Nonadiabatic coupling effects in MgB2 reexamined

Abstract

The unusual Raman spectrum of MgB2 and its formidable temperature dependence are successfully reproduced by means of a parameter-free ab initio nonadiabatic theory that accounts for the electron-hole pair scattering mechanisms with the system phonons. This example turns out to be a prototypical case where a strong nonadiabatic renormalization of the phonon frequency is partially washed out by the aforementioned scattering events, bringing along a characteristic temperature dependence. Both electron-hole pair lifetime and energy renormalization effects due to dynamical electron-phonon coupling turn out to play a crucial role. This theory could aid in comprehending other Raman spectra characterized with unconventionally strong electron-phonon interaction.Recent years have witnessed an ample interest in nonadiabatic (NA) coupling effects [1,2] and their intriguing impact on the vibrational properties of solids [3]. Particularly strong deviations from the adiabatic phonon spectrum were observed for the long wavelength (q ≈ 0) modes of carbon-based materials, such as metallic carbon nanotubes [4,5], graphite intercalation compounds [6-9], graphene [10][11][12], and boron-doped diamond [13]. The corresponding NA theory based in first principles is well established and in most instances the calculated NA phonon frequencies complement the experiments quite accurately [6,10,14]. Remarkably, in MgB 2 , both the state-of-the-art adiabatic and NA descriptions break down. Namely, the Raman measurements reveal an unusually large linewidth of the E 2g phonon peaked at around 77 meV [15][16][17][18][19], which falls just between the adiabatic (67 meV) and NA (94 meV) values [6,14].In order to resolve this discrepancy numerous explanations emerged. A significant temperature dependence of the phonon spectrum lead numerous studies to ascribe the foregoing anomalies to the anharmonicity [20][21][22][23][24]. Conversely, it was shown that the phonon-phonon corrections constitute only a small portion of the E 2g phonon linewidth and the frequency shift, as well as bring about a minor temperature change [16,[25][26][27][28]. The effects of the electron relaxation processes (e.g., higher order electron-phonon scattering) on the phonon spectrum were also taken into consideration, since it was shown that high-frequency optical modes in metallic systems might be rather sensitive to these processes when q ≈ 0 [29][30][31][32][33][34][35]. In fact, few studies have qualitatively demonstrated that it is precisely this mechanism that prompts the breakdown of the standard adiabatic and NA theories in MgB 2 [6,16,19,27,36,37]. Nevertheless, a concomitant NA theory based in first principles that can resolve this controversy is still absent. Such an in-depth quantitative survey of the NA effects is of great fundamental interest, e.g., for comprehending superconductivity mechanisms, especially in MgB 2 , * dino.novko@gmail.com where the unusually strong interaction between the E 2g phonon and electrons is suspected to underly the electron pairing p...

Broken adiabaticity induced by Lifshitz transition in MoS2 and WS2 single layers

“…In close agreement with the experiments [11,37], the linewidth of the A 1g mode shows a steeper increase as a function of doping, and is generally larger than the E 2g linewidth. This proves that the major part of the experimentally observed doping-induced phonon linewidth modifications in TMDs [11,37] is underlain by the EHP scattering processes due to the EPC (other contribution might be anharmonic coupling), as it is, for example, the case in MgB 2 where nonadiabatic effects as well play a significant role [9]. The linewidth, similarly to the frequency shift, shows a great sensitivity on the topology of the valleys, and therefore can also be used in Raman spectroscopy as an indicator of the Lifshitz transition.All in all, the phonon dynamics in doped single-layer k x a / 2 π k y a / 2 π energ y [eV] K Σ carrier density frequency shift A NA FIG.…”

“…Phonon self-energy. Using the many-body perturbation theory, the phonon spectral function can be obtained with the following formula [6,8,9],…”

“…The strength of this dynamical electronphonon coupling (EPC) can, in fact, be modified as a function of carrier concentration, which makes the Raman spectroscopy a quite powerful tool for characterization of doped two-dimensional and layered materials [7]. However, to make this characterization complete, the precise understanding of the microscopic processes underlying the NA modifications of phonons is needed [1,4,8,9]. Such renormalization of phonons is actually considered quite rare, and apart from these few cases it is not clear in what other two-dimensional materials should adiabaticity break down.Contrary to the aforesaid examples, the vibrational spectra of the single-layer transition metal dichalcogenides (TMDs) under bias voltage is believed to be adiabatic [10,11].…”

“…1(i)-(l). In particular, I show the results obtained by means of the adiabatic (A) density functional perturbation theory (DFPT) as well as the frequencies corrected with the DFT-based NA method [6,8,9] (see the Method section). The corresponding absolute values of the adiabatic frequencies for pristine systems are given in the Supplementary Table S1.…”

“…Consequently, the latter demonstrates how the Raman spectroscopy could be utilized in order to extract the right amount of carrier density required for one-to multi-valley transformations in TMDs and similar semiconductors. Also, since both superconductive state and the breakdown of the adiabaticity occur at the outset of the Lifshitz transition, it is likely that the nonadiabatic channels are open in the superconductivity of the TMDs, and thus the framework beyond the standard Migdal-Eliashberg theory [34] might be necessary to explain the corresponding superconductive pairing as well as the discrepancy between 4 the theoretically-and experimentally-obtained transition temperature T c [18].In what follows, I investigate the impact of the EPCinduced electron-hole pair (EHP) scattering processes [4,9] on phonons in TMDs. In Figs.…”