Stabilizing Role of Lattice Anharmonicity in the Bisoliton Dynamics

Abstract

We show that, in anharmonic one-dimensional lattices, the pairing of electrons or holes in a localized bisoliton (called also bisolectron) state is possible due to a coupling between the charges and the lattice deformation that can overcome the Coulomb repulsion. We show that bisolitons are dynamically stable up to the sound velocities in lattices with cubic or quartic anharmonicities, and have finite values of energy and momentum in the whole interval of bisoliton velocities up to the sound velocity in the chain. We calculate the bisoliton binding energy and the critical value of Coulomb repulsion at which the bisoliton becomes unstable and decays into two independent electrosolitons. We estimate these energies for chain parameters that are typical of biological macromolecules and some quasi-one-dimensional conducting systems and show that the Coulomb repulsion in such systems is relatively weak as compared with the binding energy. Our analytical results are in a good agreement with the results of numerical simulations in a broad interval of the parameter values. K e y w o r d s: lattice anharmonicity, bisoliton, bisolectron, Coulomb repulsion, electron, hole, exciton, polaron, model Hamiltonian.

Some Aspects of Generalized Dynamics of Quasiparticles in Crystals with Unit Cell of Arbitrary Complexity

“…These elements are determined in details in [16,17]. The condition of dynamical minimization of functional (1) is equivalent to the procedure of reduction to the diagonal type of the operator proper to (1) [5]. This procedure enables one to find the energy (k) directly at the operator level.…”

“…where (k) ≡ (k) − 0 . The comparison of expression (8) with the definition of operator (5) shows that the wave vector k can be put into accordance with the operator − ∇ n only ("minus" corresponds to the physical correctness of this accordance). As the wave vector k straightly determines a wave momentum P only, it is possible to conclude that, in the transition from the classical description to the quantum one, the operator of gradient is equivalent only to the wave momentum in the sense of the equalitŷ︀ P = − ∇ n , but not to a mechanical momentum, which is determined by the equality ( ) (k) = (k) (k) and is given in Subsection 2.1.…”

“…Electronic properties of graphene and other nanostructures of the carbon series require a general analysis of dynamical properties of quasiparticles. Their field of applications is from superconductivity [1] and superfluidity [2] up to solitary excitation transfer processes [3][4][5][6][7][8][9]. In particular, the processes of such transfer are normally associated in practice with the spatial transmission of charge or energy.…”

“…But they can also be used as information signals. Studying the fundamental properties of quasiparticles (especially dynamical properties) is important as for traditional processes [3][4][5][6], so for such updated problem as the properties of graphene [10] in, particularly, the Dirac dynamical model [11]. This is important also for a more complete understanding of the physical proper-wave momentum P = k, the quantity (k) acquires at once the sense of Hamiltonian: (k) ≡ (P).…”

“…SHMELEVA, 2016ties of real particles, especially, in connection with the mentioned dynamical Dirac model in graphenes [12].The analysis of the general dynamical properties of free quasiparticles is fulfilled on the basis of one of the major characteristics of the excited states of condensed matter. This is the dispersive dependence of the energy or frequency on a wave vector [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. We will also examine the general conditions, under which the dynamical Dirac model becomes real.…”