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

Abstract

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.

Effect of electron-phonon interaction on spectroscopies in graphene

“…The self-energy is independent of electron momentum label as well as band index, electrons or holes, a simplification they trace 19 to the Dirac nature of the electronic states in graphene. Based on these simplifying ideas, we begin with a self-energy for temperature T = 0 of the form 13,14 …”

“…To obtain a good characterization of the renormalized band profile ͑red curve͒ around the bareband edge W C , it is essential to iterate. 13,15 In a fully realistic model of graphene, one should, of course, use tight-binding bands as the Dirac cone approximation begins to fail at higher energies but band renormalization effects will occur in that case as well. We note that the top of the renormalized band extends to higher energies as compared with the bare band and the bottom extends to lower energies.…”

“…12 It also arises in finite band systems with the top and the bottom of the band are modified in a particularly important way by interactions with the phonons. [13][14][15][16] Another known result in simple metals is that the EPI renormalizations 10,11,17 drop out of the dc value of the conductivity but significantly renormalize its ac value and phonon-assisted Holstein processes become possible. For graphene the dc conductivity which is due to both intraband and interband transitions is also unaffected by the EPI.…”

Strong interplay between electron-phonon interaction and disorder in low-doped systems

“…Another example is that of a low (but finite) electron density and weak electron-phonon coupling. In this case when disorder and electron-phonon interaction are treated self-consistently impurity and phonon contributions to electron scattering are not additive when the Fermi energy is of the order of the phonon frequency 27,28 , and impurity scattering has a significant nonlinear effect 29 . In this work we approach the problem of the interplay between disorder and electron-phonon interaction starting from a weak electron-phonon coupling, going beyond the self-consistent Born approximation used in refs.…”

“…In this work we approach the problem of the interplay between disorder and electron-phonon interaction starting from a weak electron-phonon coupling, going beyond the self-consistent Born approximation used in refs. [27][28][29] by using the Coherent Potential Approximation (CPA) thus extending our treatement to the case of strong disorder. Previous studies of models in this peculiar regime concentrated on the case of classical phonons in binary alloys 30 or, in the same context, on the effects of electron-phonon interaction on transport properties at high temperature 31 .…”