Comment on “Dynamical properties of small polarons”

Firsov, Yu. A.; Kabanov, V. V.; Kudinov, E. K.; Alexandrov, A. S.

doi:10.1103/physrevb.59.12132

Cited by 31 publications

(29 citation statements)

References 13 publications

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“…However, applying the 1/λ expansion up to the second order in t one obtains the numerical t ef f very close to the perturbation t LF in the strong-coupling regime, λ > 1, (Alexandrov , 2000;Firsov et al , 1999) …”

Section: Holstein Model At Any Couplingmentioning

confidence: 66%

Fröhlich polaron and bipolaron: recent developments

2009

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It is remarkable how the Fröhlich polaron, one of the simplest examples of a Quantum Field Theoretical problem, as it basically consists of a single fermion interacting with a scalar Bose field of ion displacements, has resisted full analytical or numerical solution at all coupling since ∼ 1950, when its Hamiltonian was first written. The field has been a testing ground for analytical, semi-analytical, and numerical techniques, such as path integrals, strong-coupling perturbation expansion, advanced variational, exact diagonalisation (ED), and quantum Monte Carlo (QMC) techniques. This article reviews recent developments in the field of continuum and discrete (lattice) Fröhlich (bi)polarons starting with the basics and covering a number of active directions of research. * Electronic address: jozef.devreese@ua.ac.be † Electronic address: a.s.alexandrov@lboro.ac.uk

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Section: Holstein Model At Any Couplingmentioning

confidence: 66%

Fröhlich polaron and bipolaron: recent developments

2009

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“…Of course, by enhancing g 0 the perturbative method works better as the absence of arrows in the upper curves of Fig. 1 points out. We emphasize that the breakdown of the perturbative method is closely related to the inadequacy of the LangFirsov approach: 41,42 when the electronic and phononic subsystems are not strongly coupled the lattice deformation does not follow coherently the electron through the crystal and the polaronic unit broadens in real space. Then the crossover between a small-polaron ͑at strong g 0 ) and a large-polaron ͑at intermediate g 0 ) solution shows up in a decreased lattice deformation and associated lowering of the energy gain due to polaron formation: under these conditions the Lang-Firsov scheme becomes less appropriate.…”

Section: Numerical Resultsmentioning

confidence: 99%

Lattice-dynamics effects on small-polaron properties

Zoli

2000

Phys. Rev. B

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This study details the conditions under which strong-coupling perturbation theory can be applied to the molecular crystal model, a fundamental theoretical tool for analysis of the polaron properties. I show that lattice dimensionality and intermolecular forces play a key role in imposing constraints on the applicability of the perturbative approach. The polaron effective mass has been computed in different regimes ranging from the fully antiadiabatic to the fully adiabatic. The polaron masses become essentially dimension independent for sufficiently strong intermolecular coupling strengths and converge to much lower values than those traditionally obtained in small-polaron theory. I find evidence for a self-trapping transition in a moderately adiabatic regime at an electron-phonon coupling value of Ӎ3. Our results point to a substantial independence of the self-trapping event on dimensionality.

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“…21 is an artifact of an erroneous identification of the polaron kinetic energy. 26,44 de Mello and Ranninger 45 subsequently claimed that their definition of the polaron kinetic energy should be attributed to Holstein rather than to themselves and that their interpretation of the dynamic correlation functions of the Holstein model remains valid. We disagree with these claims.…”

Section: Two-site Holstein Model: Exact Versus Analytical Solutionmentioning

confidence: 99%

Polaron dynamics and bipolaron condensation in cuprates

Alexandrov

2000

Phys. Rev. B

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Based on the exact cluster diagonalization and recent Quantum Monte Carlo simulations we analyze dynamic properties of small polarons and bipolarons formed by short-range ͑Holstein͒ and long-range ͑Fröhlich͒ electron-phonon interactions. We show that the exact results agree well with canonical Holstein theory for a cluster and with Lang-Firsov theory for a lattice. Lang-Firsov theory of a single polaron and our 1/ perturbation expansion for a multipolaron system are practically exact in a wide range of the adiabatic parameter /t and the electron-phonon coupling for a long-range interaction. ͑Bi͒polarons exist in the itinerant Bloch states at temperatures below the characteristic phonon frequency no matter which values the parameters of the system take. We show that recent claims by several authors with regards to a breakdown of Holstein-Lang-Firsov theory of a small polaron and the ''impossibility'' of bipolaronic superconductivity are the result of an erroneous interpretation of the electronic energy levels of the two-site Holstein model and a misunderstanding of the electron-phonon interaction in ionic solids with polaronic carriers. A ''phase'' diagram in t/Ϫ space is proposed to elucidate the BCS and ͑bi͒polaronic domains. Bipolaron theory provides a parameter-free expression for the superconducting critical temperature of layered cuprates. Crystallization of the ͑bi͒polaronic liquid is shown to be impossible in the range of the parameters typical for cuprates. The small Fröhlich polaron has spectral features compatible with single-particle tunneling and photoemission in cuprates.

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Comment on “Dynamical properties of small polarons”

Cited by 31 publications

References 13 publications

Fröhlich polaron and bipolaron: recent developments

Fröhlich polaron and bipolaron: recent developments

Lattice-dynamics effects on small-polaron properties

Polaron dynamics and bipolaron condensation in cuprates

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