One-dimensional Two-band Model Research Articles

Theory of thermal conductivity of excitonic insulators

We study the thermal conductivity in the excitonic insulator using a simple quasi one-dimensional two-band model consisting of electron and hole bands with the Coulomb interactions between these bands. Based on the linear response theory within a mean-field scheme, we develop a method to identify the contributions to thermal conductivity driven by excitonic insulator. It is found that there is an additional heat current operator owing to the excitonic phase transition, and that it gives contributions to thermal conductivity which are not expressed in the form of Sommerfeld-Bethe relations written in the form of an imaginary-time derivative of the electric current operator. Finally, we discuss the relationship between the newly-found additional contribution and the heat current carried by excitons.

Crystal symmetry and polarization of high-order harmonics in ZnO

We carried out a joint theoretical and experimental study of the polarization of high-order harmonics generated from ZnO by intense, linearly-polarized, infrared laser pulses. Experimentally we found that the dependence of parallel and perpendicular polarizations on the crystal orientation for all odd harmonics are nearly identical, but they are quite different from even harmonics which also show little order dependence. A one-dimensional two-band model, combined with a linear coupled excitation model, is shown to be able to explain the observed polarization behavior, including low-order harmonics. We further note that the same odd/even order contrast have been reported in a number of other crystals, despite that the harmonics were perceived to be generated via entirely different mechanisms. We demonstrated that this universality is governed by crystal symmetry, not by specific mechanisms. Thus, polarization measurements of harmonics offers a powerful pure optical method for determining the crystal axes as well as monitoring their ultrafast changes when crystals are undergoing deformation. In addition, the ellipticity of harmonic has been studied. It shows that ellipticity of high-order harmonics from solids can be tuned precisely by changing the bond structure of the sample.

Role of the Transition Dipole Amplitude and Phase on the Generation of Odd and Even High-Order Harmonics in Crystals.

Since the first observation of odd and even high-order harmonics generated from ZnO crystals in 2011, the dependence of the harmonic yields on the orientation of the laser polarization with respect to the crystal axis has never been properly interpreted. This failure has been traced to the lack of a correct account of the phase of the transition dipole moment between the valence band and the conduction band. Using a simple one-dimensional two-band model, here we demonstrate that the observed odd harmonics is directly related to the orientation dependence of the magnitude of the transition dipole, while even harmonics is directly related to the phase of the transition dipole. Our result points out the essential role of the complex transition dipole moment in understanding harmonic generation from solids that has long been overlooked so far.

Strong second harmonic generation in two-dimensional ferroelectric IV-monochalcogenides

The two-dimensional ferroelectrics GeS, GeSe, SnS and SnSe are expected to have large spontaneous in-plane electric polarization and enhanced shift-current response. Using density functional methods, we show that these materials also exhibit the largest effective second harmonic generation reported so far. It can reach magnitudes up to which is about an order of magnitude larger than that of prototypical GaAs. To rationalize this result we model the optical response with a simple one-dimensional two-band model along the spontaneous polarization direction. Within this model the second-harmonic generation tensor is proportional to the shift-current response tensor. The large shift current and second harmonic responses of GeS, GeSe, SnS and SnSe make them promising non-linear materials for optoelectronic applications.

Discontinuous polaron transition in a two-band model

We present exact diagonalization and momentum average approximation (MA) results for the single polaron properties of a one-dimensional two-band model with phonon-modulated hopping. At strong electron-phonon coupling, we find a novel type of sharp transition, where the polaron ground state momentum jumps discontinuously from $k=\pi$ to $k=0$. The nature and origin of this transition is investigated and compared to that of the Su-Schrieffer-Heeger (SSH) model, where a sharp but smooth transition was previously reported. We argue that such discontinuous transitions are a consequence of the multi-band nature of the model, and are unlikely to be observed in one-band models. We also show that MA describes qualitatively and even quantitatively accurately this polaron and its transition. Given its computationally efficient generalization to higher dimensions, MA thus promises to allow for accurate studies of electron-phonon coupling in multi-band models in higher dimensions.

Microscopic modeling of photoluminescence of strongly disordered semiconductors

A microscopic theory for the luminescence of ordered semiconductors is modified to describe photoluminescence of strongly disordered semiconductors. The approach includes both diagonal disorder and the many-body Coulomb interaction. As a case study, the light emission of a correlated plasma is investigated numerically for a one-dimensional two-band tight-binding model. The band structure of the underlying ordered system is assumed to correspond to either a direct or an indirect semiconductor. In particular, luminescence and absorption spectra are computed for various levels of disorder and sample temperature to determine thermodynamic relations, the Stokes shift, and the radiative lifetime distribution.

Charge ordering and lattice modulation in MMX chains

Ground state phase diagrams for the MMX chains are studied in a one-dimensional two-band model by exactly diagonalizing 18-site clusters. Experimentally observed phases are reproduced by changing relative strengths of an electron–lattice coupling, the interdimer transfer integral, and an elastic constant, whose variation is roughly estimated from the interatomic spacing, the species of the halogen ion, and the presence/absence of counter ions.

Delocalization-localization transition in a one-dimensional two-band model with random clusters

We investigate the delocalization-localization transition in a one-dimensional disordered system with two hybridized bands. The effects of both disorder and interband hybridization on the energy spectrum and the properties of wavefunctions are studied by using the improved Dean method and the second-moment formula. The results show that there exist band tails in the gap regions. All subbands are widened by increasing the disorder strength, whereas when the interband hybridization increases, some subbands become narrower and the others are widened. The delocalization of the wavefunctions tends to be enhanced as the hybridization increases. The localization-delocalization transition of the wavefunctions occurs when the interband hybridization becomes larger than a critical value. The competition between disorder and hybridization determines the nature of the electronic states and the energy spectrum.

Superconductivity fluctuations in a one-dimensional two-band electron-phonon model with strong repulsive interactions

We study a one-dimensional, two-band model with short-range electron-electron repulsions (onsite U and nearest-neighbor V terms) and electron-phonon coupling. We show that there is a region of U, V and band filling in which singlet superconductivity fluctuations are dominant. This region is absent without electron-phonon interactions and includes large values of U and V.

Interface states in nitrogen incorporated gate oxides

In this letter, we calculate the interface state energy in nitrogen incorporated gate oxides by using a one-dimensional two-band model and Penn’s model connecting the refractive index with typical band gap. We estimate the number of dangling bonds which we consider to be the origin of the interface states by the minimization of the free energy. The calculated results seem to explain qualitatively the recent experimental data on NO annealed oxides.

Metal-insulator transition in an one-dimensional two-band Hubbard-like model

We consider a one-dimensional two-band model of electrons on a lattice with equal nearest-neighbour hopping, an interband splitting Delta and a Hubbard-like repulsion U. The model is defined via the SU(4) generalization of Lieb and Wu's Bethe ansatz solution of the one-dimensional Hubbard model. At T=0 the model has a Mott metal-insulator transition at a critical value Uc( Delta ) for a band filling of exactly one electron per site. Uc decreases with Delta , being zero if the excited-electron band is empty, and Uc=2.981 when the bands are degenerate. We discuss the ground-state properties, the spectrum of elemental excitations, the specific heat and the magnetic susceptibility, in both the metallic and insulating phases, as a function of the crystal-field splitting for exactly one electron per site. There are four branches of elemental excitations: (i) charge excitations, (ii) crystalline-field excitations and (iii) two branches of spin waves. The Fermi velocity is finite in the metallic phase, diverges as the metal-insulator transition is approached from the metallic side and vanishes for the insulator. Each band contributes to the susceptibility with a term that is inversely proportional to the spin-wave velocity for that band. The low-temperature specific heat is proportional to T and to the sum of the inverses of the velocities of the four branches.

Elementary relaxation processes of one-dimensional excitons coupled with lattice vibrations: A molecular dynamics study

Transient lattice relaxation in the self-trapping processes of excitons has been studied by molecular dynamics, employing a one-dimensional two-band model coupled with lattice vibrations. We have found that the initial relaxation of an exciton is composed of three processes. Due to the first process in which an exciton remains free preceding the lattice relaxation, the relaxation time for the transition from a free exciton to a self-trapped exciton has been found to be several times larger than the period of the lattice vibrations, which agreed with the experimental results of ultrafast spectroscopy on polydiacetylenes.

Theory of zone-folded optical transitions in semiconductor superlattices

A one-dimensional two-band tight-binding model is used to develop simple criteria governing the optical transition strength of a direct gap formed by zone folding in a superlattice of alternating layers of two indirect band-gap semiconductors. The model study explains the weak optical transitions calculated for the III-V superlattices as being due to the similarities of the constituents and predicts strong optical transitions for large band discontinuities and type I alignment, particularly in GaP/Si2. The optical strength in the Si2/Ge2 superlattice is found to depend strongly on the growth direction and on strain. The oscillator strength calculated by the simple model is checked in two cases against a more elaborate calculation using the sp3d5 empirical tight-binding band structure and atomic wave functions.

Optical excitations along CuO chains in copper oxides.

Optical responses in a one-dimensional two-band Peierls-Hubbard model near 5/8 filling (i.e., near 1/4 filling in the effective one-band model) are studied within inhomogeneous Hartree-Fock and random-phase approximations. Low-energy collective excitations are produced by a sliding motion of a spin-density wave. In the commensurate case (i.e., at 5/8 filling) or near this filling with moderate strength of intersite electron-lattice coupling, the spin-density wave (with polaronic defects in the latter case) is pinned by commensurability with the lattice, and the lowest-frequency optical response lies in the infrared regime. Otherwise, the spin-density wave is incommensurate and moves freely unless it is pinned by extrinsic impurities. Implications for midinfrared absorptions observed in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ and ${\mathrm{PrBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ compounds are discussed. With sufficiently weak hopping between the Cu and O sites, a ferromagnetic phase is found.

Electronic properties of a one-dimensional two-band model with period randomness

The authors investigated the electronic properties of a one-dimensional on-site disordered model, which is constructed from a linear composition of two binary compounds with random periods, having two hybridizing bands on every site. Using the improved Dean method and the second-moment formulae, the effects of both disorder and hybridization on the energy spectrum and the property of wavefunction are studied. The results show that the appearance of some special peaks in the spectrum is due to a particular arrangement of atoms that occurs randomly and the effect of disorder on the energy spectrum decreases in the case of large hybridization. The delocalization of the wavefunctions tends to be enhanced as the hybridization increases. When the hybridization becomes larger than a critical value, some delocalized wavefunctions appear.

Spin-Peierls ground states and frustration in a multiband Peierls-Hubbard model.

We discuss the consequences of including both electron-phonon and electron-electron couplings in multiband models, focusing on numerical studies of a one-dimensional two-band model in the intermediate regime for both coupling strengths. Spin-Peierls as well as long-period, frustrated ground states are identified, reminiscent of those found in axial next-nearest-neighbor Ising models. We speculate on experimentally observable signatures of this rich phase diagram.

Vibronic, Optical, and Magnetic Excitations around Solitons in a One-Dimensional Two-Band Peierls-Hubbard Model

Nonlinear doping states in a charge-density-wave background and those in a spin-density- wave background are investigated through their response functions in vibronic, optical and magnetic channels in a one-dimensional two-band Peierls-Hubbard model. A random phase approximation is used for their analysis on the basis of totally unrestricted Hartree-Fock solutions. Doping-induced changes of excitation spectra in these different channels are distinctive to the nature of individual doping states

Ground state and excitations of a one-dimensional two-band supersymmetric t-J model with crystalline field splitting.

We consider a one-dimensional two-band model of electrons on a lattice with nearest-neighbor hopping {ital t} constrained by the excluded multiple occupancy of the sites, an interband splitting, {Delta}, and intraband and interband exchange {ital J} between neighboring sites. This model is integrable at the supersymmetric point and reduces to the SU(4)-invariant supersymmetric {ital t}-{ital J} model with crystal field splitting. We present the exact solution via Bethe's ansatz and discuss ground-state properties and the excitation spectrum as a function of {Delta}.

Optical absorption in the one-dimensional two-band model

The optical-absorption spectra in the one-dimensional tow-band model with the periodic-boundary condition are conputed within the mean-field theory. The spectrum shows the charge-transfer band for non-doping, the Drude peak at the absorption energy 0 for a single hole per unit cell and the mid-infrared band for two holes per unit cell. It turns out that the strong Coulomb interaction is important in the electronic properties of the high T c copper oxides.

Stark ladders in a two-band tight-binding model

The electronic states of a one-dimensional two-band tight-binding model in a uniform electric field, in which the strength of interband coupling is varied, are studied. Eigenenergies, densities of states and wavefunctions are numerically computed for a finite length of the system in order to see the transition from Bloch bands at low electric fields to the eigenstates at high fields explicitly. The results for high electric fields indicate the existence of sets of Stark ladders arising from different bands even when interband coupling is strong.