Effective Tight-binding Hamiltonian Research Articles

Topological wave equation eigenmodes in continuous 2D periodic geometries

In this paper, we address the topological characterization of the wave equation solutions in continuous two-dimensional (2D) periodic geometries with Neumann or Dirichlet boundary conditions. This characterization is relevant in the context of 2D vibrating membranes and our approach allows one to understand the topological behavior recently observed in acoustic three-dimensional artificial lattices. In particular, the dependence of the topological behavior on the experimental positioning of the coupling channels is explained using simple arguments and a simple method of construction of an equivalent effective tight-binding Hamiltonian is presented.

Exploring the electronic potential of effective tight-binding hamiltonians

The linear combination of atomic orbitals (LCAO) is a standard method for studying solids and molecules, it is also known as the tight-binding (TB) method. In most of the implementations only the basis set and the coupling constants are provided, without the explicit definition of kinetic and potential energy operators. The tight-binding scheme is, nonetheless, capable of providing an accurate description of properties such as the electronic bands and elastic constants for many materials. However, for some applications, the knowledge of the underlying electronic potential associated with the tight-binding hamiltonian might be important to guarantee that the actual physics is preserved by the semiempirical scheme. In this work the electronic potentials that arise from the use of tight-binding effective hamiltonians it is explored. The formalism is applied to the extended Hückel tight-binding (EHTB) hamiltonian, which is a two-center Slater−Koster approach that makes explicit use of the overlap matrix.

Investigation of three topological edge states in honeycomb lattices based on graphene plasmonic crystal

In this article, three categories of the edge states in the honeycomb lattice are investigated theoretically by using the effective tight-binding Hamiltonian. The edge-bulk corresponding dispersions of zigzag, bearded, and armchair edge states analytically. The actual edge-bulk corresponding and the light field distribution of the graphene plasmonic crystals are obtained by solving Maxwell equations with boundary conditions, which are in good agreement with the analytical results. The proposed plasmonic structures provide guidance for designing the frequency range dependent property of topological structures, and show the potential applications in topological robust devices.

Smart local orbitals for efficient calculations within density functional theory and beyond.

Localized basis sets in the projector augmented wave formalism allow for computationally efficient calculations within density functional theory (DFT). However, achieving high numerical accuracy requires an extensive basis set, which also poses a fundamental problem for the interpretation of the results. We present a way to obtain a reduced basis set of atomic orbitals through the subdiagonalization of each atomic block of the Hamiltonian. The resulting local orbitals (LOs) inherit the information of the local crystal field. In the LO basis, it becomes apparent that the Hamiltonian is nearly block-diagonal, and we demonstrate that it is possible to keep only a subset of relevant LOs that provide an accurate description of the physics around the Fermi level. This reduces to some extent the redundancy of the original basis set, and at the same time, it allows one to perform post-processing of DFT calculations, ranging from the interpretation of electron transport to extracting effective tight-binding Hamiltonians, very efficiently and without sacrificing the accuracy of the results.

Analysis of Exchange Interactions in Dimers of Mn3 Single-Molecule Magnets, and Their Sensitivity to External Pressure

In light of the potential use of single-molecule magnets (SMMs) in emerging quantum information science initiatives, we report first-principles calculations of the magnetic exchange interactions in [$\mathrm{Mn}_{3}$]$_{2}$ dimers of $\mathrm{Mn}_3$ SMMs, connected by covalently-attached organic linkers, that have been synthesized and studied experimentally by magnetochemistry and EPR spectroscopy. Energy evaluations calibrated to experimental results give the sign and order of magnitude of the exchange coupling constant ($J_{12}$) between the two $\mathrm{Mn}_{3}$ units that match with fits of magnetic susceptibility data and EPR spectra. Downfolding into the $\mathrm{Mn}$ $d$-orbital basis, Wannier function analysis has shown that magnetic interactions can be channeled by ligand groups that are bonded by van der Waals interaction and/or by the linkers via covalent bonding of specific systems, and effective tight-binding Hamiltonians are obtained. We call this long-range coupling that involves a group of atoms a collective exchange. Orbital projected spin density of states and alternative Wannier transformations support this observation. To assess the sensitivity of $J_{12}$ to external pressure, stress-strain curves have been investigated for both hydrostatic and uniaxial pressure, which have revealed a switch of $J_{12}$ from ferromagnetic to antiferromagnetic with increasing pressure.

Exact continuum model for low-energy electronic states of twisted bilayer graphene

We introduce a complete physical model for the single-particle electronic structure of twisted bilayer graphene (tBLG), which incorporates the crucial role of lattice relaxation. Our model, based on $k \cdot p$ perturbation theory, combines the accuracy of DFT calculations through effective tight-binding Hamiltonians with the computational efficiency and complete control of the twist angle offered by continuum models. The inclusion of relaxation significantly changes the bandstructure at the first magic-angle twist corresponding to flat bands near the Fermi level (the "low-energy" states), and eliminates the appearance of a second magic-angle twist. We show that minimal models for the low-energy states of tBLG can be easily modified to capture the changes in electronic states as a function of twist angle.

Ferromagnetic Mott state in Twisted Graphene Bilayers at the Magic Angle.

We address the effective tight-binding Hamiltonian that describes the insulating Mott state of twisted graphene bilayers at a magic angle. In that configuration, twisted bilayers form a honeycomb superlattice of localized states, characterized by the appearance of flat bands with fourfold degeneracy. After calculating the maximally localized superlattice Wannier wave functions, we derive the effective spin model that describes the Mott state. We suggest that the system is an exotic ferromagnetic Mott insulator, with well-defined experimental signatures.

Conductance fluctuations of monolayer GeSnH2 in the topological phase using a low-energy effective tight-binding Hamiltonian

An effective tight-binding (TB) Hamiltonian for monolayer GeSnH$_2$ is proposed which has an inversion-asymmetric honeycomb structure. The low-energy band structure of our TB model agrees very well with previous {\it ab initio} calculations under biaxial tensile strain. We predict a phase transition upon 7.5\% biaxial tensile strain in agreement with DFT calculations. Upon 8.5\% strain the system exhibits a band gap of 134 meV, suitable for room temperature applications. The topological nature of the phase transition is confirmed by: 1)the calculation of the $\mathbb{Z}_2$ topological invariant, and 2)quantum transport calculations of disordered GeSnH$_2$ nanoribbons which allows us to determine the universality class of the conductance fluctuations.

Multifractality of ab initio wave functions in doped semiconductors

In Refs. [1,2] we have shown how a combination of modern linear-scaling DFT, together with a subsequent use of large, effective tight-binding Hamiltonians, allows to compute multifractal wave functions yielding the critical properties of the Anderson metal-insulator transition (MIT) in doped semiconductors. This combination allowed us to construct large and atomistically realistic samples of sulfur-doped silicon (Si:S). The critical properties of such systems and the existence of the MIT are well known, but experimentally determined values of the critical exponent ν close to the transition have remained different from those obtained by the standard tight-binding Anderson model. In Ref. [1], we found that this “exponent puzzle” can be resolved when using our novel ab initio approach based on scaling of multifractal exponents in the realistic impurity band for Si:S. Here, after a short review of multifractality, we give details of the multifractal analysis as used in [1] and show the obtained critical multifractal spectrum at the MIT for Si:S.

Compression of Wannier functions into Gaussian-type orbitals

We propose a greedy algorithm for the compression of Wannier functions into Gaussian-polynomials orbitals. The so-obtained compressed Wannier functions can be stored in a very compact form, and can be used to efficiently parameterize effective tight-binding Hamiltonians for multilayer 2D materials for instance. The compression method preserves the symmetries (if any) of the original Wannier function. We provide algorithmic details, and illustrate the performance of our implementation on several examples, including graphene, hexagonal boron-nitride, single-layer FeSe, and bulk silicon in the diamond cubic structure.

Nonlocal discrete continuity and invariant currents in locally symmetric effective Schrödinger arrays

We develop a formalism relating nonlocal current continuity to spatial symmetries of subparts in discrete Schrödinger systems. Breaking of such local symmetries hereby generates sources or sinks for the associated nonlocal currents. The framework is applied to locally inversion-(time-) and translation-(time-) symmetric one-dimensional photonic waveguide arrays with Hermitian or non-Hermitian effective tight-binding Hamiltonians. For stationary states the nonlocal currents become translationally invariant within symmetric domains, exposing different types of local symmetry. They are further employed to derive a mapping between wave amplitudes of symmetry-related sites, generalizing also the global Bloch and parity mapping to local symmetry in discrete systems. In scattering setups, perfectly transmitting states are characterized by aligned invariant currents in attached symmetry domains, whose vanishing signifies a correspondingly symmetric density. For periodically driven arrays, the invariance of the nonlocal currents is retained on period average for quasi-energy eigenstates. The proposed theory of symmetry-induced continuity and local invariants may contribute to the understanding of wave structure and response in systems with localized spatial order.

Silicene Nanoribbon Tunnel Field Effect Transistor

Scaling of metal oxide semiconductor field effect transistor (MOSFET) following the Moore’s law is approaching to its near end as the power dissipation at the chip level is becoming increasingly difficult to reduce [1]. The International Technology Roadmap for Semiconductors (ITRS) considers several non-classical devices as a future replacement of silicon-based MOSFETs among which tunnel field effect transistor (TFET) is found to be promising [2, 3]. Compared to bulk three dimensional material based TFETs, study of TFETs based on two dimensional atomically thick materials have shown potential to operate at low supply voltage with a low subthreshold slope (SS) compared to 60mV/decade in conventional MOSFETs [4]. Different forms of two dimensional materials are studied such as Dirac cone materials (graphene, silicene, gemanene, stanene), transition metal dichalcogenides (TMD), transition oxides (TO) and topological insulators (TI). Compared to the study of TFET based on other two dimensional materials, silicene TFET remained large unexplored. Silicene is the two dimensional atomically thick planer form of bulk silicon. Stable room temperature operation of FET based on silicene has recently been reported [5]. Like graphene, silicene is a Dirac cone material with devices which provide high off-state leakage current due to the lack of a significant bandgap. However, quantum confined silicene nanoribbon (SiNR) shows observable bandgap making it suitable for digital applications [6]. Moreover, being an allotrope of silicon, silicene is also expected to be suitable for fabrication technology. Here, we present our work on SiNR TFET using atomistic simulation based on self-consistent solution of the 3D Poisson and Schrödinger equations within the non-equilibrium Green’s function (NEGF) formalism. SiNR has two types of edges, armchair and zigzag. We have considered armchair configuration in our study for a channel length of 10nm of a double gate SiNR TFET. Source and drain are 10nm each. Our default SiNR width is ~4nm providing a band gap of 1.42eV. Top and bottom gate oxides of our studied TFET are 2nm of SiO2. The effective tight binding Hamiltonian is adopted from the work of Voon et al. [7] and is simulated using the simulation code proposed in [8] for Si-Si bond length of 2.25Å and hoping integral of -6.43eV with -1.12eV correction at the SiNR edges [7]. The n+-type source and p+-type drain are doped with a molecular fraction of 0.001. A drain source voltage (VDS) of 0.3V is considered in this work. The studied SiNR TFET provides an on/off current ratio of ~107 with an average steep subthreshold slope (SS) of 6mV/decade for VDS=0.3V. A record low ~0.75x10-11pW/μm off-state leakage power is estimated. We have found that the leakage level increases as the supply voltage increases. The off-state leakage current increases to 0.6pA/μm as VDS increases from 0.3V to 0.95V. As the width of SiNR increases and the corresponding band gap decreases, leakage current also increases at small band gap with a reduction in on/off current ratio. The steep subthreshold slope of our studied SiNR TFET suits low power operation. With a suitable high-k dielectric and low gate oxide thickness, on-state drive current can be improved. Performance of SiNR TFET is also compared with ITRS projected high performance (HP) requirements of 2026 nMOSFET where SiNR TFET exceeds the performance of 2026 nMOSFET by 1014 times less power dissipation at 103 times higher on/off current ratio. Acknowledgement: Part of the work is supported by the United States Air Force Research Laboratory under agreement number FA9453-10-1-0002. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon.

Spin–orbit interaction in bent carbon nanotubes: resonant spin transitions

We develop an effective tight-binding Hamiltonian for spin–orbit (SO) interaction in bent carbon nanotubes (CNT) for the electrons forming the π bonds between the nearest neighbor atoms. We account for the bend of the CNT and the intrinsic spin–orbit interaction which introduce mixing of π and σ bonds between the pz orbitals along the CNT. The effect contributes to the main origin of the SO coupling—the folding of the graphene plane into the nanotube. We discuss the bend-related contribution of the SO coupling for resonant single-electron spin and charge transitions in a double quantum dot. We report that although the effect of the bend-related SO coupling is weak for the energy spectra, it produces a pronounced increase of the spin transition rates driven by an external electric field. We find that spin-flipping transitions driven by alternate electric fields have usually larger rates when accompanied by charge shift from one dot to the other. Spin-flipping transition rates are non-monotonic functions of the driving amplitude since they are masked by stronger spin-conserving charge transitions. We demonstrate that the fractional resonances—counterparts of multiphoton transitions for atoms in strong laser fields—occurring in electrically controlled nanodevices already at moderate ac amplitudes—can be used to maintain the spin-flip transitions.

Strain-induced topological insulator phase and effective magnetic interactions in Li2IrO3

We present an effective tight-binding Hamiltonian for Li${}_{2}$IrO${}_{3}$ based on maximally localized Wannier functions for states near the Fermi level as obtained from first-principles electronic structure calculations. The majority of the Wannier orbitals are positioned on the center site with dominant ${j}_{\mathrm{eff}}=1/2$ character, while relatively small ${j}_{\mathrm{eff}}=3/2$ tails lie on the three nearest-neighbor sites. Interestingly, the spin quantization axis of the ${j}_{\mathrm{eff}}=1/2$ components deviates from the local octahedral axis and points toward the nearest-neighbor Ir direction. In our tight-binding model, there are relatively strong next-nearest- and the third-nearest-neighbor hopping terms within the two-dimensional Ir honeycomb lattice in addition to the relatively small but significant interlayer hopping terms. The ratio between the nearest-neighbor and the third-nearest-neighbor hoppings, which can be controlled by the lattice strain, plays a critical role in determinating the ${Z}_{2}$-invariant character of Li${}_{2}$IrO${}_{3}$. From our tight-binding model, we also derive an effective Hamiltonian and its parameters for the magnetic exchange interactions. Due to the complex spin-dependent next-nearest-neighbor hopping terms, our pseudospin Hamiltonian includes significant next-nearest-neighbor antiferromagnetic Kitaev terms as well as Dzyaloshinskii-Moriya and Heisenberg interactions. From our model Hamiltonian we estimate classical energies of collinear magnetic configurations as functions of the Hund's coupling of the Ir atom, from which zigzag-type magnetic order gives the lowest energy.

Localised Wannier orbital basis for the Mott insulators GaV4S8 and GaTa4Se8

We study the electronic properties of GaV4S8 (GVS) and GaTa4Se8 (GTS), two distant members within the large family of chalcogenides AM4X8, with A = {Ga, Ge}, M = {V, Nb, Ta, Mo} and X = {S, Se}. While all these compounds are Mott insulators, their ground states show many types of magnetic order, with GVS being ferromagnetic and GTS non-magnetic. Based on their band structures, calculated with density functional theory methods, we compute an effective tight-binding Hamiltonian in a localised Wannier basis set, for each of the two compounds. The localised orbitals provide a very accurate representation of the band structure, with hopping amplitudes that rapidly decrease with distance. We estimate the superexchange interactions and show that the Coulomb repulsion with Hund's coupling may account the for the different ground states observed in GVS and GTS. Our localised Wannier basis provides a starting point for realistic dynamical mean-field theory studies of strong-correlation effects in this family compounds.

Effective tight-binding model for the iron-vacancy-orderedAyFe1.6Se2

We investigate the electronic structure of the ternary iron selenide K${}_{y}$Fe${}_{1.6}$Se${}_{2}$ by considering the spatial symmetry of the $\sqrt{5}\ifmmode\times\else\texttimes\fi{}\sqrt{5}$ vacancy-ordered structure. Based on three orbitals of ${t}_{2g}$, which are believed to play major physics in iron-based superconductors, an effective two-dimensional tight-binding Hamiltonian is constructed with the vacancy-ordered structure being explicitly included. It is shown that the constructed band model, when combined with generalized Hubbard interactions, yields a spin susceptibility that exhibits both the block-checkerboard antiferromagnetism instability and the stripe antiferromagnetism instability. In particular, for large Hund's rule couplings, the block-checkerboard antiferromagnetism wins over the stripe antiferromagnetism, in agreement with the observation in experiments. We argue that such a model with correct symmetry and Fermi surface structures should be the starting point to model K${}_{y}$Fe${}_{1.6}$Se${}_{2}$. The spin fluctuations at $\mathbf{q}=(\ensuremath{\pi},\ensuremath{\pi}$) suggest that interblock fluctuations of spins might play an important role in the mechanism of superconductivity occurring in this system.

High Chern number quantum anomalous Hall phases in single-layer graphene with Haldane orbital coupling

We investigate possible phase transitions among the different quantum anomalous Hall (QAH) phases in a zigzag graphene ribbon under the influence of the exchange field. The effective tight-binding Hamiltonian for graphene is made up of the hopping term, the Kane-Mele and Rashba spin-orbit couplings as well as the Haldane orbital term. We find that the variation of the exchange field results in bulk gap-closing phenomena and phase transitions occur in the graphene system. If the Haldane orbital coupling is absent, the phase transition between the chiral (anti-chiral) edge state $\nu=+2$ ($\nu=-2$) and the pseudo-quantum spin Hall state ($\nu=0$) takes place. Surprisingly, when the Haldane orbital coupling is taken into account, an intermediate QSH phase with two additional edge modes appears in between phases $\nu=+2$ and $\nu=-2$. This intermediate phase is therefore either the hyper-chiral edge state of high Chern number $\nu=+4$ or anti-hyper-chiral edge state of $\nu=-4$ when the direction of exchange field is reversed. We present the band structures, edge state wave functions and current distributions of the different QAH phases in the system. We also report the critical exchange field values for the QAH phase transitions.

First-principles calculation of transition-metal impurities in LaFeAsO

We present a systematic ab initio study based on density-functional calculations to understand impurity effects in iron-based superconductors. Effective tight-binding Hamiltonians for the d-bands of LaFeAsO with various transition-metal impurities such as Mn, Co, Ni, Zn, and Ru are constructed using maximally-localized Wannier orbitals. Local electronic structures around the impurity are quantitatively characterized by their onsite potential and transfer hoppings to neighboring sites. We found that the impurities are classified into three groups according to the derived parameters: For Mn, Co, and Ni, their impurity-3d levels measured from the Fe-3d level are nearly 0.3 eV, -0.3 eV, and -0.8 eV, respectively, while, for the Zn case, the d level is considerably deep as -8 eV. For the Ru case, although the onsite-level difference is much smaller as O(0.1) eV, the transfer integrals around the impurity site are larger than those of the pure system by 20% \sim 30%, due to the large spatial spread of the Ru-4d orbitals. We also show that, while excess carriers are tightly trapped around the impurity site (due to the Friedel sum rule), there is a rigid shift of band structure near the Fermi level, which has the same effect as carrier doping.

Structural stability versus conformational sampling in biomolecular systems: Why is the charge transfer efficiency in G4-DNA better than in double-stranded DNA?

The electrical conduction properties of G4-DNA are investigated using a hybrid approach, which combines electronic structure calculations, molecular dynamics (MD) simulations, and the formulation of an effective tight-binding model Hamiltonian. Charge transport is studied by computing transmission functions along the MD trajectories. Though G4-DNA is structurally more stable than double-stranded DNA (dsDNA), our results strongly suggest that the potential improvement of the electrical transport properties in the former is not necessarily related to an increased stability, but rather to the fact that G4 is able to explore in its conformational space a larger number of charge-transfer active conformations. This in turn is a result of the non-negligible interstrand matrix elements, which allow for additional charge transport pathways. The higher structural stability of G4 can however play an important role once the molecules are contacted by electrodes. In this case, G4 may experience weaker structural distortions than dsDNA and thus preserve to a higher degree its conduction properties.

How grain boundaries limit supercurrents in high-temperature superconductors

The interface properties of high-temperature cuprate superconductors have been of interest for many years, and play an essential role in Josephson junctions, superconducting cables, and microwave electronics. In particular, the maximum critical current achievable in high-Tc wires and tapes is well known to be limited by the presence of grain boundaries, regions of mismatch between crystallites with misoriented crystalline axes. In studies of single, artificially fabricated grain boundaries the striking observation has been made that the critical current Jc of a grain boundary junction depends exponentially on the misorientation angle. Until now microscopic understanding of this apparently universal behavior has been lacking. We present here the results of a microscopic evaluation based on a construction of fully 3D YBCO grain boundaries by molecular dynamics. With these structures, we calculate an effective tight-binding Hamiltonian for the d-wave superconductor with a grain boundary. The critical current is then shown to follow an exponential suppression with grain boundary angle. We identify the buildup of charge inhomogeneities as the dominant mechanism for the suppression of the supercurrent.