Multi-orbital Tight-binding Model Research Articles

Edge states of hydrogen terminated monolayer materials: silicene, germanene and stanene ribbons

We investigate the energy dispersion of the edge states in zigzag silicene, germanene and stanene nanoribbons with and without hydrogen termination based on a multi-orbital tight-binding model. Since the low buckled structures are crucial for these materials, both the π and σ orbitals have a strong influence on the edge states, different from the case for graphene nanoribbons. The obtained dispersion of helical edge states is nonlinear, similar to that obtained by first-principles calculations. On the other hand, the dispersion derived from the single-orbital tight-binding model is always linear. Therefore, we find that the non-linearity comes from the multi-orbital effects, and accurate results cannot be obtained by the single-orbital model but can be obtained by the multi-orbital tight-binding model. We show that the multi-orbital model is essential for correctly understanding the dispersion of the edge states in tetragen nanoribbons with a low buckled geometry.

Disorder effect on the anisotropic resistivity of phosphorene determined by a tight-binding model

In this work we develop a compact multi-orbital tight-binding model for phosphorene that accurately describes states near the main band gap. The model parameters are adjusted using as reference the band structure obtained by a density-functional theory calculation with the hybrid HSE06 functional. We use the optimized tight-binding model to study the effects of disorder on the anisotropic transport properties of phosphorene. In particular, we evaluate how the longitudinal resistivity depends on the lattice orientation for two typical disorder models: dilute scatterers with high potential fluctuation amplitudes, mimicking screened charges in the substrate, and dense scatterers with lower amplitudes, simulating weakly bounded adsorbates. We show that the intrinsic anisotropy associated to the band structure of this material, although sensitive to the type and intensity of the disorder, is robust.

Resonant inelastic X-ray scattering spectra at the Ir L-edge in Na2IrO3

We analyze resonant X-ray scattering (RIXS) spectra in Na2IrO3 on the basis of the itinerant electron picture. Employing a multi-orbital tight-binding model on a honeycomb lattice, we find that the zigzag magnetic order is the most stable with sizable energy gap in the one-electron band within the Hartree–Fock approximation. We derive the RIXS spectra, which are connected to the generalized density–density correlation function. We calculate the spectra as a function of excitation energy ω, within the random phase approximation. The spectra consist of the peaks with ω<20meV, and of the peaks with 0.4<ω<0.8eV. The former peaks are composed of four bound states in the density–density correlation function, and may be identified as the magnetic excitations, while the latter peaks are composed of 16 bound states below the energy continuum of individual electron–hole pair excitations, and may be identified as the excitonic excitations. The calculated spectra agree qualitatively with the recent RIXS experiment.

Spin relaxation in a hole-doped transition-metal dichalcogenide monolayer and bilayer with crystal defects

We study the electronic spin relaxation effect in the hole-doped monolayer and bilayer transition-metal dichalcogenides in the presence of the crystal defects. We consider realistic models of the lattice vacancy and actually estimate the spin relaxation rate using the multi-orbital tight-binding model. In the monolayer, the spin-relaxation time is found to be extremely long compared to the momentum relaxation time, and this is attributed to the fact that the spin hybridization in the band structure is suppressed by the mirror reflection symmetry. The bilayer TMD has a much shorter spin relaxation time in contrast, and this is attributed to stronger spin hybridization due to the absence of the mirror symmetry.

Collective excitations in Na2IrO3

We study the collective excitations of Na2IrO3 in an itinerant electron approach. We consider a multi-orbital tight-binding model with the electron transfer between the Ir 5d states mediated via oxygen 2p states and the direct d–d transfer on a honeycomb lattice. The one-electron energy as well as the ground state energy are investigated within the Hartree–Fock approximation. When the direct d–d transfer is weak, we obtain nearly flat energy bands due to the formation of quasimolecular orbitals, and the ground state exhibits the zigzag spin order. The evaluation of the density–density correlation function within the random phase approximation shows that the collective excitations emerge as bound states. For an appropriate value of the direct d–d transfer, some of them are concentrated in the energy region meV (magnetic excitations) while the others lie in the energy region meV (excitonic excitations). This behaviour is consistent with the resonant inelastic x-ray scattering spectra. We also show that the larger values of the direct d–d transfer are unfavourable in order to explain the observed aspects of Na2IrO3 such as the ordering pattern of the ground state and the excitation spectrum. These findings may indicate that the direct d–d transfer is suppressed by the structural distortions in the view of excitation spectroscopy, as having been pointed out in the ab initio calculation.

DNA/RNA transverse current sequencing: intrinsic structural noise from neighboring bases.

Nanopore DNA sequencing via transverse current has emerged as a promising candidate for third-generation sequencing technology. It produces long read lengths which could alleviate problems with assembly errors inherent in current technologies. However, the high error rates of nanopore sequencing have to be addressed. A very important source of the error is the intrinsic noise in the current arising from carrier dispersion along the chain of the molecule, i.e., from the influence of neighboring bases. In this work we perform calculations of the transverse current within an effective multi-orbital tight-binding model derived from first-principles calculations of the DNA/RNA molecules, to study the effect of this structural noise on the error rates in DNA/RNA sequencing via transverse current in nanopores. We demonstrate that a statistical technique, utilizing not only the currents through the nucleotides but also the correlations in the currents, can in principle reduce the error rate below any desired precision.

Analysis of resonant inelastic x-ray scattering fromSr2IrO4in an itinerant-electron approach

We analyze the resonant x-ray scattering (RIXS) spectra from Sr$_2$IrO$_4$ in an itinerant electron approach. Employing a multi-orbital tight-binding model on the square lattice, we calculate the one-electron energy band within the Hartree-Fock approximation, which leads to an antiferromagnetic ground state. We then evaluate the two-particle Green's functions for the particle-hole pair excitations within the random phase approximation, which are connected to the RIXS spectra within the fast collision approximation. The calculated RIXS spectra exhibit two-peak structure with slightly different energies in the low-energy region, which are originated from the bound states in the two-particle Green's function. They may be interpreted as the split modes of magnon. We also obtain several $\delta$-function peaks, which arise from the bound states around the bottom of energy continuum. They may be called as the exciton modes. These characteristics are in qualitative agreement with the RIXS experiment, demonstrating that the weak coupling theory could explain both the magnon and the exciton peaks in the RIXS spectra on an equal footing.

Comparative study of tight-binding and ab initio electronic structure calculations focused on magnetic anisotropy in ordered CoPt alloy

An empirical multiorbital (spd) tight binding (TB) model including magnetism and spin–orbit coupling is applied to calculations of magnetic anisotropy energy (MAE) in CoPt L10 structure. A realistic Slater–Koster parametrisation for single-element transition metals is adapted for the ordered binary alloy. Spin magnetic moment and density of states are calculated using a full-potential linearised augmented plane-wave (LAPW) ab initio method and our TB code with different variants of the interatomic parameters. Detailed mutual comparison of this data allows for determination of a subset of the compound TB parameters tuning of which improves the agreement of the TB and LAPW results. MAE calculated as a function of band filling using the refined parameters is in broad agreement with ab initio data for all valence states and in quantitative agreement with ab initio and experimental data for the natural band filling. Our work provides a practical basis for further studies of relativistic magnetotransport anisotropies by means of local Green's function formalism which is directly compatible with our TB approach.

Calculated phase diagram of doped BaFe2As2 superconductor in a C4-symmetry breaking model

We develop a minimal multiorbital tight-binding model with realistic hopping parameters. The model breaks the symmetry of the tetragonal point group by lowering it from C4 to D2d, which accurately describes the Fermi surface evolution of the electron-doped BaFe2−xCoxAs2 and hole-doped Ba1−yKyFe2As2 compounds. An investigation of the phase diagram with a mean-field Bogoliubov-de Gennes Hamiltonian results in agreement with the experimentally observed electron- and hole-doped phase diagram with only one set of t, U and V parameters. Additionally, the self-consistently calculated superconducting order parameter exhibits -wave pairing symmetry with a small d-wave pairing admixture in the entire doping range, which is the subtle result of the weakly broken symmetry and competing interactions in the multiorbital mean-field Hamiltonian.

Phase diagram and superconducting states in LaFeAsO1−xHxbased on the multiorbital extended Hubbard model

To understand the recently established unique magnetic and superconducting phase diagram of LaFeAsO$_{1-x}$H$_x$, we analyze the realistic multiorbital tight-binding model for $x=0 \sim 0.4$ beyond the rigid band approximation. Both the spin and orbital susceptibilities are calculated in the presence of the Coulomb and charge quadrupole interactions. It is found that both orbital and spin fluctuations strongly develop at both $x \sim 0$ and 0.4, due to the strong violation of the rigid band picture in LaFeAsO$_{1-x}$H$_x$. Based on this result, we discuss the experimental phase diagram, especially the double-dome superconducting phase. Moreover, we show that the quadrupole interaction is effectively produced by the vertex correction due to Coulomb interaction, resulting in the mutual development of spin and orbital fluctuations.

Elementary excitations probed byL-edge resonant inelastic x-ray scattering in systems with weak and intermediate electron correlations

We develop a formalism to calculate the L-edge resonant x-ray scattering (RIXS) spectra from transition-metal compounds. Using a multi-orbital tight-binding model, we derive useful formulas to calculate the spectra by collecting up the ladder diagrams on the basis of the Keldysh scheme, without relying on the fast collision approximation. They are feasible in the weak and intermediate coupling regimes of itinerant electron systems, where the charge and the magnetic excitations are mixed together. We examine the difference between the present formulas and those of the fast collision approximation. Finally, to demonstrate how our theory works, we employ the formulas to study the RIXS spectra on a simple model, the single-orbital Hubbard model on the square lattice at half-filling. The intensities originated from the magnon and from the continuous states are obtained on the equal footing in the antiferromagnetic ground state.

Andreev Bound-states of vortices and surfaces in topological superconductors

We propose an experimental way to determine the pairing states for the unconventional superconductor CuxBi2Se3. Using the spectral polynomial expansion method, we numerically calculate the local density of states (LDOS) in the multi-orbital tight-binding model and analytically obtain the zero-energy solution around a vortex. Both calculations reveal that a quantized vortex is spin-polarized for the gap function categorized by "pseudo scalar" which is the isotropic odd-parity order parameter. On the other hand, no clear spin-polarization around a vortex can observed for the gap function categorized by "polar vector" which breaks the rotational isotropy in the normal states.

Intrinsic spin–orbit interaction in carbon nanotubes and curved nanoribbons

We present a theoretical study of spin–orbit interaction effects on single wall carbon nanotubes and curved graphene nanoribbons by means of a realistic multiorbital tight-binding model, which takes into account the full symmetry of the honeycomb lattice. Several effects relevant to spin–orbit interaction, namely, the importance of chirality, curvature, and a family-dependent anisotropic conduction and valence band splitting are identified. We show that chiral nanotubes and nanoribbons exhibit spin-split states. Curvature-induced orbital hybridization is crucial to understand the experimentally observed anisotropic spin–orbit splittings in carbon nanotubes. In fact, spin–orbit interaction is important in curved graphene nanoribbons, since the induced spin-splitting on the edge states gives rise to spin-filtered states.

Theoretical analysis of resonant inelastic x-ray scattering spectra inLaMnO3

We analyze the resonant inelastic x-ray scattering (RIXS) spectra at the $K$ edge of Mn in the antiferromagnetic insulating manganite ${\text{LaMnO}}_{3}$. We make use of the Keldysh-type Green's function formalism, in which the RIXS intensity is described by a product of an incident-photon-dependent factor and a density-density correlation function in the $3d$ states. We calculate the former factor using the $4p$ density of states given by an ab initio band-structure calculation and the latter using a multiorbital tight-binding model. The ground state of the model Hamiltonian is evaluated within the Hartree-Fock approximation. Correlation effects are treated within the random-phase approximation (RPA). We obtain the RIXS intensity in a wide range of energy loss (2--15 eV). The spectral shape is strongly modified by the RPA correlation, showing good agreement with the experiments. The incident-photon-energy dependence also agrees well with the experiments. The present mechanism that the RIXS spectra arise from band-to-band transitions to screen the core-hole potential is quite different from the orbiton picture previously proposed, enabling a comprehensive understanding of the RIXS spectra.

Intrinsic spin Hall effect in graphene: Numerical calculations in a multiorbital model

We study the spin Hall effect (SHE) in graphene using a realistic multi-orbital tight-binding model that includes the atomic spin-orbit interaction. The SHE is found to be induced by the spin-dependent Aharonov-Bohm phase. In the metallic case, the calculated values for the spin Hall conductivity (SHC) are much smaller than the quantized Hall conductivity for realistic parameter values of metallic graphene. In the insulating case, quantization of the SHC is violated due to the multi-orbital effect. The present study suggests that the SHE in a honeycomb lattice is enhanced by chemical doping, such as the substitution of carbon atoms with boron atoms.

Spin Hall effect in Sr 2RuO 4 and transition metals (Nb,Ta)

We study the intrinsic spin Hall conductivity (SHC) and the d-orbital Hall conductivity (OHC) in metallic d-electron systems based on the multiorbital tight-binding model. The obtained Hall conductivities are much larger than that in p-type semiconductors. The origin of these huge Hall effects is the “effective Aharonov–Bohm phase” induced by the signs of inter-orbital hopping integrals as well as atomic spin–orbit interaction. Huge SHC and OHC due to this mechanism is ubiquitous in multiorbital transition metals.

Analysis of Incident-Photon-Energy and Polarization Dependent Resonant Inelastic X-ray Scattering from La2CuO4

We present a detailed analysis of the incident-photon-energy and polarization dependences of the resonant inelastic x-ray scattering (RIXS) spectra at the Cu K edge in La 2 CuO 4 . Our analysis is based on the formula developed by Nomura and Igarashi, which describes the spectra by a product of an incident-photon-dependent factor and a density–density correlation function for 3 d states. We calculate the former factor using the 4 p density of states from an ab-initio band structure calculation and the latter using a multiorbital tight-binding model within the Hartree–Fock approximation and the random phase approximation. We obtain spectra with rich structures in the energy-loss range 2–5 eV, which vary with varying momentum and incident-photon energy, in semi-quantitative agreement with recent experiments. We clarify the origin of such changes as a combined effect of the incident-photon-dependent factor and the density–density correlation function.

Study of Intrinsic Spin and Orbital Hall Effects in Pt Based on a (6s, 6p, 5d) Tight-Binding Model

We study the origin of the intrinsic spin Hall conductivity (SHC) and the d -orbital Hall conductivity (OHC) in Pt based on a multiorbital tight-binding model with spin–orbit interaction. We find that the SHC exceeds 1000 \(\hbar e^{-1}\)·Ω -1 cm -1 when the resistivity ρ is smaller than ∼10 µΩ cm, whereas it decreases to 300 \(\hbar e^{-1}\)·Ω -1 cm -1 when ρ∼100 µΩ cm. In addition, the OHC is still larger than the SHC. The origin of the huge spin Hall effect (SHE) and d -orbital Hall effect (OHE) in Pt is the “effective Aharonov–Bohm phase” that is induced by the interorbital transition between d x y - and d x 2 - y 2 -orbitals with the aid of the strong spin–orbit interaction.

Analysis of resonant inelastic x-ray scattering at theKedge in NiO

We analyze the resonant inelastic x-ray scattering (RIXS) spectra at the Ni $K$ edge in an antiferromagnetic insulator NiO by applying the theory developed by the present authors. It is based on the Keldysh Green's function formalism, and treats the core-hole potential in the intermediate state within the Born approximation. We calculate the single-particle energy bands within the Hartree-Fock approximation on the basis of the multi-orbital tight-binding model. Using these energy bands together with the $4p$ density of states from an ab initio band structure calculation, we calculate the RIXS intensities as a function of energy loss. By taking account of electron correlation within the random phase approximation (RPA), we obtain quantitative agreement with the experimental RIXS spectra, which consist of prominent two peaks around 5 eV and 8 eV, and the former shows considerable dispersion while the latter shows no dispersion. We interpret the peaks as a result of a band-to-band transition augmented by the RPA correlation.

強磁性トンネル接合におけるＴＭＲとスピン分極率

Tunnel magnetoresistance and spin polarization in (Ni-Co)/Al2O3/(Ni-Co) tunnel junctions are studied in the framework of the linear response theory. The multi-orbital tight-binding model is used to take account of the realistic band structure of the ferromagnets. The results show a small negative spin polarization and a magnetoresistance ratio of less than one percent. It is argued that the electronic structure of Al atom oxidized incompletely at interfaces is the origin of the positive spin polarization and the large magnetoresistance ratio.