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Electron-phonon interaction on bundled structures: Static and transport properties

Meccoli I, Massimo Capone

Published Jan 1, 2001• 0 citations
OpenAlex

Abstract

We study the small-polaron problem of a single electron interacting with the lattice for the Holstein model in the adiabatic limit on a comb lattice hen the electron-phonon interaction acts only on the base sites. The ground state properties can be easily deduced from the ones of a linear chain with a appropriate rescaling of the coupling constant. On the other hand, the dynamical properties, that involve the complete spectrum of the system, present an "exotic" behavior. In the weak coupling limit the Drude weight (zero-frequency-conductivity) is enhanced with respect to its free-case value, contrary to the linear chain case, where for every finite value one has suppression of the Drude peak. More interestingly, the loss of coherent electron motion and the polaronic localization of the carrier occurs for different coupling values. Thus for intermediate coupling, a different phase appears with large kinetic energy and no coherent motion. RI Capone, Massimo/A-7762-2008

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We study the small-polaron problem of a single electron interacting with the lattice for the Holstein model in the adiabatic limit on a comb lattice hen the electron-phonon interaction acts only on the base sites. The ground state properties can be easily deduced from the ones of a linear chain with a appropriate rescaling of the coupling constant. On the other hand, the dynamical properties, that involve the complete spectrum of the system, present an "exotic" behavior. In the weak coupling limit the Drude weight (zero-frequency-conductivity) is enhanced with respect to its free-case value, contrary to the linear chain case, where for every finite value one has suppression of the Drude peak. More interestingly, the loss of coherent electron motion and the polaronic localization of the carrier occurs for different coupling values. Thus for intermediate coupling, a different phase appears with large kinetic energy and no coherent motion. RI Capone, Massimo/A-7762-2008
The polaron features for long-range electron–phonon interaction are investigated by extending a variational approach previously proposed for the study of systems with local coupling. The ground state spectral weight, the average kinetic energy, the mean number of phonons, and the electron–lattice correlation function are discussed for a wide range of model parameters focusing on the adiabatic regime and comparing the results with the short-range case (Holstein model). A strong mixing of electronic and phononic degrees of freedom for small values of the electron–phonon coupling constant is found in the adiabatic case due to the long-range interaction. Finally a polaron ‘phase diagram’ is proposed.
The spectral weight functions and the optical conductivity of the Holstein model are studied on a one-dimensional six-site lattice with periodic boundary conditions for three different electron concentrations: a single electron, two electrons of opposite spins, and half filling. A density matrix approach is used to obtain an optimal phonon basis and to truncate the phonon Hilbert space without significant loss of accuracy. This approach allows us to calculate spectral functions for electrons dressed locally by the optimal phonons as well as for bare electrons. We obtain evidence for a smooth crossover from quasifree electrons to a heavy itinerant small polaron (single-electron case) or bipolaron (two-electron case) as the electron-phonon coupling strength increases. At half filling, we observe a crossover from a quasifree-electron ground state to a quasidegenerate Peierls charge-density-wave ground state for a finite electron-phonon coupling. This crossover is marked by an abrupt drop of the Drude weight, which is vanishingly small in the Peierls phase.
A recently proposed variational approach based on an expansion in coherent states is used to investigate the single polaron features in the one-dimensional Holstein model. The method provides highly accurate results, both for static and dynamic properties, over a wide range of the polaron parameter space, from weak to strong coupling regimes, with a little numerical effort when compared with standard numerical techniques. The results for the spectral weight function and the real part of the optical conductivity are reported in the moderate adiabatic regime. We show that the spectral function exhibits a strong dependence on the polaron wave number kkk that is not present in the standard analytical approaches. The optical conductivity, in the strong coupling regime, displays a high-energy peak due to the photoionization of the small polaron, while, at lower energies, there is evidence of electronic transitions between localized states. These results show that the coherent-state basis is a very powerful basis to study interacting electron-phonon systems.
The Holstein Hubbard and Holstein t-J models are studied for a wide range of phonon frequencies, electron-electron, and electron-phonon interaction strengths on finite lattices with up to ten sites by means of direct Lanczos diagonalization. Previously the necessary truncation of the phononic Hilbert space caused serious limitations to either very small systems (four or even two sites) or to weak electron-phonon coupling, in particular in the adiabatic regime. Using parallel computers we were able to investigate the transition from ``large'' to ``small'' polarons in detail. By resolving the low-lying eigenstates of the Hamiltonian and by calculating the spectral function, we can identify a polaron band in the strong-coupling case, whose dispersion deviates from the free-particle dispersion at low and intermediate phonon frequencies. For two electrons (holes) we establish the existence of bipolaronic states and discuss the formation of a bipolaron band. For the two-dimensional Holstein t-J model, we demonstrate that the formation of hole polarons is favored by strong Coulomb correlations. Analyzing hole-hole correlation functions, we find that hole binding is enhanced as a dynamical effect of the electron-phonon interaction. \textcopyright{} 1996 The American Physical Society.
A dynamical mean-field theory of the small polaron problem is presented, which becomes exact in the limit of infinite dimensions. The ground-state properties and the one-electron spectral function are obtained for a single electron interacting with Einstein phonons by a mapping of the lattice problem onto a polaronic impurity model. The one-electron propagator of the impurity model is calculated through a continued fraction expansion, at both zero and finite temperature, for any electron-phonon coupling and phonon energy. In contrast to the ground-state properties, such as the effective polaron mass, which show a continuous behavior as the coupling is increased, spectral properties exhibit a sharp qualitative change at low enough phonon frequency: beyond a critical coupling, one energy gap and then more open in the density of states at low energy, while the high-energy part of the spectrum is broad and can be qualitatively explained by a strong coupling adiabatic approximation. As a consequence, narrow and coherent low-energy subbands coexist with an incoherent featureless structure at high energy. The subbands denote the formation of quasiparticle polaron states. Also, divergencies of the self-energy may occur in the gaps. At finite temperature such an effect triggers an important damping and broadening of the polaron subbands. On the other hand, in the large phonon frequency regime such a separation of energy scales does not exist and the spectrum always has a multipeaked structure.
We explore the quasiparticle properties of lattice polarons on the basis of a quite general electron-phonon Hamiltonian with a long-range displacement-type interaction. To treat the dynamical quantum phonons without significant loss of accuracy we adapt an exact Lanczos diagonalization method and compute various static and dynamical quantities, such as the electron-lattice correlation function, the polaron band dispersion, the effective polaron mass, the kinetic energy, the single-particle spectral function, and the optical conductivity, on finite one-dimensional lattices for a wide range of model parameters. We compare the results with those obtained for the standard Holstein model with short-range electron-phonon interaction only.