Ultrafast Hot Phonon Dynamics in MgB2 Driven by Anisotropic Electron-Phonon Coupling

Abstract

The zone-center E2g modes play a crucial role in MgB2, controlling the scattering mechanisms in the normal state as well the superconducting pairing. Here, we demonstrate via first-principles quantum-field theory calculations that, due to the anisotropic electron-phonon interaction, a hotphonon regime where the E2g phonons can achieve significantly larger effective populations than other modes, is triggered in MgB2 by the interaction with an ultra-short laser pulse. Spectral signatures of this scenario in ultrafast pump-probe Raman spectroscopy are discussed in detail, revealing also a fundamental role of nonadiabatic processes in the optical features of the E2g mode.Although MgB 2 is often regarded as a conventional high-T c superconductor, described by the Eliashberg theory for phonon-mediated superconductivity, it displays many peculiar characteristics that make it a unique case. Most remarkable is the anisotropy of the electronic and superconducting properties, where electronic states belonging to the σ bands are strongly coupled to phonons, and display thus large superconducting gaps ∆ σ , whereas electronic states associated with the π bands are only weakly coupled to the lattice, and hence exhibit small superconducting gaps ∆ π [1-10]. Such electronic anisotropy is also accompanied by a striking anisotropy in the phonon states. The electron-phonon (e-ph) coupling is indeed strongly concentrated in few in-plane E 2g phonons modes along the Γ − A path of the Brillouin zone [4,11,12], whereas the remaining e-ph coupling is spread over all other lattice modes in the Brillouin zone.Due to its pivotal role in ruling e-ph based many-body effects and in the superconducting pairing, the properties of the long-wavelength E 2g mode have been extensively investigated, both theoretically and experimentally [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. On the experimental side, Raman spectroscopy has proven particularly suitable for providing fundamental information on the lattice dynamics and on the manybody e-ph processes. Particularly debated is the origin of the large phonon linewidth Γ E2g ≈ 25 meV, and of the temperature dependence of both the phonon frequency and linewidth [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. The complexity of identifying the quantum-mechanical origin of these phenomena arises from the concomitance of the e-ph interaction, non-adiabaticity, and lattice anharmonicities, in turn responsible for phonon-phonon scattering and thermal expansion. A possible path for tuning selectively only one of these processes is thus highly desirable, in order to disentangle the different mechanisms in action.Ultrafast time-resolved optical characterizations of MgB 2 with a pump-probe setup were presented in Refs. [31][32][33], where two different relaxation times were identified in the normal states. In particular, the ob-served anomalous blueshift at a short time scale of the in-plane plasmon was qualitatively explained in Ref. [33] by assumin...

Fingerprints of hot-phonon physics in time-resolved correlated quantum lattice dynamics

“…Following Ref. [36], the predominance of the hot-phonon modes in the total coupling can be captured by splitting the total Eliashberg function in a hot and cold component,…”

“…Within this context, the possibility of a phonon bottleneck, and hence of hot phonons, has been so far associated only to semiconductors and semimetals, whereas conventional metals, with a large Fermi surface allowing scattering with many q-phonons, were thought to be incompatible with such a scenario. At odds with this belief, a novel path for inducing hot phonons has been recently proposed for unconventional metals characterized by a strong anisotropy of the el-ph coupling [35,36]. In the paradigmatic case of MgB 2 , the el-ph coupling is concentrated in a few in-plane modes at the Brillouin zone center possessing the E 2g symmetry [37][38][39][40][41][42][43][44], with a strong resemblance to the relevant modes in single-and multi-layer graphene.…”

“…In the paradigmatic case of MgB 2 , the el-ph coupling is concentrated in a few in-plane modes at the Brillouin zone center possessing the E 2g symmetry [37][38][39][40][41][42][43][44], with a strong resemblance to the relevant modes in single-and multi-layer graphene. As a consequence of such remarkable anisotropy, the energy initially pumped into the electron sector is efficiently and rapidly (∼ 50 fs) transferred only to such few lattice degrees of freedom that get a much larger population compared to the remaining lattice modes, whereas a final thermalization among the whole phonon modes and among electron and lattice degrees of freedom occurs on a much larger time scale (∼ 0.4 ps) [36]. On the experimental ground, an indirect signature of such hot-phonon scenario has been observed in the onset of unconventional features in the time-resolved optical spectra [35].…”

“…On the experimental ground, an indirect signature of such hot-phonon scenario has been observed in the onset of unconventional features in the time-resolved optical spectra [35]. More direct and precise fingerprints have been proposed at the theoretical level in the analysis of time-resolved Raman spectroscopy, both in spectral features as well as in integrated spectral weights [36]. An accurate measurement of time-resolved Raman spectra in MgB 2 needs to face with the limitations of the uncertainty principle constraining time and energy resolution [45].…”

“…In addition, it should be remarked that in both cases the presence of a non-thermal population of the in-plane E 2g modes is not directly probed via the properties of the lattice degrees of freedom, but indirectly through the el-ph driven many-body renormalization of the electronic response, i.e. in the optical response [35] or in the phonon self-energy [36,46], which is strictly related to the electronic screening.…”