Electron and phonon dispersions of the two dimensional Holstein model: Effects of vertex and non-local corrections

Abstract

I apply the newly developed dynamical cluster approximation (DCA) to the calculation of the electron and phonon dispersions in the two dimensional Holstein model. In contrast to previous work, the DCA enables the effects of spatial fluctuations (non-local corrections) to be examined. Approximations neglecting and incorporating lowest-order vertex corrections are investigated. I calculate the phonon density of states, the renormalised phonon dispersion, the electron dispersion and electron spectral functions. I demonstrate how vertex corrections stabilise the solution, stopping a catastrophic softening of the $(\pi ,\pi )$ phonon mode. A kink in the electron dispersion is found in the normal state along the $(\zeta ,\zeta )$ symmetry direction in both the vertex- and non-vertex-corrected theories for low phonon frequencies, corresponding directly to the renormalised phonon frequency at the $(\pi ,0)$ point. This kink is accompanied by a sudden drop in the quasi-particle lifetime. Vertex and non-local corrections enhance the effects at large bare phonon frequencies.

arXiv commentI am posting reprints of the final submitted versions of previous articles to improve access. Here ARPES "kinks" are discussed. Article was published in 2003. 17 pages, 9 figures

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• Breakdown of Migdal--Eliashberg theory via catastrophic vertex divergence at low phonon frequency
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• Influence of phonon renormalization in Eliashberg theory for superconductivity in 2D and 3D systems
• Superconducting states of the quasi-2D Holstein model: Effects of vertex and non-local corrections
• Enhancement of gaps in thin graphitic films for heterostructure formation
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• Charge correlations suppress unconventional pairing in the Holstein model
• Unconventional pairing in bipolaronic theories
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• Extending the theory of phonon-mediated superconductivity in quasi-2D