Tight-binding Hamiltonian Research Articles

Spin-transfer Torque and Topological Changes of Magnetic Textures

The electric manipulation of magnetic textures in nanostructures, important for applications in spintronics, can be realized through the spin-transfer torque mechanism: a spin-polarized current can modify the magnetization of skyrmions and magnetic vortices, and eventually change the topology of the magnetization. The spin-transfer torque and the intrinsic space and time scales of the topological changes are essentially quantum mechanical. We model the interaction between itinerant and fixed spins with a simple tight-binding hamiltonian in a square lattice. The dynamics is described by the Schrodinger equation for the electrons and the Landau-Lifshitz equation for the evolution of the magnetic texture. We investigate the phenomenology of the topological change of a Belavin-Polyakov skyrmion under the action of a spin-polarized current and show that adding an exchange dissipation term, regularizes the transition towards a ferromagnetic state.

Structure of vortex-bound states in spin-singlet chiral superconductors

We investigate the structure of vortex-bound states in spin-singlet chiral superconductors with ($d_{x^2-y^2} \pm i d_{xy}$)-wave and ($d_{xz} \pm id_{yz}$)-wave pairing symmetries. It is found that vortices in the ($d_{xz} \pm id_{yz}$)-wave state bind zero-energy states which are dispersionless along the vortex line, forming a doubly degenerate Majorana flat band. Vortex-bound states of ($d_{x^2-y^2} \pm i d_{xy}$)-wave superconductors, on the other hand, exist only at finite energy. Using exact diagonalization and analytical solutions of tight-binding Bogoliubov-de Gennes Hamiltonians, we compute the energy spectrum of the vortex-bound states and the local density of states around the vortex and antivortex cores. We find that the tunneling conductance peak of the vortex is considerably broader than that of the antivortex. This difference can be used as a direct signature of the chiral order parameter symmetry.

Combined first-principles and model Hamiltonian study of the perovskite seriesRMnO3(R=La,Pr,Nd,Sm,Eu, andGd)

We merge advanced ab initio schemes (standard density functional theory, hybrid functionals and the GW approximation) with model Hamiltonian approaches (tight-binding and Heisenberg Hamiltonian) to study the evolution of the electronic, magnetic and dielectric properties of the manganite family RMnO3 (R = La, Pr, Nd, Sm, Eu and Gd). The link between first principles and tight-binding is established by downfolding the physically relevant subset of 3d bands with e_g character by means of maximally localized Wannier functions (MLWFs) using the VASP2WANNIER90 interface. The MLWFs are then used to construct a tight-binding Hamiltonian. The dispersion of the TB e_g bands at all levels are found to match closely the MLWFs. We provide a complete set of TB parameters which can serve as guidance for the interpretation of future studies based on many-body Hamiltonian approaches. In particular, we find that the Hund's rule coupling strength, the Jahn-Teller coupling strength, and the Hubbard interaction parameter U remain nearly constant for all the members of the RMnO3 series, whereas the nearest neighbor hopping amplitudes show a monotonic attenuation as expected from the trend of the tolerance factor. Magnetic exchange interactions, computed by mapping a large set of hybrid functional total energies onto an Heisenberg Hamiltonian, clarify the origin of the A-type magnetic ordering observed in the early rare-earth manganite series as arising from a net negative out-of-plane interaction energy. The obtained exchange parameters are used to estimate the Neel temperature by means of Monte Carlo simulations. The resulting data capture well the monotonic decrease of the ordering temperature down the R series, in agreement with experiments.

Spin-dependent Seebeck effect in Aharonov–Bohm rings with Rashba and Dresselhaus spin–orbit interactions

We theoretically investigate the spin-dependent Seebeck effect in an Aharonov–Bohm mesoscopic ring in the presence of both Rashba and Dresselhaus spin–orbit interactions under magnetic flux perpendicular to the ring. We apply the Green's function method to calculate the spin Seebeck coefficient employing the tight-binding Hamiltonian. It is found that the spin Seebeck coefficient is proportional to the slope of the energy-dependent transmission coefficients. We study the strong dependence of spin Seebeck coefficient on the Fermi energy, magnetic flux, strength of spin–orbit coupling, and temperature. Maximum spin Seebeck coefficients can be obtained when the strengths of Rashba and Dresselhaus spin–orbit couplings are slightly different. The spin Seebeck coefficient can be reduced by increasing temperature and disorder.

Magnetism and spin transport of carbon chain between armchair graphene nanoribbon electrodes

The magnetic and spin transport properties of a carbon chain between two armchair graphene nanoribbon (AGNR) electrodes were studied using tight-binding Hamiltonian, mean-field Hubbard model and Landauer–Butikker formalism. The results showed that only odd-numbered carbon chains show intrinsic magnetic moments in chain–graphene junctions. It was also found that the electronic, magnetic and spin transport properties of carbon chain–graphene junctions strongly depend on the position and the length of the carbon chains between AGNR electrodes. Interestingly, we found a fully spin-polarized transmission near the Fermi energy in all odd-numbered carbon chain–graphene junctions, regardless of their lengths and without any magnetic field and magnetic electrodes.

Single-Site Resolution Detection of Methylation in DNA with Graphene Nanopores

Epigenetic modification of DNA where methyl groups are added at the 5-carbon position of cytosine is known as DNA methylation. It is associated with carcinogenesis, thus capable of serving as markers for detection of cancer. Nanopore analytics provides an easier and quicker route to detect methylated sites by avoiding complicated bisulfite treatment and polymerase chain reaction amplification. Graphene has a thickness of a single atom, thereby holding the potential to detect the methylation at single-site resolution. In this work, we use a self-consistent Poisson-Boltzmann formalism to simulate the translocation of methyl-CpG (MBD) proteins bound to a DNA molecule in a graphene nanopore, and detect the methylated sites along the DNA strand by computing both ionic current using molecular dynamics simulations and transverse sheet current via tight binding Hamiltonian based none-equilibrium Green's function approach.1 Evident dips are recorded in the ionic current trace through the nanopore for each methylation site, as expected, suggesting a single-site resolution. The graphene membrane with added quantum point contacts, by means of transverse sheet currents, can also detect the methylated site through local jumps in the variance of the measured transverse current. The proposed measurement strategy allows for real time, fast and high resolution DNA methylation detection.21. Girdhar, A., Sathe, C., Schulten, K., & Leburton, J. P. (2013). Graphene quantum point contact transistor for DNA sensing. Proceedings of the National Academy of Sciences, 110(42), 16748-16753.2. Sarathy, A., Qiu, H., Schulten, K., & Leburton, J. P. Single-site detection of methylation in DNA with graphene nanopores. To be published.

Donor-assisted resonant electron tunneling in double-barrier heterostructures under tilted magnetic fields: A theoretical study

A theoretical study of the current-voltage characteristics of a double-barrier heterostructure doped with a layer of shallow donors in the middle of the well and subjected to a magnetic field tilted with respect to the growth direction is reported. The parent materials are assumed to possess simple cubic lattices, the electronic structure of the system is modeled by means of a one-band tight-binding Hamiltonian, and the current is evaluated employing the Keldysh nonequilibrium formalism. The results reveal the magnetocompression of the donor wavefunction, in good qualitative agreement with the experimental report of Patané et al [Phys Rev Lett 105 236804 (2010)].

Lloyd-model generalization: Conductance fluctuations in one-dimensional disordered systems.

We perform a detailed numerical study of the conductance G through one-dimensional (1D) tight-binding wires with on-site disorder. The random configurations of the on-site energies ε of the tight-binding Hamiltonian are characterized by long-tailed distributions: For large ε, P(ε)∼1/ε^{1+α} with α∈(0,2). Our model serves as a generalization of the 1D Lloyd model, which corresponds to α=1. First, we verify that the ensemble average 〈-lnG〉 is proportional to the length of the wire L for all values of α, providing the localization length ξ from 〈-lnG〉=2L/ξ. Then, we show that the probability distribution function P(G) is fully determined by the exponent α and 〈-lnG〉. In contrast to 1D wires with standard white-noise disorder, our wire model exhibits bimodal distributions of the conductance with peaks at G=0 and 1. In addition, we show that P(lnG) is proportional to G^{β}, for G→0, with β≤α/2, in agreement with previous studies.

Accurate tight-binding Hamiltonian matrices fromab initiocalculations: Minimal basis sets

Projection of Bloch states obtained from quantum-mechanical calculations onto atomic orbitals is the fastest scheme to construct ab-initio tight-binding Hamiltonian matrices. However, the presence of spurious states and unphysical hybridizations of the tight-binding eigenstates has hindered the applicability of this construction. Here we demonstrate that those spurious effects are due to the inclusion of Bloch states with low projectability. The mechanism for the formation of those effects is derived analytically. We present an improved scheme for the removal of the spurious states which results in an efficient scheme for the construction of highly accurate ab-initio tight-binding Hamiltonians.

Double gate graphene nanoribbon field effect transistor with electrically induced junctions for source and drain regions

In this paper a novel graphene nanoribbon transistor with electrically induced junction for source and drain regions is proposed. An auxiliary junction is used to form electrically induced source and drain regions beside the main regions. Two parts of same metal are implemented at both sides of the main gate region. These metals which act as side gates are connected to each other to form auxiliary junction. A fixed voltage is applied on this junction during voltage variation on other junctions. Side metals have smaller workfunction than the middle one. Tight-binding Hamiltonian and nonequilibrium Green's function formalism are used to perform atomic scale electronic transport simulation. Due to the difference in metals workfunction, additional gates create two steps in potential profile. These steps increase horizontal distance between conduction and valance bands at gate to drain/source junction and consequently lower band to band tunneling probability. Current ratio and subthreshold swing improved at different channel lengths. Furthermore, device reliability is improved where electric field at drain side of the channel is reduced. This means improvement in leakage current, hot electron effect behavior and breakdown voltage. Application to multi-input logic gates shows higher speed and smaller power delay product in comparison with conventional platform.

Edge magnetization in Bernal-stacked trilayer zigzag graphene nanoribbons

We have used a tight-binding Hamiltonian of an ABA-stacked trilayer zigzag graphene nanoribbon with β-alignment edges to study the edge magnetizations. Our model includes the effect of the intralayer next-nearest-neighbor hopping, the interlayer hopping responsible for the trigonal warping and the interaction between electrons, which is considered by a single band Hubbard model in the mean field approximation. Firstly, in the neutral system we analyzed the two magnetic states in which both edge magnetizations reach their maximum value; the first one is characterized by an intralayer ferromagnetic coupling between the magnetizations at opposite edges, whereas in the second state that coupling is antiferromagnetic. The band structure, the location of the edge-state bands and the local density of states resolved in spin are calculated in order to understand the origins of the edge magnetizations. We have also introduced an electron doping so that the number of electrons in the ribbon unit cell is higher than in neutral case. As a consequence, we have obtained magnetization steps and charge accumulation at the edges of the sample, which are caused by the edge-state flat bands.

Spin relaxation in hydrogenated graphene

We calculate the spin transport of hydrogenated graphene using the Landauer-B\"uttiker formalism with a spin-dependent tight-binding Hamiltonian. The advantages of using this method is that it simultaneously gives information on sheet resistance and localization length as well as spin relaxation length. Furthermore, the Landauer-B\"uttiker formula can be computed very efficiently using the recursive Green's function technique. Previous theoretical results on spin relaxation time in hydrogenated graphene have not been in agreement with experiments. Here, we study magnetic defects in graphene with randomly aligned magnetic moments, where interference between spin-channels is explicitly included. We show that the spin relaxation length and sheet resistance scale nearly linearly with the impurity concentration. Moreover, the spin relaxation mechanism in hydrogenated graphene is Markovian only near the charge neutrality point or in the highly dilute impurity limit.

Ab initio tight-binding Hamiltonian for transition metal dichalcogenides

We present an accurate \textit{ab-initio} tight-binding hamiltonian for the transition-metal dichalcogenides, MoS$_2$, MoSe$_2$, WS$_2$, WSe$_2$, with a minimal basis (the \textit{d} orbitals for the metal atoms and \textit{p} orbitals for the chalcogen atoms) based on a transformation of the Kohn-Sham density function theory (DFT) hamiltonian to a basis of maximally localized Wannier functions (MLWF). The truncated tight-binding hamiltonian (TBH), with only on-site, first and partial second neighbor interactions, including spin-orbit coupling, provides a simple physical picture and the symmetry of the main band-structure features. Interlayer interactions between adjacent layers are modeled by transferable hopping terms between the chalcogen \textit{p} orbitals. The full-range tight-binding hamiltonian (FTBH) can be reduced to hybrid-orbital k $\cdot$ p effective hamiltonians near the band extrema that captures important low-energy excitations. These \textit{ab-initio} hamiltonians can serve as the starting point for applications to interacting many-body physics including optical transitions and Berry curvature of bands, of which we give some examples.

Transport of quantum excitations coupled to spatially extended nonlinear many-body systems

The role of noise in the transport properties of quantum excitations is a topic of great importance in many fields, from organic semiconductors for technological applications to light-harvesting complexes in photosynthesis. In this paper we study a semi-classical model where a tight-binding Hamiltonian is fully coupled to an underlying spatially extended nonlinear chain of atoms. We show that the transport properties of a quantum excitation are subtly modulated by (i) the specific type (local versus non-local) of exciton–phonon coupling and by (ii) nonlinear effects of the underlying lattice. We report a non-monotonic dependence of the exciton diffusion coefficient on temperature, in agreement with earlier predictions, as a direct consequence of the lattice-induced fluctuations in the hopping rates due to long-wavelength vibrational modes. A standard measure of transport efficiency confirms that both nonlinearity in the underlying lattice and off-diagonal exciton–phonon coupling promote transport efficiency at high temperatures, preventing the Zeno-like quench observed in other models lacking an explicit noise-providing dynamical system.

Band Structure Effects in Extremely Scaled Silicon Nanowire MOSFETs With Different Cross Section Shapes

A multiscale simulation package based on ab initio calculation is used to study the band structure effects in extremely scaled gate-all-around silicon nanowire (SNW) MOSFETs with different cross-sectional shapes. All the interactions are computed directly from ab initio method without semiempirical parameters, and the effects of crystal atom relaxations and boundary atom dangling bond saturations are included intrinsically. The tight-binding Hamiltonian is obtained from ab initio results with maximally localized Wannier functions. The device performances are obtained with nonequilibrium Green’s function method. With this simulation flow, the band structure and its impacts on the device performance of SNWs with different cross-sectional shapes are studied. Simulation results show that the crystal relaxation has notable effects on the band structure with different cross-sectional shapes and sizes. The SNWs with triangular cross-sectional shape are very competitive due to a smaller average conductivity effective mass ascribed to the valley splitting at extremely scaled size.

Numerical Study of Spin-Dependent Transport Through a Magnetic Quantum Wire with Lattice Vacancy

The impact of lattice vacancy on the spin dependent transport properties of a magnetic-quantum wire (MQW) has been investigated. A simple tight binding Hamiltonian to describe the model is used, where the quantum wire is attached to two semi-infinite one-dimensional non-magnetic electrodes. Based on the Landauer–Buttiker formalism all the calculations are performed numerically which describe two-terminal conductance. The results suggest that in presence of vacancy the transmission reduces and vacancy creates quasilocalized states around zero energy (E f = 0). In order to investigate spin-filtering effect of (MQW), the degree of polarization in the presence and absences of vacancy has been studied. Also it is found that the effect of vacancy decreases when the size of MQW increases. The results show that a magnetic quantum wire can be used as a spin filter. The application of the predicted results may be useful in designing molecular spin-polarized transistors in the future.

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.

Spectral butterfly and electronic localization in rippled-graphene nanoribbons: Mapping onto effective one-dimensional chains

We report an exact map into one dimensional effective chains, of the tight-binding Hamiltonian for electrons in armchair and zigzag graphene nanoribbons with any uniaxial ripple. This mapping is used for studying the effect of uniaxial periodic ripples, taking into account the relative orientation changes between $\pi$ orbitals. Such effects are important for short wavelength ripples, while for long-wave ones, the system behaves nearly as strained graphene. The spectrum has a complex nature, akin to the Hofstadter butterfly with a rich localization behavior. Gaps at the Fermi level and dispersionless bands were observed, as well. The complex features of the spectrum arise as a consequence of the quasiperiodic or periodic nature of the effective one dimensional system. Some features of these systems are understandable by considering weakly coupled dimers. The eigenenergies of such dimers are highly degenerated and the net effect of the ripple can be seen as a perturbation potential that splits the energy spectrum. Several particular cases were analytically solved to understand such feature.

Bosonic Kondo-Hubbard model

We study, using quantum Monte-Carlo simulations, the bosonic Kondo-Hubbard model in a two dimensional square lattice. We explore the phase diagram and analyse the mobility of particles and magnetic properties. At unit filling, the transition from a paramagnetic Mott insulator to a ferromagnetic superfluid appears continuous, contrary to what was predicted with mean field. For double occupation per site, both the Mott insulating and superfluid phases are ferromagnetic and the transition is still continuous. Multiband tight binding Hamiltonians can be realized in optical lattice experiments, which offer not only the possibility of tuning the different energy scales over wide ranges, but also the option of loading the system with either fermionic or bosonic atoms.

Effective tight-binding model forMX2under electric and magnetic fields

We present a systematic method for developing a five band Hamiltonian for the metal d orbitals that can be used to study the effect of electric and magnetic fields on multilayer MX2 (M=Mo,W and X=S,Se) systems. On a hexagonal lattice of d orbitals, the broken inversion symmetry of the monolayers is incorporated via fictitious s orbitals at the chalcogenide sites. A tight-binding Hamiltonian is constructed and then downfolded to get effective d orbital overlap parameters using quasidegenerate perturbation theory. The steps to incorporate the effects of multiple layers, external electric and magnetic fields are also detailed. We find that an electric field produces a linear-k Rashba splitting around the Γ point, while a magnetic field removes the valley pseudospin degeneracy at the ±K points. Lastly, our model provides a simple tool to understand the recent experiments on electric and magnetic control of valley pseudospin in monolayer dichalcogendies.