One-dimensional Tight-binding Model Research Articles

Dynamic Formation of Bipolaron-Exciton Complexes in Conducting Polymers.

The recombination dynamics of two oppositely charged bipolarons within a single polymer chain is numerically studied in the scope of a one-dimensional tight-binding model that considers electron-electron and electron-phonon (e-ph) interactions. By scanning among values of e-ph coupling and electric field, novel channels for the bipolaron recombination were yielded based on the interplay between these two parameters. The findings point to the formation of a compound species formed from the coupling between a bipolaron and an exciton. Depending on the electric field and e-ph coupling strengths, the recombination mechanism may yield two distinct products: a trapped (and almost neutral) or a moving (and partially charged) bipolaron-exciton. These results might enlighten the understanding of the electroluminescence processes in organic light-emitting devices.

Localization in one-dimensional tight-binding model with chaotic binary sequences

We have numerically investigated localization properties in the one-dimensional tight-binding model with chaotic binary on-site energy sequences generated by a modified Bernoulli map with the stationary-nonstationary chaotic transition (SNCT). The energy sequences in question might be characterized by their correlation parameter B and the potential strength W. The quantum states resulting from such sequences have been characterized in the two ways: Lyapunov exponent at band centre and the dynamics of the initially localized wavepacket. Specifically, the B−dependence of the relevant Lyapunov exponent’s decay is changing from linear to exponential one around the SNCT (B ≃ 2). Moreover, here we show that even in the nonstationary regime, mean square displacement (MSD) of the wavepacket is noticeably suppressed in the long-time limit (dynamical localization). The B−dependence of the dynamical localization lengths determined by the MSD exhibits a clear change in the functional behaviour around SNCT, and its rapid increase gets much more moderate one for B ≥ 2. Moreover we show that the localization dynamics for B > 3/2 deviates from the one-parameter scaling of the localization in the transient region.

Wavepacket dynamics in one-dimensional system with long-range correlated disorder

We numerically investigate dynamical property in the one-dimensional tight-binding model with long-range correlated disorder having power spectrum 1/fα (α: spectrum exponent) generated by Fourier filtering method. For relatively small α<αc(=2) time-dependence of mean square displacement (MSD) of the initially localized wavepacket shows ballistic spread and localizes as time elapses. It is shown that α-dependence of the dynamical localization length determined by the MSD exhibits a simple scaling law in the localization regime for the relatively weak disorder strength W. Furthermore, scaled MSD by the dynamical localization length almost obeys an universal function from the ballistic to the localization regime in the various combinations of the parameters α and W.

Chaos-based potentials in the one-dimensional tight-binding model probed by the inverse participation ratio

Chaos-based potentials are defined and implemented in the one-dimensional tight-binding model as a way of simulating disorder-controlled crystalline lattices. In this setting, disorder is handled with the aid of the chaoticity parameter. The inverse participation ratio $(IPR)$ probes the response of the system to three different such potentials and shows consistent agreement with results given by the Lyapunov exponent $Ly$: the greater $Ly(r)$ for the chaotic sequence as a function of the chaoticity parameter $r$, the greater the asymptotic value $IPR(r)$ for the large-system ground state.

Effect of electron–electron interaction on polarization and dissociation of the charged oligomer after single-photon absorption

By using the extended Hubbard model under the Hartree–Fock approximation, we theoretically investigate the effect of electron–electron interaction on the polarization of the single-photon excited state of the charged [Formula: see text]-conjugated oligomer. In the framework of one-dimensional tight-binding model, a uniform weak electric field is applied for polarization. The results show that the polarization property will vary with the electron–electron interaction. For example, with the increase of on-site Coulomb interaction strength, the value of the induced dipole moment is decreased. Its physical origin is revealed by analyzing the wavefunction of the localized energy level. In addition, the relation between the critical electric field for the dissociation of the single-photon excited state of the charged oligomer and the electron–electron interaction strength is also discussed.

Role of surface-bound hole states in electric-field-driven superconductivity at the (110)-surface of diamond

Hole states in electric-field-driven superconductivity at the (110)-surface of diamond are examined by means of first-principles calculations and one-dimensional tight-binding model calculations. It is found that surface-bound hole states confined near the surface by application of an electric field $E$ play a key role in superconductivity. Indeed, there is a critical external electric field $|{E}_{\mathrm{c}}|$ ($\ensuremath{\simeq}0.4$ V/\AA{}) for observing the superconductivity, which can be attributed to the second surface-bound hole state. With McMillan's formula and calculated phonon-electron coupling constants, we demonstrate that, in electric fields $l|{E}_{\mathrm{c}}|$ which correspond to a surface carrier density of $\ensuremath{\sim}2.3\ifmmode\times\else\texttimes\fi{}{10}^{13}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$, superconductivity may not be practically observed while the superconductivity transition temperature suddenly increases at $|{E}_{\mathrm{c}}|$.

Investigation of charge injection and transport behavior in multilayer structure consisted of ferromagnetic metal and organic polymer under external fields

In this paper a five layer organic electronic device with alternately placed ferromagnetic metals and organic polymers: ferromagnetic metal/organic layer/ferromagnetic metal/organic layer/ferromagnetic metal, which is injected a spin-polarized electron from outsides, is studied theoretically using one-dimensional tight binding model Hamiltonian. We calculated equilibrium state behavior after an electron with spin is injected into the organic layer of this structure, charge density distribution and spin polarization density distribution of this injected spin-polarized electron, and mainly studied possible transport behavior of the injected spin polarized electron in this multilayer structure under different external electric fields. We analyze the physical process of the injected electron in this multilayer system. It is found by our calculation that the injected spin polarized electron exists as an electron-polaron state with spin polarization in the organic layer and it can pass through the middle ferromagnetic layer from the right-hand organic layer to the left-hand organic layer by the action of increasing external electric fields, which indicates that this structure may be used as a possible spin-polarized charge electronic device and also may provide a theoretical base for the organic electronic devices and it is also found that in the boundaries between the ferromagnetic layer and the organic layer there exist induced interface local dipoles due to the external electric fields.

Emergence of Bloch oscillations in one-dimensional systems

Electrons in periodic potentials exhibit oscillatory motion in the presence of an electric field. Such oscillations are known as Bloch oscillations. In this article we theoretically investigate the emergence of Bloch oscillations for systems where the electric field is confined to a finite region, like in typical electronic devices. We use a one-dimensional tight-binding model within the single-band approximation to numerically study the dynamics of electrons after a sudden switching-on of the electric field. We find a transition from a regime with direct current to Bloch oscillations when increasing the system size or decreasing the field strength. We propose a pump-probe scheme to observe the oscillations by measuring the accumulated charge as a function of the pulse length.

Phase diagram of a family of one-dimensional nearest-neighbor tight-binding models with an exact mobility edge**Project supported by the National Natural Science Foundation of China (Grant Nos. 61475075 and 61170321).

Recently, an interesting family of quasiperiodic models with exact mobility edges (MEs) has been proposed (Phys. Rev. Lett. 114 146601 (2015)). It is self-dual under a generalized duality transformation. However, such transformation is not obvious to map extended (localized) states in the real space to localized (extended) ones in the Fourier space. Therefore, it needs more convictive evidences to confirm the existence of MEs. We use the second moment of wave functions, Shannon information entropies, and Lypanunov exponents to characterize the localization properties of the eigenstates, respectively. Furthermore, we obtain the phase diagram of the model. Our numerical results support the existing analytical findings.

Temperature effect on polaron recombination in conjugated polymers

The microcosmic mechanism of electroluminescence in polymer light emitting diodes (PLEDs) is the recombination of the oppositely charged polarons. In previous studies, it has been demonstrated that the temperature-induced irregular lattice vibration may have non-negligible influence on polaron dynamics. Nevertheless, there are few reports about thermal effect on recombination process between polaron pair, although it is very important for the performance of PLEDs. In this paper, we adopt the modified one-dimensional tight-binding model, including to which the thermal random force, and explore the temperature effect on polaron collision driven by electric field with different strengths. The dynamical simulation is performed by using the non-adiabatic evolution method. The results show that under the influence of electric field, the oppositely charged polarons could recombine into either an exciton with one lattice distortion, or the mixed state of polaron pair and exciton with two lattice distortions. It depends on both field strength and temperature. Anyway, after including temperature effect, a significant improvement of exciton yield is obtained. In addition, the new-formed exciton could perform a random walk along the polymer chain driven by the thermal random force when its strength is large enough. If we further increase the temperature, the stability of exciton would become worse.

Effective lattice model for the collective modes in a Fermi liquid with spin-orbit coupling

A Fermi-liquid (FL) with spin-orbit coupling (SOC) supports a special type of collective modes--chiral spin waves--which are oscillations of magnetization even in the absence of the external magnetic field. We study the chiral spin waves of a two-dimensional FL in the presence of both the Rashba and Dresselhaus types of SOC and also subject to the in-plane magnetic field. We map the system of coupled kinetic equations for the angular harmonics of the occupation number onto an effective one-dimensional tight-binding model, in which the lattice sites correspond to angular-momentum channels. Linear-in-momentum SOC ensures that the effective tight-binding model has only nearest-neighbor hopping on a bipartite lattice. In this language, the continuum of spin-flip particle-hole excitations becomes a conduction band of the lattice model, whereas electron-electron interaction, parameterized by the harmonics of the Landau function, is mapped onto lattice defects of both on-site and bond type. Collective modes correspond to bound states formed by such defects. All the features of the collective-mode spectrum receive natural explanation in the lattice picture as resulting from the competition between on-site and bond defects.

Bloch oscillations in organic and inorganic polymers.

The transport of polarons above the mobility threshold in organic and inorganic polymers is theoretically investigated in the framework of a one-dimensional tight-binding model that includes lattice relaxation. The computational approach is based on parameters for which the model Hamiltonian suitably describes different polymer lattices in the presence of external electric fields. Our findings show that, above critical field strengths, a dissociated polaron moves through the polymer lattice as a free electron performing Bloch oscillations. These critical electric fields are considerably smaller for inorganic lattices in comparison to organic polymers. Interestingly, for inorganic lattices, the free electron propagates preserving charge and spin densities' localization which is a characteristic of a static polaron. Moreover, in the turning points of the spatial Bloch oscillations, transient polaron levels are formed inside the band gap, thus generating a fully characterized polaron structure. For the organic case, on the other hand, no polaron signature is observed: neither in the shape of the distortion-those polaron profile signatures are absent-nor in the energy levels-as no such polaron levels are formed during the simulation. These results solve controversial aspects concerning Bloch oscillations recently reported in the literature and may enlighten the understanding about the charge transport mechanism in polymers above their mobility edge.

Multi-particle localization for weakly interacting Anderson tight-binding models

We establish the complete spectral exponential and the strong Hilbert-Schmidt dynamical localization for the one-dimensional multi-particle Anderson tight-binding model and for weakly interacting particle system. In other words, we show the stability of the one-dimensional localization from the single-particle to multi-particle systems with an arbitrarily large but finite number of particles and for sufficient weakly interacting models. The proof uses the multi-scale analysis estimates for multi-particle systems. The common probability distribution function of the random external potential in the Anderson model is assumed to be log-Hölder continuous, so the results apply to a large class of Anderson models.

Multihole edge states in Su-Schrieffer-Heeger chains with interactions

We address the effect of nearest-neighbor (NN) interactions on the topological properties of the Su-Schrieffer-Heeger (SSH) chain, with alternating hopping amplitudes t1 and t2. Both numerically and analytically, we show that the presence of interactions induces phase transitions between topologically different regimes. In the particular case of one-hole excitations in a half-filled SSH chain, the V=t2 vs. t1=t2 phase diagram has topological phases at diagonal regions of the phase plane. The interaction acts in this case as a passivation potential. For general filling of the SSH chain, different eigensubspaces of the SSH Hamiltonian may be classified as topologically trivial and non-trivial. The two-hole case is studied in detail in the large interaction limit, and we show that a mapping can be constructed of the two-hole SSH eigensubspaces into one-particle states of a non-interacting one-dimensional (1D) tight-binding model, with interfaces between regions with different hopping constants and local potentials. The presence of topological edge states in the equivalent chain can be readily identifed, as well as their correspondence to the original two-hole states. Furthermore, we found that the presence of the NN interaction generates a state where two holes occupy two consecutive edge states. Such many-body states should also occur for arbitrary filling leading to the possibility of a macroscopic hole gathering at the surface (at consecutive edge states).

Noise, delocalization, and quantum diffusion in one-dimensional tight-binding models.

As an unusual type of anomalous diffusion behavior, namely (transient) superballistic transport, has been experimentally observed recently, but it is not yet well understood. In this paper, we investigate the white noise effect (in the Markov approximation) on quantum diffusion in one-dimensional tight-binding models with a periodic, disordered, and quasiperiodic region of size L attached to two perfect lattices at both ends in which the wave packet is initially located at the center of the sublattice. We find that in a completely localized system, inducing noise could delocalize the system to a desirable diffusion phase. This controllable system may be used to investigate the interplay of disorder and white noise, as well as to explore an exotic quantum phase.

Dynamic dissociation of trions in conjugated polymers

Within a one-dimensional tight-binding model, the dynamic dissociation processes of trions under an external electric field have been investigated using a nonadiabatic evolution method. We demonstrate that the dissociation of the trion under an applied electric field is more difficult than in the case for either the polaron or the bipolaron. Considering the effect of the electron-electron interactions, it is found that the on-site Coulomb interactions reduce while the nearest-neighbor interactions enhance the stability of the trion. Furthermore, due to the competition between the on-site Coulomb and the nearest-neighbor interactions, the static trion presents two typical configurations in general, i.e., a bound state of an exciton and a polaron or a bound state of a bipolaron and an opposite charged polaron. Accordingly, the outcome of the trion dissociation is closely related to its static configuration.

Intermediate Coherent–Incoherent Charge Transport: DNA as a Case Study

We study an intermediate quantum coherent-incoherent charge transport mechanism in metal-molecule-metal junctions using Buttiker’s probe technique. This tool allows us to include incoherent effects in a controlled manner, and thus to study situations in which partial decoherence affects charge transfer dynamics. Motivated by recent experiments on intermediate coherent-incoherent charge conduction in DNA molecules, we focus on two representative structures: alternating (GC)n and stacked GnCn sequences; the latter structure is argued to support charge delocalization within G segments and, thus, an intermediate coherent–incoherent conduction. We begin our analysis with a highly simplified one-dimensional tight-binding model while introducing environmental effects through Buttiker’s probes. This minimal model allows us to gain fundamental understanding of transport mechanisms and derive analytic results for molecular resistance in different limits. We then use a more detailed ladder-model Hamiltonian to repre...

Statistical mechanics approach to the electric polarization and dielectric constant of band insulators

We develop a theory for the analytic computation of the free energy of band insulators in the presence of a uniform and constant electric field. The two key ingredients are a perturbation-like expression of the Wannier-Stark energy spectrum of electrons and a modified statistical mechanics approach involving a local chemical potential in order to deal with the unbounded spectrum and impose the physically relevant electronic filling. At first order in the field, we recover the result of King-Smith, Vanderbilt and Resta for the electric polarization in terms of a Zak phase - albeit at finite temperature - and, at second order, deduce a general formula for the electric susceptibility, or equivalently for the dielectric constant. Advantages of our method are the validity of the formalism both at zero and finite temperature and the easy computation of higher order derivatives of the free energy. We verify our findings on two different one-dimensional tight-binding models.

Fundamental processes of exciton scattering at organic solar-cell interfaces: One-dimensional model calculation

Fundamental processes of exciton scattering at organic solar-cell interfaces were studied using a one-dimensional tight-binding model and by performing a time-evolution simulation of electron–hole pair wave packets. We found the fundamental features of exciton scattering: the scattering promotes not only the dissociation of excitons and the generation of interface-bound (charge-transferred) excitons but also the transmission and reflection of excitons depending on the electron and hole interface offsets. In particular, the dissociation increases in a certain region of an interface offset, while the transmission shows resonances with higher-energy bound-exciton and interface bound-exciton states. We also studied the effects of carrier-transfer and potential modulations at the interface and the scattering of charged excitons, and we found trap dissociations where one of the carriers is trapped around the interface after the dissociation.

Delocalization in one-dimensional tight-binding models with fractal disorder II: existence of mobility edge

In the previous work, we investigated the correlation-induced localization-delocalization transition (LDT) of the wavefunction at band center ($E=0$) in the one-dimensional tight-binding model with fractal disorder [Yamada, EPJB (2015) 88, 264]. In the present work, we study the energy ($E \neq 0$) dependence of the normalized localization length and the delocalization of the wavefunction at the different energy in the same system. The mobility edges in the LDT arise when the fractal dimension of the potential landscape is larger than the critical value depending on the disorder strength, which is consistent with the previous result.In addition, we present the distribution of individual NLL and Lyapunov exponent in the system with LDT.