Role of the E2g phonon in the superconductivity of MgB2: a Raman scattering study

Temperature dependent Raman scattering studies in polycrystalline MgB2 (10 < T < 300 K) reveal that the E2g phonon does not experience any self energy renormalization effect across the superconducting critical temperature TC ≈ 40 K, in contrast with most of the current theoretical models. In the presence of our results, those models must be reviewed. The analysis of the temperature dependence of the E2g phonon frequency yields an isobaric Grüneisen parameter of | γE2g |. 1, smaller than the value of 3.9 obtained from isothermal Raman experiments under pressure. It is suggested that this apparent disagreement can be explained in terms of pressure induced changes of the topology of the Fermi surface. 74.25.Jb,74.25Kc,63.20.Kr Typeset using REVTEX 1 MgB2, has attracted much recent interest due to its remarkable physical properties such as: i)relatively high superconducting transition, TC = 39 K, for a binary compound with a simple crystal structure, ii) large and anisotropic coherence lengths, critical fields and current densities, and iii) critical currents that are not limited by grain boundaries (absence of weak link effects). [1] MgB2 forms in a hexagonal structure with space group P6/mmm (D6h). The B atoms are located on a primitive honeycomb lattice consisting of graphite-type sheets. The B2-layers are intercalated with Mg-layers that also form a honeycomb lattice with a Mg atom in the center. For this space group, factor-group analysis predicts four modes at the Γ point: Eu+ A2u+ E2g + B1g, where only the E2g mode is Raman active and the B1g mode is silent. The E2g phonon is a doubly degenerate in-plane B-B bond-stretching mode [2] with the nonvanishing Raman tensor elements (αxx −αyy) and αxy. First principles lattice dynamics calculations indicate that these modes would be observed at 327 cm(Eu), 405 cm (A2u), 572 cm(E2g) and 702 cm (B1g). [3] In analogy with high TC superconductors (HTS) Hall effect measurements [4] indicate that the charge carriers in MgB2 are holes with a hole density at 300 K of 1.7 − 2.8×10 23 holes/cm. In fact, hole mediated superconductivity has been proposed by An and Pickett for MgB2. [5] These authors attribute the relatively high value of TC to the strong coupling between holes and the in-plane boron phonon, E2g modes. According to this model the holes originate in the σ (sp orbitals) bands due to charge transfer from the σ bands to the π (pz orbitals) bands. Based on this model several papers have discussed the possibility of E2g phonon being a frozen-in mode, strongly coupled to the σ electronic bands near the Fermi level. [2,3,6,7] It is claimed that the E2g phonon due to its rather strong coupling to the σ electronic bands would be highly anharmonic, presenting a very large linewidth. However, Boeri et al [8] pointed out that neither the presence at the Fermi level of the σ bands nor their strong coupling to the E2g phonon are sufficient to induce such anharmonic effects and therefore the strong anharmonicity would be mainly related to the small value of the σ conduction holes Fermi energy (≃ 0.45 eV) in the unperturbed crystal. Boeri et al also 2 predicted similar results for heavily hole-doped graphite. On the other hand, in a perfect harmonic crystal, the equilibrium size would not depend on temperature. Consequently, the phonon frequency would be temperature independent and its linewidth should tend to zero. Hence, it is expected that, for strong anharmonicity, the E2g mode in MgB2 would be very broad and its frequency change strongly with temperature. Isothermal pressure dependent Raman scattering results and lattice parameters measurements by Goncharov et al [9] have given some evidence for this anharmonic behavior. They have observed at room temperature a very broad (300 cm) Raman mode at 620 cm associated to the E2g mode and an anomalously large mode Grüneisen parameter, γE2g = 3.9± 0.4. The correlation between TC and the resistivity ratio between room and near TC temperatures, known as the Testardi correlation, is evidence in favor of a dominant electron-phonon mechanism in MgB2. [1] Moreover, the boron isotope effect shows that the boron modes may play a significant role in the MgB2 superconductivity. [10] Besides, TC = 39 K for MgB2 is at the extreme end of TC ’s predicted by the BCS theory [11] that would require an electronphonon coupling (EPC) of λ ≈ 1. [2] However, experimental results [12] give λ ≈ 0.6− 0.7 while first principle calculations [3,7,13] yield an EPC of λ ≈ 0.7 − 0.9. Nevertheless, in these papers there is a consensus about the importance of the E2g phonon in the superconducting mechanism of MgB2. Particularly, Liu et al [2] suggested that the strongest EPC arises along the Γ−A line for the E2g mode, and a 12% hardening below TC at the Γ point is predicted. Therefore, the aim and the important contribution of the present work is to study by means of Raman scattering, the temperature dependence of the E2g mode both below and above TC . Raman spectroscopy is an excellent technique to investigate low energy elementary excitations, particularly in superconductors, because it was one of the first spectroscopic techniques to reveal both the existence of the superconducting gap and its strong coupling to some of the active Raman phonons. [14] In general, for strong electron phonon coupling, the theoretical models predict that a phonon with the symmetry of the gap and comparable en3 ergy should soften or harden below TC , depending on whether the phonon frequency is higher or lower than twice the superconducting energy gap, 2∆0. [15,16] Also, the phonon linewidth should change in the superconducting state; phonons with energy below 2∆0 should sharpen and phonons with energy above 2∆0 should broaden. [15,16] These behaviors have been observed in most of the HTS. [17–19] Besides, the temperature dependence of the phonon frequency and linewidth measured by Raman scattering can give some insight about the anharmonicity of the E2g mode. In general, due to the lattice expansion contribution, [20] the harmonic phonon frequency is temperature dependent and in the lowest-order is given by: