One-dimensional Electron-lattice Systems Research Articles

One-dimensional electron lattice system with a long-range interelectron repulsion on a disordered host lattice

We study what happens to a generalized Wigner crystal, GWC (a regular structure formed by narrow-band electrons on a one-dimensional periodic host lattice), when the host lattice suffers a random distortion that does not break its long-range order. We show that an arbitrarily weak distortion of this kind gives rise to soliton-like GWC defects (discrete solitons, DS) in the ground state, and thereby converts the ordered GWC into a new disordered macroscopic state—lattice Wigner glass (LWG). The ground-state DS concentration is found to be proportional to λ4 (λ is the typical host-lattice strain). We show that the low-temperature LWG thermodynamics and kinetics are fully described in DS terms. A new phenomenon of a super-slow logarithmic relaxation in the LWG is revealed. Its time turns out to be tens orders of magnitude greater than the microscopic ones. Analytical dependences of LWG thermodynamic quantities on temperature and λ are obtained for an arbitrary relationship between the relevant Coulomb energies and the electron bandwidth.

Delocalization of Polaron of the Extended Peierls–Hubbard System in the Mott Phase

One-dimensional strongly correlated electron system, which is accompanied by interaction with the lattice, has attracted a great deal of interest in both experimental and theoretical studies. At half-filling, this system is a Mott insulator when the electron–lattice interaction is weak. We performed a theoretical investigation of the stable ground state of the one-dimensional strongly correlated electron system with electron–lattice interaction in which one electron is doped from half-filling. We used an extended Peierls–Hubbard model. We report here that, contrary to “common sense” suppositions about the one-dimensional electron–lattice system, a polaron solution appears under conditions of comparatively strong electron–lattice interaction in the Mott phase and that the polaron delocalizes under conditions of weak electron–lattice interaction. These two states are separated by the strength of the electron–lattice interaction.

Collisions among Acoustic Polarons and Acoustic Bipolarons in One-Dimensional Electron-Lattice System

The collision processes between two acoustic polarons, two acoustic bipolarons, and a polaron and a bipolaron in a one-dimensional electron-lattice system are analyzed by numerical simulations based on Su, Schrieffer and Heeger's model extended to include short-ranged Coulombic electron-electron interactions. The collisions between two polarons with the same spin and between two bipolarons are essentially elastic because of a rather strong repulsion due to the Pauli principle. On the other hand, those between two polarons with opposite spins and between a polaron and a bipolaron show some inelastic behaviors depending on the relative velocity of the two objects before the collision. This knowledge will serve to understand the dynamics of the system when many polarons and/or bipolarons are created in the system e.g. by photoexcitation.

Roles of Intersite Interactions and Energy Dissipation in Photoinduced Phase Transitions by Domino Mechanism

The photoinduced domino effect for the phase transition dynamics in one-dimensional electron-lattice systems is investigated to clarify the dependence on the friction (energy dissipation rate) and the interaction between neighboring sites. We find a novel photoinduced domino process in the case of strong intersite interaction and weak friction. In this domino motion the photoexcited site remains in an excited electronic state, which is in striking contrast to the conventional domino effect. We identify a region where the domino processes take place as a function of the intersite interaction and the friction. It is shown that the novel process remains, even in the case of a higher potential barrier between two phases.

Electric Conduction Due to an Acoustic Bipolaron in One-Dimensional Electron-Lattice System

In order to estimate the mobility of an acoustic bipolaron in a typical non-degenerated polymer such as polydiacetylene (PDA), which can be regarded as a one-dimensional electron-lattice system, the dynamical behavior of an acoustic bipolaron in an external electric field is numerically investigated in the presence of a phenomenological damping of the lattice motion. In these simulations, we use the Su, Schrieffer and Heeger (SSH) Hamiltonian extended to include on-site and nearest-neighbor Coulomb repulsion terms, and the damping is introduced by adding a phenomenological friction term in the lattice equation of motion. The repulsive interactions are treated within the unrestricted time-dependent Hartree–Fock approximation. It is confirmed that the mobility of a bipolaron increases with the increase of the repulsion strength and that the relevant quantity determining the mobility of a bipolaron is its width as far as the phenomenological friction is kept fixed. The mobility of a bipolaron is compared wit...

Dynamics of an Acoustic Bipolaron in One-Dimensional Electron-Lattice Systems

The dynamical properties of an acoustic bipolaron in non-degenerate conjugated polymers such as polydiacetylene (PDA), which can be regarded as one-dimensional electron-lattice systems, are studied through numerical simulations. In these simulations, use has been made of Su-Schrieffer-Heeger's model extended to involve on-site as well as nearest-neighbor electron-electron Coulomb repulsion terms. The electron-electron interactions are treated within the unrestricted Hartree-Fock approximation. It is confirmed that the velocity of the acoustic bipolaron accelerated by a constant electric field saturates at the sound velocity of the system, and that the width of the bipolaron shrinks to zero as its velocity approaches the saturation velocity (= sound velocity). The effective mass of a bipolaron is estimated to be several hundred times as heavy as the free electron mass, in the case of PDA. These properties are compared with those of a polaron.

The nonlinear optical susceptibilities of polydiacetylenes

We present a general formalism of the NLO susceptibilities by using the Genkin-Mednis approach for a one-dimensional electron-lattice system. Based on the SSH model, we obtained an analytic expression for the third-order nonlinear optical susceptibilities χ (3)( ω) for polydiacetylenes (PDAs) after considering the case of conjugated chains, in which there is no adjustable parameter. The results are in good agreement with experiments on PDAs. Furthermore, the origin of the second peak in the χ (3)( ω) spectrum of PDAs is discussed, and a transition mechanism is proposed. It is believed that when the external light field is applied along the centrosymmetric polymer backbone, the parity symmetry of the system is broken, there occurs a mixing between the even- and odd-parity exciton states, leading to the transition from the ground state to the A g excited state, and accordingly a second sharp peak appears in the χ (3)( ω) spectrum which could be attributed to the three-photon resonance with the A g exciton generation process at around 2.2 eV.

Dynamics of an Acoustic Polaron in One-Dimensional Electron-Lattice System

The dynamical behavior of an acoustic polaron in typical non-degenerate conjugated polymer, polydiacetylene, is numerically studied by using Su-Schrieffer-Heeger's model for the one dimensional electron-lattice system. It is confirmed that the velocity of a polaron accelerated by a constant electric field shows a saturation to a velocity close to the sound velocity of the system, and that the width of a moving polaron decreases as a monotonic function of the velocity tending to zero at the saturation velocity. The effective mass of a polaron is estimated to be about one hundred times as heavy as the bare electron mass. Furthermore the linear mode analysis in the presence of a polaron is carried out, leading to the conclusion that there is only one localized mode, i.e. the translational mode. This is confirmed also from the phase shift of extended modes. There is no localized mode corresponding to the amplitude mode in the case of the soliton in polyacetylene. Nevertheless the width of a moving polaron shows small oscillations in time. This is found to be related to the lowest odd symmetry extended mode and to be due to the finite size effect.

Dynamics of a Fractionally Charged Soliton in a One-Dimensional Electron-Lattice System

Dynamics of a fractionally charged soliton in a nearly 1/3-filled one-dimensional electron- lattice system is numerically investigated with recently developed simulation method of accelerating charged solitons by an external electric field. For the Hamiltonian, SuSchrieffer-Heeger's model is assumed. A soliton with −2e/3 charge is treated; the numbers of lattice sites and electrons are chosen to be 119 and 80, respectively. The time dependences of the soliton velocity and of the different parts of the system energy are analyzed. The soliton dynamics is studied by decomposing the space-dependent Peierls order parameter into phase and amplitude

Third-harmonic generation of polyacetylene.

We present an exact calculation of third-harmonic generation (THG) for a one-dimensional electron-lattice system. The result shows that once the conjugated length of a polyene is finite, the transitions between inside-band electronic states will be important. A random distribution of conjugated lengths is used to simulate the polymer chains of polyacetylene. The average spectrum of THG distinctly demonstrates two peaks: one is the three-photon resonance exactly at one-third of the energy gap; the other sits near half of the energy gap, which is induced by the transitions between the inside-band states. This spectrum agrees quite well with that of THG experiments for trans-polyacetylene.

Nonlinear optical susceptibilities of conducting polymers.

By use of the Genkin-Mednis approach, a general formalism of the nonlinear optical susceptibilities has been derived for one-dimensional electron-lattice systems. Based on the Su-Schrieffer-Heeger model, we get an analytic expression of the third-harmonic generation ${\mathrm{\ensuremath{\chi}}}^{(3)}$(\ensuremath{\omega}) of conducting polymers. After considering the effects of finite lifetime of the excited states, the cusp at \ensuremath{\Elzxh}\ensuremath{\omega}=\ensuremath{\Delta} is greatly depressed so that it becomes too small to interpret the observed peak of ${\mathrm{\ensuremath{\chi}}}^{(3)}$(\ensuremath{\omega}) at 0.9 eV. The case of nondegenerate polymers and the effect of electron-electron interaction in the unrestricted Hartree-Fock approximation are also discussed. Our results imply that the electron interaction would play an important role in the nonlinear optical properties of conducting polymers.

Vibrational modes around the soliton in strongly coupled one-dimensional electron-lattice systems.

The vibrational properties of strongly coupled one-dimensional electron-lattice systems are distinct from those of weakly coupled ones. While the weakly coupled systems have only four localized modes around the soliton and there is overlap between acoustic and optical phonon branches, the strongly coupled system can possess more localized modes, and no overlap exists. In terms of the coupling constant \ensuremath{\lambda}, the boundary between strong and weak coupling is ${\ensuremath{\lambda}}_{c}$=0.2119. The number of localized modes depends on \ensuremath{\lambda}, and each localized mode can only exist for a certain region of \ensuremath{\lambda}. Then the whole range [0,2/\ensuremath{\pi}] of \ensuremath{\lambda} can be divided into seven regions, each of which has a characteristic disposition of the localized modes.