Self-consistent modification to the electron density of states due to electron-phonon coupling in metals

Doğan, Fatih; Marsiglio, F.

doi:10.1103/physrevb.68.165102

Cited by 28 publications

(38 citation statements)

References 11 publications

(9 reference statements)

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“…For weak electronphonon coupling λ ≪ 1 in the adiabatic limithω/E F ≪ 1, Migdal theory describes electron dynamics 11 . With increasing strength of interaction and increasing phonon frequency ω finite bandwidth 12,13 and vertex corrections 14 become important. The neglect of vertex corrections in the Migdal approximation breaks down entirely at λ ∼ 1 for any value of the adiabatic ratiohω/E F because the bandwidth is narrowed and the Fermi energy is renormalized down exponentially.…”

Section: Introductionmentioning

confidence: 99%

Effects of lattice geometry and interaction range on polaron dynamics

et al. 2006

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We study the effects of lattice type on polaron dynamics using a continuous-time quantum MonteCarlo approach. Holstein and screened Fröhlich polarons are simulated on a number of different Bravais lattices. The effective mass, isotope coefficients, ground state energy and energy spectra, phonon numbers, and density of states are calculated. In addition, the results are compared with weak and strong coupling perturbation theory. For the Holstein polaron, it is found that the crossover between weak and strong coupling results becomes sharper as the coordination number is increased. In higher dimensions, polarons are much less mobile at strong coupling, with more phonons contributing to the polaron. The total energy decreases monotonically with coupling. Spectral properties of the polaron depend on the lattice type considered, with the dimensionality contributing to the shape and the coordination number to the bandwidth. As the range of the electron-phonon interaction is increased, the coordination number becomes less important, with the dimensionality taking the leading role.

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Section: Introductionmentioning

confidence: 99%

Effects of lattice geometry and interaction range on polaron dynamics

et al. 2006

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“…Further details of this model will be provided elsewhere [26]. We also refer the reader to papers [17]- [20] in which coupling of the electrons to phonons is considered within a Migdal-Eliashberg self-consistent approximation.…”

Section: Formalismmentioning

confidence: 99%

“…To this end we assume a constant electron density of states with sharp cut-offs at the band edges [17]- [20]. We also assume that the electrons are coupled to Einstein oscillators of frequency ω E .…”

Section: Introductionmentioning

confidence: 99%

Optical sum increase due to electron undressing

2004

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For a system with a fixed number of electrons, the total optical sum is a constant, independent of many-body interactions, of impurity scattering and of temperature. For a single band in a metal, such a sum rule is no longer independent of the interactions or temperature, when the dispersion and/or finite bandwidth is accounted for. We adopt such a model, with electrons coupled to a single Einstein oscillator of frequency ωE, and study the optical spectral weight. The optical sum depends on both the strength of the coupling and on the characteristic phonon frequency, ωE. A hardening of ωE, due, for example, to a phase transition, leads to electron undressing and translates into a decrease in the electron kinetic energy and an increase in the total optical sum, as observed in recent experiments in the cuprate superconductors.

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“…The former function in principle comes from a band structure calculation; we will simply model it either as a constant with finite bandwidth or a Lorentzian [3]. The RDOS is a product of our calculation, and is given by…”

Section: The Formalismmentioning

confidence: 99%

“…In the last few years, a number of authors have investigated the effect of a finite Fermi energy on the properties of an interacting electron system [1,2,3,4,5,6,7]. In the past, with the understanding that only properties near the Fermi level were important, the Fermi energy was assumed to be infinite, to facilitate integrations over electronic energies [8].…”

Section: Introductionmentioning

confidence: 99%

Electron-Phonon vs. Electron-Impurity Interactions with Small Electron Bandwidths

Doğan

Marsiglio

2007

J Supercond

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It is common practice to try to understand electron interactions in metals by defining a hierarchy of energy scales. Very often, the Fermi energy is considered the largest, so much so that frequently bandwidths are approximated as infinite. The reasoning is that attention should properly be focused on energy levels near the Fermi level, and details of the bands well away from the Fermi level are unimportant. However, a finite bandwidth can play an important role for low frequency properties: following a number of recent papers, we examine electron-impurity and electron-phonon interactions in bands with finite widths. In particular, we examine the behaviour of the electron self energy, spectral function, density of states, and dispersion, when the phonon spectral function is treated realistically as a broad Lorentzian function. With this phonon spectrum, impurity scattering has a significant non-linear effect.

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Self-consistent modification to the electron density of states due to electron-phonon coupling in metals

Cited by 28 publications

References 11 publications

Effects of lattice geometry and interaction range on polaron dynamics

Effects of lattice geometry and interaction range on polaron dynamics

Optical sum increase due to electron undressing

Electron-Phonon vs. Electron-Impurity Interactions with Small Electron Bandwidths

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