Nonadiabatic contribution to the quasiparticle self-energy in systems with strong electron-phonon interaction

Danylenko, O. V.; Dolgov, O. V.

doi:10.1103/physrevb.63.094506

Cited by 21 publications

(25 citation statements)

References 27 publications

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“…During last years quite a few numerical and analytical studies have confirmed this conclusion [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] (and references theirein). On the other hand a few others (see, for example, [29,30]) still argue that the breakdown of the Migdal-Eliashberg theory might happen only at λ ≥ E F /ω >> 1. Indeed numerical study of the finite bandwidth effects [31] and some analytical calculations of the vertex corrections to the vertex function [32,33,30] with the standard Feynman-Dyson perturbation technique confirm the second conclusion.…”

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confidence: 99%

“…On the other hand a few others (see, for example, [29,30]) still argue that the breakdown of the Migdal-Eliashberg theory might happen only at λ ≥ E F /ω >> 1. Indeed numerical study of the finite bandwidth effects [31] and some analytical calculations of the vertex corrections to the vertex function [32,33,30] with the standard Feynman-Dyson perturbation technique confirm the second conclusion. In this letter I compare the Migdal solution of the Holstein Hamiltonian with the exact one in the extreme adiabatic regime, ω/E F → 0, to show that the ground state of the system is a self-trapped insulating state with broken translational symmetry already at λ ≥ 1.…”

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confidence: 99%

“…[23] the critical value of λ was found to be 1.3 in the adiabatic limit). Meanwhile, some authors [30,29], who relay on the perturbation expansion in powers of λ, fail to notice the self-trapping transition, erroneously claiming that the Migdal-Eliashberg theory could be applied at practically any λ in the extreme adiabatic regime.…”

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confidence: 99%

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Breakdown of the Migdal-Eliashberg theory in the strong-coupling adiabatic regime

Alexandrov

2001

Europhys. Lett.

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In view of some recent works on the role of vertex corrections in the electron-phonon system we readress an important question of the validity of the Migdal-Eliashberg theory. Based on the solution of the Holstein model and 1/λ strongcoupling expansion, we argue that the standard FeynmanDyson perturbation theory by Migdal and Eliashberg with or without vertex corrections cannot be applied if the electronphonon coupling is strong (λ ≥ 1) at any ratio of the phonon, ω and Fermi, EF energies. In the extreme adiabatic limit (ω << EF ) of the Holstein model electrons collapse into self-trapped small polarons or bipolarons due to spontaneous translational-symmetry breaking at λ ≃ 1. With the increasing phonon frequency the region of the applicability of the theory shrinks to lower values of λ < 1.PACS numbers: 74.65.+n,74.60.Mj The theory of ordinary metals is based on 'Migdal's' theorem [1], which showed that the contribution of the diagrams with 'crossing' phonon lines (so called 'vertex' corrections) is small. This is true if the parameter λω/E F is small. It was then shown that if the adiabatic BornOppenheimer approach is properly applied to a metal, there is only negligible renormalisation of the phonon frequencies of the order of the adiabatic ratio, ω/E F << 1 for any value of λ [3]. The conclusion was that the standard electron-phonon interaction could be applied to electrons for any value of λ but it should not be applied to renormalise phonons [4]. As a result, many authors used the Migdal-Eliashberg theory with λ much larger than 1 (see, for example, Ref.[5]).However, starting from the infinite coupling limit, λ = ∞ and applying the inverse (1/λ) expansion technique [6] we showed [7][8][9] that the many-electron system collapses into small polaron regime at λ ∼ 1 almost independent of the adiabatic ratio. In this letter I compare the Migdal solution of the Holstein Hamiltonian with the exact one in the extreme adiabatic regime, ω/E F → 0, to show that the ground state of the system is a self-trapped insulating state with broken translational symmetry already at λ ≥ 1.The vertex corrections and the finite bandwidth are rather technical issues, playing no role in the extreme adiabatic limit [1,32,31]. There is, however, another basic assumption of the canonical Migdal-Eliashberg theory. That is the electron and phonon Green functions (GF) are translationally invariant. As a result one takes G(r, r ′ , τ ) = G(r− r ′ , τ ) with Fourier component G(k, Ω) prior to solving the Dyson equations. This assumption excludes the possibility of local violation of the translational symmetry due to the lattice deformation in any order of the Feynman-Dyson perturbation theory. This is similar to the absence of the anomalous (Bogoliubov) averages in any order of the perturbation theory. To enable electrons to relax into the lowest polaronic states, one has to introduce an infinitesimal translationally noninvariant potential, which should be set equal to zero only in the final solution for the GF [8]. As in the case of the...

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Breakdown of the Migdal-Eliashberg theory in the strong-coupling adiabatic regime

Alexandrov

2001

Europhys. Lett.

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“…Many works have been devoted to superconductivity in nonadiabatic systems and to constructing a theory extending beyond the Migdal theorem (see [7]). It follows from these investigations that for ε F ∼ ω 0 , the vertex functions become negative and therefore reduce the electron-phonon interaction constant, not leading to high values of the superconducting transition temperature T c .…”

Section: Introductionmentioning

confidence: 99%

Two-band superconductivity theory beyond the Migdal theorem

Palistrant

Ursu

2006

Theor Math Phys

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We propose a superconductivity theory of two-band nonadiabatic systems with strong electron correlations in the linear approximation in nonadiabaticity. Assuming a weak electron-phonon interaction, we obtain analytic expressions for the vertex and "intersecting" functions for each of the two bands. With the diagrams involving intersections of two electron-phonon interaction lines taken into account (which means going beyond the Migdal theorem), we determine mass operators of the Green's functions and use them to derive the basic equations of the superconductivity theory for two-band systems. We find an analytic expression for the superconducting transition temperature Tc that differs from the expression in the case of the standard two-band systems by an essential renormalization of the relevant quantities that results from the nonadiabaticity effects and strong electron correlations. We study the dependence of Tc and of the isotopic coefficient α on the Migdal parameter m = ω0/εF and show that accounting for the overlap of energy bands on the Fermi surface and for the nonadiabaticity effects at small values of the transferred momentum (q 2pF) allows obtaining high values of Tc even for the weak electron-phonon interaction.

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“…обзор [7]). Из этих исследований вытекает, что вершинные функции при ε F ∼ ω 0 оказываются отрица-тельными и, следовательно, уменьшают константу электрон-фононного взаимодей-ствия, не приводя к высоким значениям температуры сверхпроводящего перехода T c .…”

Section: Introductionunclassified

Выход За Рамки Теоремы Мигдала В Теории Двухзонной Сверхпроводимости

Palistrant¹,

Ursu²,

Ursu³

2006

ТМФ

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Предложена теория сверхпроводимости двухзонных неадиабатических си-стем с сильными электронными корреляциями в линейном приближении по неадиабатичности. В предположении слабого электрон-фононного взаимодей-ствия получены аналитические выражения для вершинной и "пересекающейся" функций для каждой из двух зон. С учетом диаграмм с пересечением двух линий электрон-фононного взаимодействия (выход за рамки теоремы Мигда-ла) определены массовые операторы функций Грина и на их основе получены основные уравнения теории сверхпроводимости двухзонных систем. Найдено аналитическое выражение для температуры сверхпроводящего перехода Tc, ко-торое отличается от случая обычных двухзонных систем существенной перенор-мировкой входящих в него величин, связанной с эффектами неадиабатичности и сильными электронными корреляциями. Изучена зависимость величины Tc и изотопического коэффициента α от параметра Мигдала m = ω0/εF. Показано, что учет перекрытия энергетических полос на поверхности Ферми и эффек-тов неадиабатичности при малых значениях передаваемого импульса (q 2pF) позволяет получить высокие значения Tc даже при слабом электрон-фононном взаимодействии.Ключевые слова: сверхпроводимость, неадиабатическая система, электрон-фононное взаимодействие, теорема Мигдала.

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Nonadiabatic contribution to the quasiparticle self-energy in systems with strong electron-phonon interaction

Cited by 21 publications

References 27 publications

Breakdown of the Migdal-Eliashberg theory in the strong-coupling adiabatic regime

Breakdown of the Migdal-Eliashberg theory in the strong-coupling adiabatic regime

Two-band superconductivity theory beyond the Migdal theorem

Выход За Рамки Теоремы Мигдала В Теории Двухзонной Сверхпроводимости

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