevant case study, we report our results for germanium. We identify oscillations in the eigenenergies and in the populations which roughly follow either the field or its square, with some phase shifts with respect to the field.

Complete spin and valley polarization by total external reflection from potential barriers in bilayer graphene and monolayer transition metal dichalcogenides

It is shown that potential barriers in bilayer graphene (BLG) and monolayer transition metal dichalcogenides (TMDs) can split a valley unpolarized incident current into reflected and transmitted currents with opposite valley polarization. Valley asymmetric transmission inevitably occurs because of the low symmetry of the total Hamiltonian and when total external reflection occurs the transmission is 100% valley polarized in BLG and 100% spin and valley polarized in TMDs, except for exponentially small corrections. By adjusting the potential, 100% polarization can be obtained regardless of the crystallographic orientation of the barrier. A valley polarizer can be realized by arranging for a collimated beam of carriers to be incident on a barrier within the range of angles for total external reflection. The transmission coefficients of barriers with a relative rotation of $\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/3$ are related by symmetry. This allows two barriers to be used to demonstrate that the current is valley polarized. A soft-walled potential is used to model the barrier and the method used to find the transmission coefficients is explained. In the case of monolayer TMDs, a four-band $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ Hamiltonian is used and the $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ parameters are obtained by fitting to ab initio band structures.

Emergent electronic properties in Co-deposited superatomic clusters.

We report an intercluster compound based on co-deposition of the Au cluster [Au9(PPh3)8](NO3)3 and the fulleride KC60(THF). Electronic properties characteristic for a charge interaction between superatoms emerge within the solid state material [Au9(PPh3)8](NO3)3-x(C60)x, as confirmed by UV-VIS and Raman spectroscopy and I-V measurements. These emergent properties are related to the superatomic electronic states of the initial clusters. The material is characterized by Fourier-transform infrared spectroscopy, x-ray diffraction, Raman spectroscopy, and electrical measurements. Structural optimization and ab initio band structure calculations are performed with density functional theory to interpret the nature of the electronic states in the material; Bader charge calculations assigneffective oxidation states in support of the superatomic model of cluster interactions.

Understanding the ferromagnetic insulating state in Cr-doped VO2 : Density functional and tight binding calculations

Experimentally Cr doping in the rutile phase of VO$_2$ is found to stabilize a charge ordered ferromagnetic insulating state in the doping range of 10\% to 20\%. In this work, we investigated its origin at 12.5\% Cr doping using a combination of ab-initio electronic structure calculations as well as microscopic modeling. Our calculations are found to reproduce the ferromagnetic insulating state as well as a charge ordering at the V and Cr sites. The mapping of the ab-initio band structure onto a tight-binding Hamiltonian allows one to calculate the energy gain from different exchange pathways. This gain is quantified in this work for the first time and the role of charge ordering in stabilizing a ferromagnetic insulating state is understood.

Emergence of metamagnetic transition, re-entrant cluster glass and spin phonon coupling in Tb2CoMnO6

The double perovskite compound Tb2CoMnO6 has been investigated using x-ray absorption spectroscopy (XAS), Raman spectroscopy, magnetic measurements and ab initio band structure calculations. It is observed that both anti-ferromagnetic (AFM) and ferromagnetic (FM) phase coexist in this material. The presence of anti-site disorder (ASD) has been established from the analysis of neutron diffraction data. Moreover, a prominent metamagnetic transition is observed in the M(H) behavior that has been explained with the drastic reorientation of the pinned domain which are aligned antiparallel by the antiphase boundaries (APBs) at zero field. The ASD further gives rise to spin frustration at low temperature which leads to the re-entrant cluster glass ∼33 K. The coupling between phononic degree of freedom and spin in the system has also been demonstrated. It is observed that the theoretical calculation is consistent with that of the experimentally observed behavior.

Symmetry-enforced band crossings in tetragonal materials: Dirac and Weyl degeneracies on points, lines, and planes

We study the occurrence of symmetry-enforced topological band crossings in tetragonal crystals with strong spin-orbit coupling. By computing the momentum dependence of the symmetry eigenvalues and the global band topology in the entire Brillouin zone, we determine all symmetry-enforced band crossings in tetragonal space groups. In particular, we classify all Dirac and Weyl degeneracies on points, lines, and planes, and find a rich variety of topological degeneracies. This includes, among others, double Weyl points, fourfold-double Weyl points, fourfold-quadruple Weyl points, Weyl and Dirac nodal lines, as well as topological nodal planes. For the space groups with symmetry-enforced Weyl points, we determine the minimal number of Weyl points for a given band pair and, remarkably, find that materials in space groups 119 and 120 can have band pairs with only two Weyl points in the entire Brillouin zone. This simplifies the topological responses, which would be useful for device applications. Using the classification of symmetry-enforced band crossings, we perform an extensive database search for candidate materials with tetragonal space groups. Notably, we find that Ba$_5$In$_4$Bi$_5$ and NaSn$_5$ exhibit twofold and fourfold Weyl nodal lines, respectively, which cross the Fermi energy. Hf$_3$Sb and Cs$_2$Tl$_3$ have band pairs with few number of Weyl points near the Fermi energy. Furthermore, we show that Ba$_3$Sn$_2$ has Weyl points with an accordion dispersion and topological nodal planes, while AuBr and Tl$_4$PbSe$_3$ possess Dirac points with hourglass dispersions. For each of these candidate materials we present the ab-initio band structures and discuss possible experimental signatures of the nontrivial band topology.

Thermoelectric and magnetic properties of Ce3Cu3−xAuxSb4 compounds

We present the result of magnetic and thermoelectric investigations of the series of Ce3Cu3−xAuxSb4 compounds. The experimentally obtained data are discussed based on ab initio band structure calculations. It has been shown that structural disorder resulting from doping of Ce3Cu3Sb4 with Au induces a spin-glass-like behavior in the Ce3Cu3−xAuxSb4 series. All components x exhibit a negative temperature coefficient of the resistivity and metallic behavior of thermopower S(T) in the temperature region of T > 100 K. The maximal S value of 250 μV/K was measured for the pristine Ce3Au3Sb4 sample, while the highest figure of merit ZT = 0.06 was obtained for sample x = 1.5 at the highest measured temperature (T = 390 K).

Hidden bulk and surface effects in the spin polarization of the nodal-line semimetal ZrSiTe

In non-magnetic materials the combination of inversion symmetry breaking (ISB) and spin-orbit coupling (SOC) determines the spin polarization of the band structure. However, a local spin polarization can also arise in centrosymmetric crystals containing ISB subunits. This is namely the case for the nodal-line semimetal ZrSiTe where, by combining spin- and angle-resolved photoelectron spectroscopy with ab initio band structure calculations, we reveal a complex spin polarization. In the bulk, the valence and conduction bands exhibit opposite spin orientations in two spatially separated two-dimensional ZrTe sectors within the unit cell, yielding no net polarization. We also observe spin-polarized surface states that are well separated in energy and momentum from the bulk bands. A layer-by-layer analysis of the spin polarization allows us to unveil the complex evolution of the signal in the bulk states near the surface, thus bringing the intertwined nature of surface and bulk effects to the fore.

Current-Driven Domain Wall Dynamics in Ferrimagnetic Nickel-Doped Mn4N Films: Very Large Domain Wall Velocities and Reversal of Motion Direction across the Magnetic Compensation Point.

Spin-transfer torque (STT) and spin-orbit torque (SOT) are spintronic phenomena allowing magnetization manipulation using electrical currents. Beyond their fundamental interest, they allow developing new classes of magnetic memories and logic devices, in particular based on domain wall (DW) motion. In this work, we report the study of STT-driven DW motion in ferrimagnetic manganese nickel nitride (Mn4-xNixN) films, in which magnetization and angular momentum compensation can be obtained by the fine adjustment of the Ni content. Large domain wall velocities, approaching 3000 m/s, are measured for Ni compositions close to the angular momentum compensation point. The reversal of the DW motion direction, observed when the compensation composition is crossed, is related to the change of direction of the angular momentum with respect to that of the spin polarization. This is confirmed by the results of ab initio band structure calculations.

Machine learning method for tight-binding Hamiltonian parameterization from ab-initio band structure

The tight-binding (TB) method is an ideal candidate for determining electronic and transport properties for a large-scale system. It describes the system as real-space Hamiltonian matrices expressed on a manageable number of parameters, leading to substantially lower computational costs than the ab-initio methods. Since the whole system is defined by the parameterization scheme, the choice of the TB parameters decides the reliability of the TB calculations. The typical empirical TB method uses the TB parameters directly from the existing parameter sets, which hardly reproduces the desired electronic structures quantitatively without specific optimizations. It is thus not suitable for quantitative studies like the transport property calculations. The ab-initio TB method derives the TB parameters from the ab-initio results through the transformation of basis functions, which achieves much higher numerical accuracy. However, it assumes prior knowledge of the basis and may encompass truncation error. Here, a machine learning method for TB Hamiltonian parameterization is proposed, within which a neural network (NN) is introduced with its neurons acting as the TB matrix elements. This method can construct the empirical TB model that reproduces the given ab-initio energy bands with predefined accuracy, which provides a fast and convenient way for TB model construction and gives insights into machine learning applications in physical problems.

Origin of the magnetic and orbital ordering in α−Sr2CrO4

Motivated by recent experimental progress in transition metal oxides with the ${\mathrm{K}}_{2}\mathrm{Ni}{\mathrm{F}}_{4}$ structure, we investigate the magnetic and orbital ordering in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Sr}}_{2}\mathrm{Cr}{\mathrm{O}}_{4}$. Using first-principles calculations, first we derive a three-orbital Hubbard model, which reproduces the ab initio band structure near the Fermi level. The unique reverse splitting of ${t}_{2g}$ orbitals in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Sr}}_{2}\mathrm{Cr}{\mathrm{O}}_{4}$, with the $3{d}^{2}$ electronic configuration for the ${\mathrm{Cr}}^{4+}$ oxidation state, opens up the possibility of orbital ordering in this material. Using real-space Hartree-Fock for multiorbital systems, we constructed the ground-state phase diagram for the two-dimensional compound $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Sr}}_{2}\mathrm{Cr}{\mathrm{O}}_{4}$. We found stable ferromagnetic, antiferromagnetic, antiferro-orbital, and staggered orbital stripe ordering in robust regions of the phase diagram. Furthermore, using the density matrix renormalization group method for two-leg ladders with the realistic hopping parameters of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Sr}}_{2}\mathrm{Cr}{\mathrm{O}}_{4}$, we explore magnetic and orbital ordering for experimentally relevant interaction parameters. Again, we find a clear signature of antiferromagnetic spin ordering along with antiferro-orbital ordering at moderate to large Hubbard interaction strength. We also explore the orbital-resolved density of states with Lanczos, predicting insulating behavior for the compound $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Sr}}_{2}\mathrm{Cr}{\mathrm{O}}_{4}$, in agreement with experiments. Finally, an intuitive understanding of the results is provided based on a hierarchy between orbitals, with ${d}_{xy}$ driving the spin order, while electronic repulsion and the effective one dimensionality of the movement within the ${d}_{xz}$ and ${d}_{yz}$ orbitals driving the orbital order.

Theoretical Designing of Novel Donor Acceptor Type Copolymer Comprising of Thiophene

Using ab initio band structure results of three novel donor acceptor polymers (A)x PCDT, (B)x PMCT and (C)x PFTh as the input, the electronic structures and conduction properties of their periodic and aperiodic copolymer (AmBnCk)x have been investigated. The method involves using negative factor counting method based on Dean’s negative eigenvalue theorem. In this article, the quasi-one-dimensional Type II staggered copolymers comprising of thiophene units on the basis of the band alignments of the constituent homopolymers were studied. The trends in their electronic structures and conduction properties as a function of (i) block sizes (m, n, k) and (ii) arrangement of the blocks (periodic or aperiodic) in the various copolymer chains are discussed. These trends are important guidelines to the experimentalists for designing novel electrically conducting polymers with tailor made conduction properties.

Electronic band structure of semiconductor alloys: From ab initio to k[formula omitted]p via computational alchemy, on example of [formula omitted] alloy

First principles calculations are increasingly often used in device modelling. However, due to their complexity and high computational costs, simplified but reliable models are of great value. In this work, we present an original method of finding the 30-band k·p parameters on an example of Ge1-xSnx alloy. It allows to reproduce the electronic band structure in the full BZ and in the full composition range. The method uses the state-of-the-art supercell based ab initio calculations as the reference. A direct fitting of the k·p parameters from ab initio supercell band structures is difficult since the assignment of the k·p bands to correct eigenvalues of the reference band structures may be ambiguous. For this reason, the ab initio computational alchemy is used as an intermediate step. Owing to its properties, the supercell unfolded eigenvalues are approximated with continuous curves, which enables a straigthforward way to fit the 30-band k·p parameters. As an example of application, the optical gain in bulk Ge0.91Sn0.09 has been calculated. The advantage of using the 30-band over the often used 8-band k·p approach is clearly seen. The presented method can be applied to any mixed, isovalent and isostructural system, eg. III-V, or II-VI alloys.

Ab initio based description of the unusual increase of the electric field gradient with temperature at Ti sites in rutile TiO2

Combining a precise ab initio electron band structure calculation of the TiO2 rutile structure with the temperature evolution of the Ti mean-square displacements, we reproduce a puzzling temperature increase of the electric field gradient at Ti sites in TiO2, observed experimentally. Our method employs a procedure of averaging two quadrupole electron density components (L = 2) inside a sphere vibrating with the Ti nucleus at its center, where the key factor introducing the temperature dependence is the square root of the Debye-Waller factor. Although the Debye-Waller factor always reduces the corresponding Fourier component, in TiO2 due to the interplay between terms of opposite signs, it results in a net increase of the whole sum with temperature, leading to the growth of the electric field gradient. Quantitatively, we find that the increase of electric field gradient is only half of the experimental value, which we ascribe to anharmonic effects or a strong oxygen position influence. In addition, our method reproduces the unusual temperature dependence of the asymmetry parameter eta, which first decreases with temperature, goes to zero and then increases.

Magnetic Interactions in ZnMnO3: Active Role of Zn 3d10 Orbitals, in Comparison with MgMnO3.

The ilmenite-type MgMnO3 and ZnMnO3 with honeycomb Mn layers exhibit distinctive magnetic ground states. In experiments, MgMnO3 exhibits a Néel antiferromagnetic alignment, in which both nearest-neighbor (NN) J1 and next-nearest-neighbor (NNN) J2 exchange interactions are antiferromagnetic, while ZnMnO3 has zigzag antiferromagnetic ordering with NN ferromagnetic and NNN antiferromagnetic coupling. On the basis of ab initio band structure calculations, we explain the deviation of NN J1 exchange coupling from antiferromagnetic (MgMnO3) to ferromagnetic (ZnMnO3) as originating from the intensive hybridization between the occupied Zn 3d10 orbitals with those of the bridging O 2p states, strongly depending on the position of the orbitals. In addition, our results indicate that, in combination with the NN J1 coupling, the considerably large third-nearest-neighbor (TNN) J3 exchange interaction plays an important role in erecting the magnetic ground states, rather than the experimentally proposed NNN J2. Furthermore, our findings highlight the important role of not only the electronic configurations but also the positions of the nonmagnetic cations in determining the essence of the magnetic exchange interactions. Therefore, the hybridization effect of nonmagnetic cations should not be dismissed in an analysis of the magnetic properties of transition-metal oxides.

Optical conductivity and resistivity in a four-band model for ZrTe5 from ab initio calculations

ZrTe$_5$ is considered a potential candidate for either a Dirac semimetal or a topological insulator in close proximity to a topological phase transition. Recent optical conductivity results motivated a two-band model with a conical dispersion in 2D, in contrast to density functional theory calculations. Here, we reconcile the two by deriving a four-band model for ZrTe$_5$ using $\textbf{k} \cdot \textbf{p}$ theory, and fitting its parameters to the ab-initio band structure. The optical conductivity with an adjusted electronic structure matches the key features of experimental data. The chemical potential varies strongly with temperature, to the point that it may cross the gap entirely between zero and room temperature. The temperature-dependent resistivity displays a broad peak, and confirms theoretically the conclusions of recent experiments attributing the origin of the resistivity peak to the large shift of the chemical potential with temperature.

Electronic structure studies on single crystalline Nd2PdSi3, an exotic Nd-based intermetallic: evidence for Nd 4f hybridization

In the series R2PdSi3, Nd2PdSi3 is an anomalous compound in the sense that it exhibits ferromagnetic order unlike other members in this family. The magnetic ordering temperature is also unusually high compared to the expected value for a Nd-based system, assuming 4f localization. Here, we have studied the electronic structure of single crystalline Nd2PdSi3 employing high resolution photoemission spectroscopy and ab initio band structure calculations. Theoretical results obtained for the effective on-site Coulomb energy of 6 eV corroborate well with the experimental valence band spectra. While there is significant Pd 4d–Nd 4f hybridization, the states near the Fermi level are found to be dominated by hybridized Nd 4f–Si 3p states, which is possibly responsible for the ferromagnetism in Nd compound. Nd 3d core level spectrum exhibits multiple features manifesting strong final state effects due to electron correlation, charge transfer and collective excitations. These results serve as one of the rare demonstrations of hybridization of Nd 4f states with the conduction electrons possibly responsible for the exoticity of this compound.

Ab initio construction of symmetry-adapted k·p Hamiltonians for the electronic structure of semiconductors

While $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ Hamiltonians are frequently used for the description of electronic states in quantum nanostructures, a method is lacking to obtain them in their symmetrized form directly from ab initio band structure calculations of bulk material. We developed a method for obtaining the parameters and the symmetry-adapted form of the $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ Hamiltonian from the output of an ab initio band structure calculation. The method consists of (i) evaluation of momentum matrix elements between the wave functions obtained from band structure calculation; (ii) identification of the unitary transformation that transforms these wave functions to the symmetry-adapted basis; (iii) transformation of the $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ Hamiltonian to the symmetry-adapted basis. We illustrate the methodology by obtaining $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ Hamiltonians that describe the band structure of zinc-blende CdSe and then we use the Hamiltonians obtained to calculate the electronic states in CdSe quantum wells. Excellent agreement between density functional theory and $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ is obtained for the electronic structure, even for quite thin wells.

Influence of anisotropy, tilt and pairing of Weyl nodes: the Weyl semimetals TaAs, TaP, NbAs and NbP

By means of ab initio band structure methods and model Hamiltonians we investigate the electronic, spin and topological properties of four monopnictides crystallizing in bct structure. We show that the Weyl bands around a WP W1 or W2 possess a strong anisotropy and tilt of the accompanying Dirac cones. These effects are larger for W2 nodes than for W1 ones. The node tilts and positions in energy space significantly influence the DOS of single-particle Weyl excitations. The node anisotropies destroy the conventional picture of (anti)parallel spin and wave vector of a Weyl fermion. This also holds for the Berry curvature around a node, while the monopole charges are independent as integrated quantities. The pairing of the nodes strongly modifies the spin texture and the Berry curvature for wave vectors in between the two nodes. Spin components may change their orientation. Integrals over planes perpendicular to the connection line yield finite Zak phases and winding numbers for planes between the two nodes, thereby indicating the topological character.Graphical abstract