Optimization of ab-initio based tight-binding models

Graphene, with impressive electronic properties, have high potential in the microelectronic field. However, graphene itself is a zero bandgap material which is not suitable for digital logic gates and its application. Thus, much focus is on graphene nanoribbons (GNRs) that are narrow strips of graphene. During GNRs fabrication process, the occurrence of defects that ultimately change electronic properties of graphene is difficult to avoid. The modelling of GNRs with defects is crucial to study the non-idealities effects. In this work, nearest-neighbor tight-binding (TB) model for GNRs is presented with three main simplifying assumptions. They are utilization of basis function, Hamiltonian operator discretization and plane wave approximation. Two major edges of GNRs, armchair-edged GNRs (AGNRs) and zigzag-edged GNRs (ZGNRs) are explored. With single vacancy (SV) defects, the components within the Hamiltonian operator are transformed due to the disappearance of tight-binding energies around the missing carbon atoms in GNRs. The size of the lattices namely width and length are varied and studied. Non-equilibrium Green.s function (NEGF) formalism is employed to obtain the electronics structure namely band structure and density of states (DOS) and all simulation is implemented in MATLAB. The band structure and DOS plot are then compared between pristine and defected GNRs under varying length and width of GNRs. It is revealed that there are clear distinctions between band structure, numerical DOS and Green\'s function DOS of pristine and defective GNRs.

It is known that while group VII 4$d$ Tc and 5$d$ Re have hexagonally close-packed (hcp) ground states, 3$d$ Mn adopts a complex $\ensuremath{\chi}$-phase ground state, exhibiting complex noncollinear magnetic ordering. Density functional theory (DFT) calculations have shown that without magnetism, the $\ensuremath{\chi}$ phase is still the ground state of Mn implying that magnetism and the resultant atomic-size difference between large- and small-moment atoms are not the critical factors, as is commonly believed, in driving the anomalous stability of the $\ensuremath{\chi}$ phase over hcp. Using a canonical tight-binding (TB) model, it is found that for a more than half-filled $d$ band, while harder potentials stabilize close-packed hcp, a softer potential stabilizes the more open $\ensuremath{\chi}$ phase. By analogy with the structural trend from open to close-packed phases down the group IV elements, the anomalous stability of the $\ensuremath{\chi}$ phase in Mn is shown to be due to 3$d$ valent Mn lacking $d$ states in the core which leads to an effectively softer atomic repulsion between the atoms than in 4$d$ Tc and 5$d$ Re. Subsequently, an analytic bond-order potential (BOP) is developed to investigate the structural and magnetic properties of elemental Mn at 0 K. It is derived within BOP theory directly from a new short-ranged orthogonal $d$-valent TB model of Mn, the parameters of which are fitted to reproduce the DFT binding energy curves of the four experimentally observed phases of Mn, namely, $\ensuremath{\alpha}$, $\ensuremath{\beta}$, $\ensuremath{\gamma}$, $\ensuremath{\delta}$, and $\ensuremath{\epsilon}$-Mn. Not only does the BOP reproduce qualitatively the DFT binding energy curves of the five different structure types, it also predicts the complex collinear antiferromagnetic (AFM) ordering in $\ensuremath{\alpha}$-Mn, the ferrimagnetic ordering in $\ensuremath{\beta}$-Mn, and the AFM ordering in $\ensuremath{\gamma}$-, $\ensuremath{\delta}$-, and $\ensuremath{\epsilon}$-Mn that are found by DFT. A BOP expansion including 14 moments is sufficiently converged to reproduce most of the properties of the TB model with the exception of the elastic shear constants, which require further moments. The current TB model, however, predicts values of the shear moduli and the vacancy formation energies that are approximately a factor of 2 too small, so that a future more realistic model for MD simulations will require these properties to be included from the outset in the fitting database.

We study the different ways of introducing light-matter interaction in first-principle tight-binding (TB) models. The standard way of describing optical properties is the velocity gauge, defined by linear coupling to the vector potential. In finite systems a transformation to represent the electromagnetic radiation by the electric field instead is possible, albeit subtleties arise in periodic systems. The resulting dipole gauge is a multi-orbital generalization of Peierl's substitution. In this work, we investigate accuracy of both pathways, with particular emphasis on gauge invariance, for TB models constructed from maximally localized Wannier functions. Focusing on paradigmatic two-dimensional materials, we construct first-principle models and calculate the response to electromagnetic fields in linear response and for strong excitations. Benchmarks against fully converged first-principle calculations allow for ascertaining the accuracy of the TB models. We find that the dipole gauge provides a more accurate description than the velocity gauge in all cases. The main deficiency of the velocity gauge is an imperfect cancellation of paramagnetic and diamagnetic current. Formulating a corresponding sum rule however provides a way to explicitly enforce this cancellation. This procedure corrects the TB models in the velocity gauge, yielding excellent agreement with dipole gauge and thus gauge invariance.

We present a simplified tight-binding (TB) model to describe the low-energy physics of monolayer 1T’ transition metal dichalcogenides (TMDCs). The TB model is constructed by combining symmetry analysis and first-principle calculations. Our TB model accurately reproduces the electronic structures near the Fermi energy and provides a better representation of energy band inversion. By considering spin–orbit coupling (SOC), our TB model successfully reproduces the opening of the bandgap, characterizes nontrivial topology, and predicts corresponding helical edge states. Additionally, using this TB model, we observe that quantized electronic conductance remains robust under significant disorder intensity. However, the robustness of the edge states can be suppressed by the Zeeman fields and SOC strength in the scattering zone. Furthermore, moderate concentrations of vacancy disorder destroy the topological protection and eliminate quantized conductance. Our TB model serves as a starting point for a comprehensive understanding of the properties of these materials and can guide future research on superconductivity, strain, and correlation effects.

Single-atom alloys (SAAs) are an increasingly popular platform for heterogeneous catalysis because of their distinct electronic structures and ability to break catalytic linear scaling relationships. This popularity has led to a proliferation of computational studies probing SAA reactivity at the density functional theory (DFT) level. However, some phenomena such as photo- and electrocatalysis require use of electronic structure methods beyond DFT; such studies are both rare and fundamentally challenging. Density functional embedding theory (DFET)/embedded correlated wavefunction (ECW) studies of reactions on metal surfaces have been shown to provide a reliable way to correct for DFT-related errors. DFET/ECW studies of chemistry involving SAAs, however, could require active spaces beyond the capabilities of traditional multireference methods when transition-metal dopants give rise to many degenerate states. To overcome this limitation, we combined our DFET/ECW methodology with the density matrix renormalization group (DMRG) complete active space self-consistent field (DMRGSCF) and DMRG N-electron valence state second-order perturbation theory (DMRG-NEVPT2) methods in the PySCF code. Using embedded DMRGSCF and embedded DMRG-NEVPT2, we analyze CO adsorption on Ni-, Rh-, Pd-, and Pt-doped Ag(100) with different active spaces. We show that the active spaces approachable with conventional multireference methods lead to overbinding of CO due to an inability to treat all of the dopant d-orbitals on equal footing. Larger active spaces, which are easily treated by both DMRGSCF and DMRG-NEVPT2, yield much more reasonable adsorption free energies. Our findings suggest that future multireference calculations of these systems should similarly employ active spaces containing all of the dopant d-orbitals along with sp-band orbitals of the host metal near the Fermi level. Emb-DMRG-NEVPT2 is a method that can be broadly applied to study catalytic reactions on metal surfaces when large active spaces are required.

Density Functional Theory Investigations of Metal/Oxide Interfaces and Transition Metal Catalysts

Moir\'e patterns made of two-dimensional (2D) materials represent highly tunable electronic Hamiltonians, allowing a wide range of quantum phases to emerge in a single material. Current modeling techniques for moir\'e electrons require significant technical work specific to each material, impeding large-scale searches for useful moir\'e materials. In order to address this difficulty, we have developed a material-agnostic machine learning approach and test it here on prototypical one-dimensional (1D) moir\'e tight-binding models. We utilize the stacking dependence of the local density of states (SD-LDOS) to convert information about electronic band structure into physically relevant images. We then train a neural network that successfully predicts moir\'e electronic structure from the easily computed SD-LDOS of aligned bilayers. This network can satisfactorily predict moir\'e electronic structures, even for materials that are not included in its training data.

van Hove singularities and tight-binding model in high-temperature superconductor H3Se

PySCF-NAO: An efficient and flexible implementation of linear response time-dependent density functional theory with numerical atomic orbitals

GaSb quantum dots (QDs) in a GaAs matrix have attracted much attention for the potential ability to extend the accessible wavelength of QD emitters towards a wavelength of > 1.3 μm owing to their unique electronic and optical properties caused by their staggered (type-II) band alignment. North et al. calculated the electronic structure of self-assembled GaSb/GaAs dots by using the simple one-band model (effective mass model). Therefore it is interesting to carry out the detailed calculations using a more accurate method, in particular in the view of the new experiments. The aim of this work is to study the electronic properties of GaSb/GaAs self-assembled quantum dots (SAD) by using the sp 3 s * empirical tight-binding method. The influence of strain on the electronic structure is determined by minimizing the elastic energy within the Valence Force Field Approach and the piezoelectric potential is calculated by solving the corresponding 3D Poisson equation. Single-particle bound-state energies are computed as a function of the dot sizes. Finally we have found that the theoretical PL spectra are in a good agreement with the experiment and k.p method. empirical models are widely implemented to study a large quantum dots. There are three empirical models, the k.p approximation (9), the pseudopotential model (10) and the tight-binding model (11), (12). The k.p approximation treats a quantum dot as a confined bulk and continuum system, while the pseudopotential and tight-binding models treat the system with the atomistic description. The distinction between the two atomistic models is the degree of atomic detail included in the model. Within the tight-binding model, the atomistic detail is limited to a small basis set, while in the pseudopotential model the feature of wave functions is described with a large basis set. Therefore the tight-binding model is computationally less costly than the pseudopotential model. The tight-binding model is a good candidate for the study of relatively big and complicated systems. At the moment, the theoretical calculations of the type-II quantum dots have not been extensively investigated and there are only few papers that we can mention here. North and co-authors (13) investigated the electronic structure of type-II GaSb/GaAs quantum dots by using the multiband effective-mass calculation. K. Gradkowski and et al. (2) reported the results of the room temperature photoreflectance (PR) and photoluminescence (PL) measurements of molecular beam epitaxy (MBE) grown GaAsSb/GaAs quantum dot structure: one with a capping quantum well and one without it. PL technique is employed to probe the ground-state transition energies. Using the experimental data, they calculated a band structure of these dots by using the 8-band k.p approach. The theoretical analysis accounts well in both GaAsSb/GaAs quantum dot with a capping quantum well and one without it. In this paper, we report the tight-binding calculations of the type-II GaSb/GaAs quantum dots. The strain distribution of the quantum dot is calculated by using the Valence Force Field method. The piezoelectricity is also obtained by solving the 3D Poisson's equation. Then we numerically calculate the electronic structure of the quantum dot as a function of the dot sizes. Finally we compare our calculated results with the experiment and another numerical analysis.

Theory-Guided Machine Learning Finds Geometric Structure-Property Relationships for Chemisorption on Subsurface Alloys

We analyze the origin of spin-orbit coupling (SOC) in fluorinated graphene using Density Functional Theory (DFT) and a tight-binding model for the relevant orbitals. As it turns out, the dominant source of SOC is the atomic spin-orbit of fluorine adatoms and not the impurity induced SOC based on the distortion of the graphene plane as in hydrogenated graphene. More interestingly, our DFT calculations show that SOC is strongly affected by both the type and concentrations of the graphene's carriers, being enhanced by electron doping and reduced by hole doping. This effect is due to the charge transfer to the fluorine adatom and the consequent change in the fluorine-carbon bonding. Our simple tight-binding model, that includes the SOC of the $2p$ orbitals of F and effective parameters based on maximally localized Wannier functions, is able to account for the effect. The strong enhancement of the SOC induced by graphene doping opens the possibility to tune the spin relaxation in this material.

The twofold coordinated heavier group-VI elements tellurium and selenium with the trigonal crystal structure have unshared electron pairs (lone pairs) which control the interplay of the intra- and inter-chain interactions and their sensitivity on pressure and temperature. We have developed tight-binding (TB) parameters for the helical structures of tellurium and selenium using the Naval Research Laboratory Tight-Binding (NRL-TB) method. The TB parameters were derived by fitting to the band structures and total energies of density functional theory (DFT) calculations. We have applied the TB parameters to study the phase stabilities of different structures under hydrostatic pressure. We have predicted (without fitting) the volume dependence of the rhombohedral and diamond structures, the bcc to rhombohedral and rhombohedral to simple cubic phase transitions and the elastic constants of the trigonal structures, all in agreement with ab initio and experimental results. While the results for the unrelaxed vacancy formation energies and surface energies are in good agreement with the DFT values, we find large discrepancies for the relaxed values indicating that the present set of TB parameters cannot accurately capture the inter-chain interactions.

Electronic structures and magnetism of Zr-, Th-, and U-based metal-organic frameworks (MOFs) by density functional theory

The observation of ultrafast and coherent control of spins in magnetic materials at room temperature [1-2] has prompted the experimental and theoretical efforts to understand the underlying mechanisms driving such magnetic phenomena. In order to understand the driving mechanisms, in this non-equilibrium regime, it is necessary to disentangle the relevant interactions (exchange, spin-lattice, electron-phonon, coulomb etc.).Stoichiometric B2 ordered epitaxial (001) FeRh undergoes a first order magnetic phase transition from antiferromagnetic (AFM) to ferromagnetic (FM) at ≈ 380K. In the AFM phase of FeRh, only Fe has net magnetic moment, whereas in the FM phase both Fe and Rh carry net moments. The phase transition is also accompanied by a ≈ 1% isotropic lattice expansion in the bulk BCC structure, and changes in electronic structure, see [3-5] and refs. therein. Since magnetic and structural dynamics can occur at different timescales, it makes FeRh an ideal candidate for disentangling relevant interaction mechanisms at different timescales. The phase transition has been extensively studied theoretically and experimentally [6-10], in thermal equilibrium (static heating) and at ultrafast time scales (fs- optical excitation), but a precise knowledge of the roles of the electronic, phononic and spin sub-systems remains elusive.We have studied the laser-driven AFM to FM phase transition in FeRh with X-ray absorption spectroscopy (tr-XAS) around the Fe L3 edge. The experiments were performed at the SCS Instrument of the European XFEL. We also performed the density functional theory (DFT) calculations to simulate the XAS spectra at different time delays including magnetic, lattice and temperature changes. Temperature modelling was done using two temperature model (2TM).In this contribution, we will discuss the changes in the electronic band structure of FeRh in the femto- and picosecond timescales, derived from the X-ray absorption spectroscopy measurements at the Fe L3 absorption and compare them with the density functional theory simulations. **