Relative importance of nonlinear electron-phonon coupling and vertex corrections in the Holstein model

Dee, Philip M.; Coulter, Jennifer; Kleiner, Kevin G.; Johnston, S.

doi:10.1038/s42005-020-00413-2

Cited by 31 publications

(10 citation statements)

References 35 publications

(52 reference statements)

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“…This comparison can be improved somewhat with 'renormalized ME' theory in which the phonon propagator is dressed by electron-hole bubbles [34]. Recently, there has been renewed interest in examining the limits of ME theory and when it breaks down [35][36][37][38][39]. Indeed, it has been shown that ME can work well for ω 0 << E F provided the electron phonon coupling is not too large, enabling estimates of T SC to be made by extrapolating DQMC results down to lower temperatures using ME calculations [35].…”

Section: Introductionmentioning

confidence: 99%

Superconductivity and charge density wave order in the 2D Holstein model

Bradley,

Batrouni,

Scalettar

2020

Preprint

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The Holstein Hamiltonian describes fermions hopping on a lattice and interacting locally with dispersionless phonon degrees of freedom. In the low density limit, dressed quasiparticles, polarons and bipolarons, propagate with an effective mass. At higher densities, pairs can condense into a low temperature superconducting phase and, at or near commensurate filling on a bipartite lattice, to charge density wave (CDW) order. CDW formation breaks a discrete symmetry and hence occurs via a second order (Ising) transition, and therefore at a finite T cdw in two dimensions. Quantum Monte Carlo calculations have determined T cdw for a variety of geometries, including square, honeycomb, and Lieb lattices. The superconducting transition, on the other hand, in d = 2 is in the Kosterlitz-Thouless (KT) universality class, and is much less well characterized. In this paper we determine Tsc for the square lattice, for several values of the density ρ and phonon frequency ω0. We find that quasilong range order sets in at Tsc t/20, where t is the near neighbor hopping amplitude, consistent with previous rough estimates from simulations which only extrapolated to the temperatures we reach from considerably higher T . We also show evidence for a discontinuous evolution of the density as the CDW transition is approached at half-filling.

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Section: Introductionmentioning

confidence: 99%

Superconductivity and charge density wave order in the 2D Holstein model

Bradley,

Batrouni,

Scalettar

2020

Preprint

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“…Thus, the harmonic description of phononic excitations in the medium provided by the Holstein model may not be sufficient, and the effects of anharmonic terms on the phases of Holstein systems should be taken into account. [32][33][34][35][36][37][39][40][41] Several approaches to include anharmonic effects have been considered, for example nonlinear coupling terms between fermions and phonons, [32][33][34][35][36][37] or quartic [38][39][40] or Gaussian 41 contributions to the phonon potential energy. Anharmonicity has also been considered in the context of Migdal-Eliashberg theory.…”

Section: Introductionmentioning

confidence: 99%

Quantum Monte Carlo study of an anharmonic Holstein model

Paleari,

Hébert,

Cohen-Stead

et al. 2021

Preprint

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We study the effects of anharmonicity on the physics of the Holstein model, which describes the coupling of itinerant fermions and localized quantum phonons, by introducing a quartic term in the phonon potential energy. We find that the presence of this anharmonic term reduces the extent of the charge density wave phase (CDW) at half-filling as well as the transition temperature to this phase. Doping away from half-filling, we observe a first order phase transition between the CDW and a homogeneous phase which is also present in the harmonic model. In addition, we study the evolution of the superconducting susceptibility in the doped region and show that anharmonicity can enhance the superconducting response.

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“…Characteristics of the superconducting state in such studies are found only by extrapolation from normal state properties, and, in addition, the QMC calculations are performed on relatively small lattices due to the huge complexity of the problem. The most commonly studied system in these works is the 2D Holstein model [8,[11][12][13][14][15][16], often with additional constraints such as half-filling, while 3D systems are rarely considered in numerical calculations, presumably due to the large computational complexity.…”

Section: Introductionmentioning

confidence: 99%

Influence of phonon renormalization in Eliashberg theory for superconductivity in 2D and 3D systems

Schrodi,

Aperis,

Oppeneer

2020

Preprint

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Eliashberg's foundational theory of superconductivity is based on the application of Migdal's approximation, which states that vertex corrections to first order electron-phonon scattering are negligible if the ratio between phonon and electron energy scales is small. The resulting theory incorporates the first Feynman diagrams for electron and phonon self-energies. However, the latter is most commonly neglected in numerical analyses. Here we provide an extensive study of fullbandwidth Eliashberg theory in two and three dimensions, where we include the full back reaction of electrons onto the phonon spectrum. We unravel the complex interplay between nesting properties, Fermi surface density of states, renormalized electron-phonon coupling, phonon softening, and superconductivity. We propose furthermore a scaling law for the maximally possible critical temperature T max c ∝ λ(Ω) Ω 2 0 − Ω 2 in 2D and 3D systems, which embodies both the renormalized electron-phonon coupling strength λ(Ω) and softened phonon spectrum Ω. Also, we analyze for which electronic structure properties a maximal Tc enhancement can be achieved.

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Relative importance of nonlinear electron-phonon coupling and vertex corrections in the Holstein model

Cited by 31 publications

References 35 publications

Superconductivity and charge density wave order in the 2D Holstein model

Superconductivity and charge density wave order in the 2D Holstein model

Quantum Monte Carlo study of an anharmonic Holstein model

Influence of phonon renormalization in Eliashberg theory for superconductivity in 2D and 3D systems

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