Tight-binding Hamiltonian Research Articles

Electronic frustration, Berry’s phase interference and slow dynamics in some tight-binding systems coupled to harmonic baths

Conical intersections in two-state systems require a coordinate-dependent coupling. This paper identifies and investigates conical intersections in cyclic tight-binding system-bath Hamiltonians with an odd number of sites and a constant site-to-site coupling. In the absence of bath degrees of freedom, such tight-binding systems with a positive coupling parameter exhibit electronic frustration and a doubly-degenerate ground state. When these systems interact with a harmonic bath, the degeneracy becomes a conical intersection between the adiabatic ground and first excited states. Under weak system-bath coupling, overlapping wavefunctions associated with different sites give rise to distinct pathways with interfering geometric phases, which lead to considerably slower transfer dynamics. The effect is most pronounced in the presence of low-temperature dissipative baths characterized by a continuous spectral density. It is found that the transfer dynamics and equilibration time of a cyclic dissipative three-site system with a positive coupling exceeds that of a similar three-site system with a negative coupling, as well as that of cyclic four-site systems, by an order of magnitude.

Truncated atomic plane wave method for subband structure calculations of moiré systems

We propose a highly efficient and accurate numerical scheme named the truncated atomic plane wave method to determine the subband structure of twisted bilayer graphene (TBG) inspired by the Bistritzer-MacDonald model. Our method utilizes real-space information of carbon atoms in the moir\'e unit cell and projects the full tight-binding Hamiltonian into a much smaller subspace using atomic plane waves. Using our method, we are able to present accurate electronic band structures of TBG in a wide range of twist angles together with the detailed moir\'e potential and screened Coulomb interaction at the first magic angle. Furthermore, we generalize our formalism to solve the problem of low-frequency moir\'e phonons in TBG.

Electric-field-induced quasi-phase-matched three-wave mixing in silicon-based superlattice-on-insulator integrated circuits

We present a theoretical investigation, based on the tight-binding Hamiltonian, of efficient electric-field-induced three-waves mixing (EFIM) in an undoped lattice-matched short-period superlattice (SL) that integrates quasi-phase-matched (QPM) SL straight waveguides and SL racetrack resonators on an opto-electronic chip. Periodically reversed DC voltage is applied to electrode segments on each side of the strip waveguide. The spectra of χxxxx(3) and of the linear susceptibility have been simulated as a function of the number of the atomic monolayers for “non-relaxed” heterointerfaces, and by considering all the transitions between valence and conduction bands. The large obtained values ofχxxxx(3) make the (ZnS)3/(Si2)3 short-period SL a good candidate for realizing large effective second-order nonlinearity, enabling future high-performance of the SLOI PICs and OEICs in the 1000-nm and 2000-nm wavelengths ranges. We have made detailed calculations of the efficiency of second-harmonic generation and of the performances of the optical parametric oscillator (OPO). The results indicate that the (ZnS)N/(Si2)M QPM is competitive with present PPLN technologies and is practical for classical and quantum applications.

Tuning the thermoelectric properties of doped silicene nanoribbon heterostructures

In this work, we investigate the thermoelectrical properties of a silicene nanoribbon heterostructure composed of a central conductor fully doped with ad-atoms and connected to two pristine leads of the same material. Using a tight-binding Hamiltonian, we have calculated the system’s thermoelectric properties as a function of the geometrical confinement and external field. Our results exhibit an enhancement of the thermopower when a transverse electric field is applied to the conductor region for different temperatures. In addition, a violation of the Wiedemann–Franz law is observed around the ad-atom energy. Our results suggest the thermoelectric properties of doped silicene nanoribbons can be efficiently tuned with external perturbations.

Relationship between two-particle topology and fractional Chern insulator

Lattice generalizations of fractional quantum Hall (FQH) systems, called fractional Chern insulators (FCIs), have been extensively investigated in strongly correlated systems. Despite many efforts, previous studies have not revealed all of the guiding principles for the FCI search. In this paper, we investigate a relationship between the topological band structure in the two-particle problem and the FCI ground states in the many-body problem. We first formulate the two-particle problem of a bosonic on-site interaction projected onto the lowest band of a given tight-binding Hamiltonian. We introduce a reduced Hamiltonian whose eigenvalues correspond to the two-particle bound-state energies. By using the reduced Hamiltonian, we define the two-particle Chern number and numerically check the bulk-boundary correspondence that is predicted by the two-particle Chern number. We then propose that a nontrivial two-particle Chern number of dominant bands roughly indicates the presence of bosonic FCI ground states at filling factor $\ensuremath{\nu}=1/2$. We numerically investigate this relationship in several tight-binding models with Chern bands and find that it holds well in most of the cases, albeit two-band models being exceptions. Although the two-particle topology is neither a necessary nor a sufficient condition for the FCI state as other indicators in previous studies, our numerical results indicate that the two-particle topology characterizes the degree of similarity to the FQH systems.

Valley transport in strained silicene heterojunctions with zigzag and armchair interfaces

We study the carrier transport through a strained silicene heterojunction based on the tight-binding Hamiltonian, focusing on the effect of the interfaces, i.e., zigzag or armchair, on the valley polarization. We find that inter-valley transmission is prevented in the zigzag configuration owing to the conservation of transverse momentum, but this restriction is lifted for the armchair configuration. More importantly, the preservation of certain valley symmetries of the Fermi surfaces in the zigzag configuration even under strain distortion results in complete cancellation of the valley polarization after summing over all incident angles. In contrast, such symmetries are absent in the forward-propagating states for the strained armchair configuration, resulting in a sizable net valley polarization even after summation over all incident angles. Our findings provide insight toward the key role of interfaces in strained silicene-based valleytronics.

Mott Transition in the Hubbard Model on Anisotropic Honeycomb Lattice with Implications for Strained Graphene: Gutzwiller Variational Study.

The modification of interatomic distances due to high pressure leads to exotic phenomena, including metallicity, superconductivity and magnetism, observed in materials not showing such properties in normal conditions. In two-dimensional crystals, such as graphene, atomic bond lengths can be modified by more than 10 percent by applying in-plane strain, i.e., without generating high pressure in the bulk. In this work, we study the strain-induced Mott transition on a honeycomb lattice by using computationally inexpensive techniques, including the Gutzwiller Wave Function (GWF) and different variants of Gutzwiller Approximation (GA), obtaining the lower and upper bounds for the critical Hubbard repulsion (U) of electrons. For uniaxial strain in the armchair direction, the band gap is absent, and electron correlations play a dominant role. A significant reduction in the critical Hubbard U is predicted. Model considerations are mapped onto the tight-binding Hamiltonian for monolayer graphene by the auxiliary Su-Schrieffer-Heeger model for acoustic phonons, assuming zero stress in the direction perpendicular to the strain applied. Our results suggest that graphene, although staying in the semimetallic phase even for extremely high uniaxial strains, may show measurable signatures of electron correlations, such as the band narrowing and the reduction in double occupancies.

Topological properties of half Heusler compounds: Tuned by the spin-orbit coupling and p-d hybridization

The topological properties of Half Heusler compounds XYZ (X=Na, K; Y=Cu, Ag, Au; Z=S, Se, Te) are studied by the density functional theory (DFT) and tight-binding model Hamiltonian. The Y-s, Y-d and Z-p states form the bands around the Fermi level and determine their topological properties. When the energy of Y-s state is much larger than the other states, the compounds are normal insulators, just like NaCuS and NaCuS. On the contrary, when the Y-s state energy is only a little higher than the other states, the compounds are topological insulators (TI) or Dirac semi-metal (DSM) depended on the effective spin orbital coupling (SOC), which can be tuned by the relation between positive SOC Z-p and Y-d states. The compounds with negative effective SOC are TI such as NaAgS, NaAuS, while the compounds possessing positive SOC are DSM, just like NaAgTe and NaAuTe. Our simple tight-binding model can be used to design topological materials before the time consuming DFT calculations.

The longitudinal spin-conductivity of τ-type organic conductors

The Kubo formula is used to evaluate the real part of the longitudinal spin conductivity for τ -type organic layered conductors. These conductors are described by a four-band model, consisting of the tight binding Hamiltonian of the system. This Hamiltonian may be written as a direct sum of two two-band models, describing the spins up and down respectively. The longtudinal spin conductivity of the system is analytically evaluated by means of Kubo formula applied to the two-band model corresponding to the spin up carriers. Our results show that the regular real part of the longitudinal spin-conductivity of the system becomes zero for sufficiently large values of the spin–orbit coupling constant ( λ > 0 . 04 ) and only ballistic propagation occurs in this case. The ballistic propagation is more favourable for smaller values of the temperature in the system studied here.

TBPLaS: A tight-binding package for large-scale simulation

TBPLaS is an open-source software package for the accurate simulation of physical systems with arbitrary geometry and dimensionality utilizing the tight-binding (TB) theory. It has an intuitive object-oriented Python application interface (API) and Cython/Fortran extensions for the performance-critical parts, ensuring both flexibility and efficiency. Under the hood, numerical calculations are mainly performed by both exact diagonalization and the tight-binding propagation method (TBPM) without diagonalization. Especially, the TBPM is based on the numerical solution of the time-dependent Schrödinger equation, achieving linear scaling with system size in both memory and CPU costs. Consequently, TBPLaS provides a numerically cheap approach to calculate the electronic, optical, plasmon and transport properties of large tight-binding models with billions of atomic orbitals. Current capabilities of TBPLaS include the calculations of band structure, density of states, local density of states, quasi-eigenstates, optical conductivity, electrical conductivity, Hall conductivity, polarization function, dielectric function, plasmon dispersion, carrier mobility and velocity, localization length and free path, Z2 topological invariant, wave-packet propagation, etc. All the properties can be obtained with only a few lines of code. Other algorithms involving tight-binding Hamiltonians can be implemented easily due to the extensible and modular nature of the code. In this paper, we discuss the theoretical framework, implementation details and common workflow of TBPLaS, and give a few demonstrations of its applications. Program summaryProgram Title:TBPLaSCPC Library link to program files:https://doi.org/10.17632/5cjmzj9jwm.1Code Ocean capsule:https://codeocean.com/capsule/8296734Licensing provisions: BSD 3-clauseProgramming language: Python, Cython, FortranNature of problem: The TB method is a powerful tool for investigating the electronic structures and many other properties in condensed matter physics. However, the costs of memory and CPU time using standard diagonalization-based TB techniques scale as O(N2) and O(N3) with the model size N, severely limiting their applications in large complex systems. The development of numerical methods to solve TB problems without any diagonalization, as well as the implementation of these techniques in software packages, are urgently needed to promote the capability of TB methods to large systems with billions of atoms.Solution method: We proposed the TBPM and implemented it in the TBPLaS package. In TBPM, the electronic properties of a TB model are calculated numerically by solving the time-dependent Schrödinger equation without any diagonalization, which ensures a linear scaling of both memory and CPU costs with the system size. Models with billions of atoms (orbitals) can be easily handled, with many properties available from the evolution of time-dependent correlation functions. The TBPLaS package features an intuitive object-oriented Python API and Cython/Fortran extensions for performance-critical parts, ensuring both flexibility and efficiency. Moreover, TBPLaS implements hybrid MPI+OpenMP parallelism, which can exploit the modern hardware of high-performance computers.

Electronic Spectrum and Optical Properties of Y-Shaped Kekulé-Patterned Graphene: Band Nesting Resonance as An Optical Signature

Employing tight-binding model we investigate the effects of a uniform Y-shaped Kekulé lattice distortion on the electronic spectrum and optical conductivity of graphene. We derive a low-energy effective Hamiltonian which is found to be in excellent agreement with one calculated from a diagonalization of the full tight-binding Hamiltonian. Then using the low-energy Hamiltonian and Kubo formula we obtain an analytical expression for the real part of the optical conductivity used to explore the effects of chemical potential, temperature and on-site and hopping energy deviations in details. In particular we find that Y-shaped Kekué-patterned graphene at finite chemical potential displays a large optical response called band nesting resonance. This effect is shown to be robust against increasing temperature, facilitating its detection as an optical signature for the Y-shaped Kekulé distortion even at room temperature.

BinPo: An open-source code to compute the band structure of two-dimensional electron systems

We introduce BinPo, an open-source Python code to compute electronic properties of two-dimensional electron systems. A bulk tight binding Hamiltonian is constructed from relativistic density functional theory calculations represented in the basis of maximally localized Wannier functions. BinPo has a Schrödinger-Poisson solver, integrating an electric field-dependent relative permittivity to obtain self-consistently the confining electrostatic potential energy term in the derived tight binding slab system. The band structure, energy slices, and other properties, along with different projections and orientations can be computed. High resolution and publishable figures of the simulations can be generated. In BinPo, priority has been given to ease-of-use, efficiency, readability and modularity, therefore becoming suitable to produce reliable electronic structures simulations at low computational cost. Along with the code itself, we provide files from first-principles calculations for some materials, instructions of use, and detailed examples of its wide range of capabilities. The code was developed with a focus on the ABO3 perovskite structure-based systems, such as SrTiO3 and KTaO3, because of their increasing impact in the materials community. Some features, such as the projection onto orbital states, are restricted to calculations using the relevant t2g orbitals for this family of materials, yet it is possible to include more elements in the basis for the band structure determination of other systems. The use of a relativistic approach allows for the inspection of the role of spin-orbit coupling and the resulting Rashba effect on the systems. We detail the approaches used in the code, so that it can be further exploited and adapted to other problems, such as adding new materials and functionalities which can strength the initial code scopes. Program summaryProgram title: BinPoCPC Library link to program files:https://doi.org/10.17632/zk4xy7vfy4.1Developer's repository link:https://github.com/emanuelm33/BinPoCode Ocean capsule:https://codeocean.com/capsule/0987578Licensing provisions: GPLv3Programming language: PythonExternal routines/libraries: NumPy, SciPy, Matplotlib, ASE.Nature of problem: Compute the band structure and other electronic properties in two-dimensional electron systems.Solution method: Construction of a slab Hamiltonian from one built using a basis of maximally localized Wannier functions. Solve the Schrödinger-Poisson scheme to get the self-consistent potential energy along the slab. Use this potential to compute the band structure and additional properties by solving the Schrödinger equation.Additional comments including restrictions and unusual features: Other features included are the visualization of the self-consistent process and final solutions, band structure and energy slices with different projections. High resolution and customizable figures can be obtained in all cases.

Disorder-induced phase transitions in double Weyl semimetals

The double Weyl semimetal (DWSM) is a newly proposed topological material that hosts Weyl points with chiral charge n=2. The disorder effect in DWSM is investigated by adopting the tight-binding Hamiltonian. Using the transfer matrix method and the noncommutative Kubo formula, we numerically calculate the localization length and the Hall conductivity in the presence of the on-site nonmagnetic disorder or orbital (spin-flip) disorders, and give the corresponding global phase diagrams. For the on-site nonmagnetic disorder, the system undergoes the DWSM-3D quantum anomalous hall (3D QAH) and normal insulator (NI)-DWSM phase transitions, and evolves into the diffusive metal (DM) phase before being localized by strong disorders, which is consistent with the Weyl semimetal. For \sigma_x orbital disorder, we find that increasing disorder can generate a pair of Weyl nodes at the boundary of the Brillouin zone and induce a 3D QAH-DWSM phase transition. Then we investigate the combined effect of orbital disorders for both disordered 3D QAH phase and DWSM phase. The disorder-induced transitions can be well understood in terms of an effective medium theory based on self-consistent Born approximation.

Effects of chirality in the electron transmission through step-like potential in zigzag, armchair, and (2m,m) carbon nanotubes

We report the one-electron spectrum and eigenstates of infinite achiral and chiral (2m,m) carbon nanotubes found by using the analytic solution to the Schrödinger equation for the tight-binding Huckel-type Hamiltonian. With the help of matching the wave functions on the interfaces between the regions, where electrons have different site energies, we find and compare the transmission coefficients for zigzag, armchair and chiral nanotubes subjected to the action of an applied step-like potential. The correspondence between the nanotube band structure and the energy dependence of the transmission coefficient is demonstrated. It is shown that the (2m,m) nanotubes with a medium chiral angle reveal intermediate transport properties as compared with the achiral armchair, and zigzag nanotubes.

CO2 adsorption and activation on Ag(1 1 1) surfaces in the presence of surface charge density: A static gas phase DFT study

The CO2 reduction reaction on Ag in the presence of surface plasmons are of strong interest in photocatalysis. Here, two Density Functional Theory (DFT) approaches are proposed to localize charges at the Ag surface to mimic surface plasmon excitation. These calculations predict charge localization at the outermost surface layer, a result confirmed via light excitation at the plasmon resonance modeled by Density Functional Tight Binding Hamiltonian (DFTB) theory. The CO2(gas) reduction initial steps are studied by DFT models showing that bonded species can be created on top of an Ag-atom in the presence of extra charges. A second CO2 molecule can assist the first molecule, decreasing the charge carrier density requirement for CO2 reduction bonded species. A Molecular Dynamics (MD) study shows a possible interaction among CO2 molecule. These results show that a static DFT simulation can mimic charge localization resulting from surface plasmon effects, thus enabling studies on surface plasmon-enhanced chemical reactions, paving the way for future time-dependent (TD) studies.

Direct visualization of Rashba-split bands and spin/orbital-charge interconversion at KTaO3 interfaces

Rashba interfaces have emerged as promising platforms for spin-charge interconversion through the direct and inverse Edelstein effects. Notably, oxide-based two-dimensional electron gases display a large and gate-tunable conversion efficiency, as determined by transport measurements. However, a direct visualization of the Rashba-split bands in oxide two-dimensional electron gases is lacking, which hampers an advanced understanding of their rich spin-orbit physics. Here, we investigate KTaO3 two-dimensional electron gases and evidence their Rashba-split bands using angle resolved photoemission spectroscopy. Fitting the bands with a tight-binding Hamiltonian, we extract the effective Rashba coefficient and bring insight into the complex multiorbital nature of the band structure. Our calculations reveal unconventional spin and orbital textures, showing compensation effects from quasi-degenerate band pairs which strongly depend on in-plane anisotropy. We compute the band-resolved spin and orbital Edelstein effects, and predict interconversion efficiencies exceeding those of other oxide two-dimensional electron gases. Finally, we suggest design rules for Rashba systems to optimize spin-charge interconversion performance.

Loschmidt-echo approach to error estimation in Krylov-subspace approximation

The Krylov subspace method is a traditional approach to approximate quantum evolution, allowing us to treat systems with large Hilbert spaces. Despite its popularity, current bounds typically overestimate the error, which translates into more expensive simulation routines. In this paper, we tackle this problem by realizing that the error can be understood as a Loschmidt echo in a one-dimensional (1D) noninteracting tight-binding Hamiltonian. We show that the different time regimes of the approximation can be understood using simple physical ideas. More importantly, we obtain computationally cheap error bounds that describe with high precision the actual error in the approximation.

High-Performance Pockels Effect Modulation and Switching in Silicon-Based GaP/Si, AlP/Si, ZnS/Si, AlN/3C-SiC, GaAs/Ge, ZnSe/GaAs, and ZnSe/Ge Superlattice-On-Insulator Integrated Circuits.

We propose new a Si-based waveguided Superlattice-on-Insulator (SLOI) platforms for high-performance electro-optical (EO) 2 × 2 and N × M switching and 1 × 1 modulation, including broad spectrum and resonant. We present a theoretical investigation based on the tight-binding Hamiltonian of the Pockels EO effect in the lattice-matched undoped , , , , , , and wafer-scale short-period superlattices that are etched into waveguided networks of small-footprint Mach-Zehnder interferometers and micro-ring resonators to yield opto-electronic chips. The spectra of the Pockels r33 coefficient have been simulated as a function of the number of the atomic monolayers for “non-relaxed” heterointerfaces. The large obtained r33 values enable the SLOI circuit platforms to offer a very favorable combination of monolithic construction, cost-effective manufacturability, high modulation/switching speed, high information bandwidth, tiny footprint, low energy per bit, low switching voltage, near-IR-and-telecom wavelength coverage, and push-pull operation. By optimizing waveguide, clad, and electrode dimensions, we obtained very desirable values of the VπL performance metric, in the range of 0.062 to 0.275 V·cm, portending a bright future for a variety of applications, such as sensor networks or Internet of Things (IoT).

Horizon physics of quasi-one-dimensional tilted Weyl cones on a lattice

To simulate the dynamics of massless Dirac fermions in curved space-times with one, two, and three spatial dimensions, we construct tight-binding Hamiltonians with spatially varying hoppings. These models represent tilted Weyl semimetals where the tilting varies with position, in a manner similar to the light cones near the horizon of a black hole. We illustrate the gravitational analogies in these models by numerically evaluating the propagation of wave packets on the lattice and then comparing them to the geodesics of the corresponding curved space-time. We also show that the motion of electrons in these spatially varying systems can be understood through the conservation of energy and the quasiconservation of quasimomentum. This picture is confirmed by calculations of the scattering matrix, which indicate an exponential suppression of any noncontinuous change in the quasimomentum. Finally, we show that horizons in the lattice models can be constructed also at finite energies using specially designed tilting profiles.

Particlelike valleytronics in graphene

Particlelike scattering states allow for noiseless transport through quantum dots by closely retracing bundles of classical trajectories. We identify such raylike states for electron transport through graphene ribbons. Remarkably, we find that these quasiclassical scattering states can be unambiguously associated with well-defined quantum numbers of the valley degree of freedom specific to graphene. Trigonal warping---i.e., deviations of the band structure from a perfectly isotropic two-dimensional Dirac equation due to the hexagonal lattice structure---results in preferred propagation directions and scattering time delays that depend on the valley the particlelike wave travels in. By implementing a truncated mode basis of Bloch states, we achieve simulations of micrometer-sized quantum dots starting from an atomic-scale tight-binding Hamiltonian.