Hopping Constant Research Articles

Two-dimensional extended Hubbard model at half-filling

We consider the extended Hubbard model on a two-dimensional square lattice at half-filling. The model is investigated using the strong coupling diagram technique. We sum infinite series of ladder diagrams allowing for full-scale charge and spin fluctuations and the actual short-range antiferromagnetic order for nonzero temperatures. In agreement with earlier results, we find the first-order phase transition in the charge subsystem occurring at v = v c ≳ U/4 with v and U the intersite and on-site Coulomb repulsion constants. The transition reveals itself in an abrupt sign change of a sharp maximum in the zero-frequency charge susceptibility at the corner of the Brillouin. States arising at the transition have alternating deviations of electron occupations from the mean value on neighboring sites. Due to fluctuations, these alternating occupation deviations have short-range order. For the considered parameters, such behavior is found for U ≲ 5t with t the hopping constant. For the insulating case U ≳ 6t, in which the transition is not observed, we find a continuous growth of the Mott gap with v. The evolution of the electron density of states with increasing v is also considered.

Exact solutions of topological superconductor model with Hubbard interactions

We study a two-dimensional model of topological superconductor with equal spin pairing and repulsive Hubbard interaction. When the pairing gap equals to the hopping constant, half of the spectrum of this model are flat bands, which makes this model exact solvable. The band structure and topological properties of the exact solutions of the interacting model are analyzed in details. It is found that the ground state corresponds to a staggered distribution of the conserved quantities.

Correlation dynamics of nitrogen vacancy centers located in crystal cavities

In this contribution, we investigate the bipartite non-classical correlations (NCCs) of a system formed by two nitrogen-vacancy (N-V) centers placed in two spatially separated single-mode nanocavities inside a planar photonic crystal (PC). The physical system is mathematically modeled by time-dependent Schrödinger equation and analytically solved. The bipartite correlations of the two N-V centers and the two-mode cavity have been analyzed by skew information, log-negativity, and Bell function quantifiers. We explore the effects of the coupling strength between the N-V-centers and the cavity fields as well as the cavity-cavity hopping constant and the decay rate on the generated correlation dynamics. Under some specific parameter values, a large amount of quantum correlations is obtained. This shows the possibility to control the dynamics of the correlations for the NV-centers and the cavity fields.

A study of the poly(dA)-poly(dT) DNA electric field-dependence: density of states (DOS) analysis

Study of poly(dA)-poly(dT) DNA molecule electronic structure, by analysing its density of states (DOS), had been conducted. This research employed Green’s function method as tool to determine electron DOS of the DNA numerically. Electric field that was applied along z-axis is used as perturbation to modify electron hopping constant between sites in the molecule. In order to include electric field in the calculation, Miller-Abraham formula was used. Medium interaction with backbone molecules was considered as well within the calculation in the form of backbone disorder. By increasing electric field, the band in electron DOS spectrum appeared to become narrower and several states experience the decrement of DOS.

I-V characteristics on G4 DNA molecule: Electric field and current dependent hopping amplitude model

We study the charge transport property of G4 DNA molecule by calculating the I-V characteristics at several temperatures. The G4 DNA we used consists of 32 G-tetrads built from four guanine bases and is contacted to metallic electrodes at both ends. The molecule is represented mathematically by using tight binding Hamiltonian model. Miller-abrahams scheme is used in calculating electron hopping constant under electric field which is applied along the molecular axis of DNA. Temperature is considered in the model by assuming twisting angles are distributed following Gaussian distribution. The current as voltage function is calculated using Landauer-Buttiker formalism from transmission probabilities. The result show that twisting motion due thermal agitation weakens the effect of electric field.

Influence of magnetic and electric field on I-V characteristic of the G4 DNA molecule

The I-V characteristics of G4 DNA molecule in applied magnetic and electric fields has been calculated. We use DNA molecule in the form of stacked of 32 guanine quadruplex (G4) structures. The DNA molecule is contacted to the metallic electrode at both ends. The system under investigation is modeled using tight-binding Hamiltonian approach. Magnetic and electric field affects electron hopping constant following Peirels Phase Factor and Miller-Abraham, respectively. The result shows slight current increment with the magnetic field and current increment with electric fields after certain voltage value.

Manifestations of spin and charge fluctuations in spectra of the Hubbard model

The influence of long-range spin and charge fluctuations on spectra of the two-dimensional (2D) fermionic Hubbard model is considered using the strong coupling diagram technique (SCDT). Infinite sequences of diagrams containing ladder inserts, which describe the interaction of electrons with these fluctuations, are summed, and obtained equations are self-consistently solved for the range of Hubbard repulsions 4t [Formula: see text]U [Formula: see text] 8t and temperatures 0.3t [Formula: see text] T [Formula: see text] t with t the intersite hopping constant. It was found that a metal–insulator transition curve goes from larger U and T to smaller values of these parameters. The temperature decrease causes the transition to the long-range antiferromagnetic order. It is responsible for the splitting out of a narrow band from a Hubbard subband with doping for U = 8t and low T. This segregated band is located near the Fermi level and forms a pseudogap here.

Influence of spin and charge fluctuations on spectra of the two-dimensional Hubbard model

The influence of spin and charge fluctuations on spectra of the two-dimensional fermionic Hubbard model is considered using the strong coupling diagram technique. Infinite sequences of diagrams containing ladder inserts, which describe the interaction of electrons with these fluctuations, are summed, and obtained equations are self-consistently solved for the ranges of Hubbard repulsions , temperatures and electron concentrations with t the intersite hopping constant. For all considered U the system exhibits a transition to the long-range antiferromagnetic order at . At the same time no indication of charge ordering is observed. Obtained solutions agree satisfactorily with results of other approaches and obey moments sum rules. In the considered region of the U-T plane, the curve separating metallic solutions passes from at the highest temperatures to U = 2t at for half-filling. If only short-range fluctuations are allowed for the remaining part of this region is occupied by insulating solutions. Taking into account long-range fluctuations leads to strengthening of maxima tails, which transform a part of insulating solutions into bad-metal states. For low T, obtained results allow us to trace the gradual transition from the regime of strong correlations with the pronounced four-band structure and well-defined Mott gap for to the Slater regime of weak correlations with the spectral intensity having a dip along the boundary of the magnetic Brillouin zone due to an antiferromagnetic ordering for . For and doping leads to the occurrence of a pseudogap near the Fermi level, which is a consequence of the splitting out of a narrow band from a Hubbard subband. Obtained spectra feature waterfalls and Fermi arcs, which are similar to those observed in hole-doped cuprates.

Modulational Instability and Quantum Discrete Breather States of Cold Bosonic Atoms in a Zig-Zag Optical Lattice

A theoretical study on modulational instability and quantum discrete breather states in a system of cold bosonic atoms in zig-zag optical lattices is presented in this work. The time-dependent Hartree approximation is employed to deal with the multiple body problem. By means of a linear stability analysis, we analytically study the modulational instability, and estimate existence conditions of the bright stationary localized solutions for different values of the second-neighbor hopping constant. On the other hand, we get analytical bright stationary localized solutions, and analyze the influence of the second-neighbor hopping on their existence conditions. The predictions of the modulational instability analysis are shown to be reliable. Using these stationary localized single-boson wave functions, the quantum breather states corresponding to the system with different types of nonlinearities are constructed.

Twisting Motion Frequency Dependent I-V Characteristics of 102 Base Pairs Poly(dG)-Poly(dC) DNA Molecule

The I-V characteristic of 102 base pair Poly(dG)-Poly(dC) DNA molecule have been calculated for several base pairs twisting motion frequencies. The calculation is carried out on doubled-stranded DNA model sandwiched in between two metallic electrodes. The effect is studied by taking into account twisting angle dependent on-site energy and hopping constant in the tight binding Hamiltonian of double-strand DNA model. We use semi-empirical Slater-Koster theory in the twisting angle dependent intra- and inter-strand hopping constant. We consider the temperature dependent sugar-phosphate backbone on-site energy by employing random energy disorder using uniform distribution function. The standard deviation of twisting angle is obtained by assuming that the average kinetic energy of twisting motions is proportional to system temperature. The transfer and scattering matrix methods are used simultaneously in calculating the transmission probability of charge on the molecule. We choose the contacts between molecule and both electrodes such that the main features of transport properties of the molecule do not change much by the presence of metallic electrodes. By assuming the voltage drops symmetrically at the contacts, Landauer-Buttiker Formalism is used in calculating the I-V characteristic of the molecule from transmission probability. The results show that the magnitude of current increases by twisting motion frequency increment. Larger current magnitude increment is observed at higher voltage. The influence of twisting motion frequency on the I-V characteristic is stronger at higher temperature, in the range of considered temperature.

The effect of twisting motion dependent diagonal hopping on the I-V characteristics of poly(dG)-poly(dC) DNA molecule

The effect of twisting motion dependent diagonal hopping on the I-V characteristic of Poly(dG)-Poly(dC) DNA molecule has been studied. Twisting angle dependent hopping constant is model using semi-empirical Slater-Koster theory. The I-V characteristic of DNA molecule is calculated from transmission probability using Landauer-Buttiker formalism by assuming symmetric voltage drop at the contacts. The transmission probability of charge on the molecule is calculated using transfer and scattering matrix methods, simultaneously. The calculation is carried out on 32 base pairs doubled-stranded DNA molecule model sandwiched in between two metallic electrodes. The results show that at low voltage the magnitude of current is not influenced much by the change of diagonal hopping term caused by base pair twisting motion. Larger influenced is observed at higher voltages, after decreases by increasing the coupling parameter of vibration and diagonal hopping constant up to some value, current increases. This trend is observed in the I-V characteristic of DNA molecule for all frequencies and temperatures used. Lower twisting motion frequency shows larger influences of diagonal hopping term on the current than the one at higher frequencies.

Strong coupling diagram technique for the three-band Hubbard model

Strong coupling diagram technique equations are derived for hole Green’s functions of the three-band Hubbard model, which describes Cu–O planes of high-[Formula: see text] cuprates. The equations are self-consistently solved in the approximation, in which the series for the irreducible part in powers of the oxygen–copper hopping constant is truncated to two lowest-order terms. For parameters used for hole-doped cuprates, the calculated energy spectrum consists of lower and upper Hubbard subbands of predominantly copper nature, oxygen bands with a small admixture of copper states and the Zhang–Rice states of mixed nature, which are located between the lower Hubbard subband and oxygen bands. The spectrum contains also pseudogaps near transition frequencies of Hubbard atoms on copper sites.

Exciton-phonon system on a star graph: A perturbative approach.

Based on the operatorial formulation of the perturbation theory, the properties of an exciton coupled with optical phonons on a star graph are investigated. Within this method, the dynamics is governed by an effective Hamiltonian, which accounts for exciton-phonon entanglement. The exciton is dressed by a virtual phonon cloud whereas the phonons are clothed by virtual excitonic transitions. In spite of the coupling with the phonons, it is shown that the energy spectrum of the dressed exciton resembles that of a bare exciton. The only differences originate in a polaronic mechanism that favors an energy shift and a decay of the exciton hopping constant. By contrast, the motion of the exciton allows the phonons to propagate over the graph so that the dressed normal modes drastically differ from the localized modes associated to bare phonons. They define extended vibrations whose properties depend on the state occupied by the exciton that accompanies the phonons. It is shown that the phonon frequencies, either red shifted or blue shifted, are very sensitive to the model parameter in general, and to the size of the graph in particular.

Dynamics of a narrow-band exciton coupled with optical phonons: A time-convolutionless master-equation approach

A time-convolutionless master equation is established for studying the dynamics of a narrow-band exciton coupled with optical phonons. Within the nonadiabatic weak-coupling limit, the diagonal hypothesis works quite well so that the exciton-phonon dynamics is mainly governed by the so-called time-dependent dephasing function. It has been shown that the dephasing function tends to zero by exhibiting damped oscillations that characterize a series of dephasing-rephasing mechanisms. Indeed, the correlation time of the exciton-phonon interaction is defined as the time needed to the exciton to cover a few lattice sites. Therefore this correlation time is sufficiently long so that the system dynamics remains sensitive to the coherent nature of the lattice vibrations. Because the phonon memory recurs periodically, the exciton experiences a series of dephasing-rephasing processes. Although each rephasing does not exactly compensate the previous dephasing, the coherence survives. Consequently, the exciton keeps its wavelike nature and a coherent energy transfer occurs according to an effective hopping constant smaller than the bare hopping constant.

A variant transfer matrix method suitable for transport through multi-probesystems

We have developed a variant transfer matrix method that is suitable for transportthrough multi-probe systems. Using this method, we have numerically studiedthe quantum spin Hall effect (QSHE) on 2D graphene with both intrinsic(Vso) andRashba (Vr) spin–orbit (SO) couplings. The integer QSHE arises in the presence of intrinsicSO interaction and is gradually destroyed by the Rashba SO interaction anddisorder fluctuation. We have numerically determined the phase boundariesseparating integer QSHE and spin Hall liquid. We have found that whenVso≥0.2t with t the hopping constant the energy gap needed for the integer QSHE is the largest satisfying|E|<t. Forsmaller Vso the energy gap decreases linearly. In the presence of Rashba SO interaction ordisorders, the energy gap diminishes. With Rashba SO interaction the integerQSHE is robust at the largest energy within the energy gap while at the smallestenergy within the energy gap the integer QSHE is insensitive to the disorder.

Fast energy transfer mediated by multi-quanta bound states in a nonlinear quantum lattice

By using a Generalized Hubbard model for bosons, the energy transfer in a nonlinear quantum lattice is studied, with special emphasis on the interplay between local and nonlocal nonlinearity. For a strong local nonlinearity, it is shown that the creation of v quanta on one site excites a soliton band formed by bound states involving v quanta trapped on the same site. The energy is first localized on the excited site over a significant timescale and then slowly delocalizes along the lattice. When the nonlocal nonlinearity increases, a faster dynamics occurs and the energy propagates more rapidly along the lattice. Nevertheless, the larger is the number of quanta, the slower is the dynamics. However, it is shown that when the nonlocal nonlinearity reaches a critical value, the lattice suddenly supports a very fast energy propagation whose dynamics is almost independent of the number of quanta. The energy is transfered by specific bound states formed by the superimposition of states involving v − p quanta trapped on one site and p quanta trapped on the nearest neighbour sites, with p = 0 , … , v − 1 . These bound states behave as independent quanta and they exhibit a dynamics which is insensitive to the nonlinearity and controlled by the single quantum hopping constant.

Vibrons in a one-dimensional lattice of hydrogen-bonded peptide units: Influence of the inhomogeneous mass distribution in the amino acid sequence

The influence of the inhomogeneous mass distribution in the amino acid sequence on amide-I vibrons in alpha-helices is studied within the small polaron approach in a one-dimensional (1D) model. It is shown that inhomogeneities in the sequence favor a randomness in the polaron Hamiltonian via the dressing mechanism. The polaron dynamics is thus described by a 1D tight binding model with correlated off-diagonal disorder. At low temperature, the polaron hopping constants exhibit small fluctuations around a large average value so that the polaron Hamiltonian appears weakly disordered. Extended states occur over a wide range of energies around the band center whereas the states close to the band edges appear localized. By contrast, at biological temperature, a stronger disorder takes place which originates in a drastic decrease of the average hopping constant. The number of localized states increases but few states close to the band center exhibit a localization length about to or greater than the lattice size. The extended nature of these latter states is attributed to the occurrence of short range correlations in the random hopping constants.

Vibron-polaron critical localization in a finite size molecular nanowire

The small polaron theory is applied to describe the vibron dynamics in an adsorbed nanowire with a special emphasis onto finite size effects. It is shown that the finite size of the nanowire discriminates between side molecules and core molecules which experience a different dressing mechanism. Moreover, the inhomogeneous behavior of the polaron hopping constant is established and it is shown that the core hopping constant depends on the lattice size. However, the property of a lattice with translational invariance is recovered when the size of the nanowire is greater than a critical value. Finally, it is pointed out that these features yield the occurrence of high energy localized states in which both the nature and the number are summarized in a phase diagram in terms of the relevant parameters of the problem (small polaron binding energy, temperature, lattice size).

Holstein polarons in a strong electric field: Delocalized and stretched states

The coherent dynamics of a Holstein polaron in strong electric fields is considered under different regimes. Using analytical and numerical analysis, we show that even for small hopping constant and weak electron-phonon interaction, the original discrete Wannier-Stark (WS) ladder electronic states are each replaced by a semi-continuous band if a resonance condition is satisfied between the phonon frequency and the ladder spacing. In this regime, the original localized WS states can become {\em delocalized}, yielding both `tunneling' and `stretched' polarons. The transport properties of such a system would exhibit a modulation of the phonon replicas in typical tunneling experiments. The modulation will reflect the complex spectra with nearly-fractal structure of the semi-continuous band. In the off-resonance regime, the WS ladder is strongly deformed, although the states are still localized to a degree which depends on the detuning: Both the spacing between the levels in the deformed ladder and the localization length of the resulting eigenfunctions can be adjusted by the applied electric field. We also discuss the regime beyond small hopping constant and weak coupling, and find an interesting mapping to that limit via the Lang-Firsov transformation, which allows one to extend the region of validity of the analysis.

Two-vibron state dynamics in an anharmonic confined adlayer

The two-vibron dynamics of an anharmonic molecular monolayer confined between surface steps is investigated. Using the number states method, the equivalence between the two-vibron dynamics and the dynamics of a single fictitious particle moving in a three-dimensional lattice is established. This latter lattice contains local defects which characterize both the influence of the confinement and the effect of the anharmonicity, and give rise to localized states. The anharmonicity is responsible for the occurrence of localized two-vibron bound states, for which two quanta are located on the same molecule adsorbed close to the surface step. These states are more strongly localized than the corresponding single-vibron states. In addition, the sensitivity of the spectral response of the two-vibron states to the structure and the confinement size is demonstrated using a limited set of dynamical parameters (anharmonicity, lateral hopping constant, and internal vibration frequency). As a result, two-vibron spectroscopy appears as a powerful tool to investigate the growth of molecular monolayers adsorbed on stepped surfaces.