We report observation of Leggett's collective mode in a multiband MgB2 superconductor with Tc=39 K arising from the fluctuations in the relative phase between two superconducting condensates. The novel mode is observed by Raman spectroscopy at 9.4 meV in the fully symmetric scattering channel. The observed mode frequency is consistent with theoretical considerations based on first-principles computations.

We present a Raman scattering study of the E2g phonon anharmonicity and of superconductivity induced self-energy effects in MgB2 single crystals. We show that anharmonic two phonon decay is mainly responsible for the unusually large linewidth of the E2g mode. We observe ∼ 2.5% hardening of the E2g phonon frequency upon cooling into the superconducting state and estimate the electron-phonon coupling strength associated with this renormalization. PACS numbers: 74.70.Ad, 74.25.Ha, 74.25.Gz, 78.30.Er High-T c superconductivity in MgB 2 is known to be promoted mainly due to the boron layers 1 , thus the high frequency lattice vibrations of light boron atoms beneficially increase the electron-phonon coupling. The E 2g Raman active in-plane boron vibrational mode contributes significantly to superconductivity; this fact is reflected by the Eliashberg function α 2 F (ω) peaking in the same frequency range where a high phononic density of states is accounted for by Van Hove singularities of the E 2g branch in the Γ and A points of the Brillouin zone (BZ) 2,3 . The reason the E 2g mode plays a prominent role in the superconducting (SC) mechanism is that the mode strongly couples to the σ-type states of the boron plane as can be seen from the basic geometry of the electronic configuration 4 . Raman spectra exhibit unusually broad linewidth of the E 2g mode 5,6,7 which has been the subject of numerous speculations. While high impurity scattering in earlier low quality samples has been suggested as one of the possible reasons, this mechanism can be readily excluded with recent high quality single crystals. The two remaining contributions to the E 2g phonon rapid decay are (i) strong electron-phonon coupling and (ii) multiphononic decay (subsequently referred to as anharmonicity). The relative importance of the electronphonon coupling and anharmonicity in this matter is under intense debate. On one hand a density functional theory calculation asserts that the anharmonic contribution to the E 2g phonon linewidth is negligible (∼ 1 meV) 8 . On the other hand analysis of the phonon self-energy in the long wavelength limit shows that the σ-band contribution to the phonon decay is vanishing 9 . Thus, even when contributions of the spectral weight of α 2 F (ω)| ω<ωE 2g to the damping of the E 2g phonon are accounted for, 10 the experimentally observed linewidth of 25-35 meV at low temperatures 5,6 cannot be explained with electron-phonon coupling alone whose part in the E 2g mode linewidth at low temperatures amounts to about 6 meV even in such an elaborate scenario as that in Ref.10 . Raman scattering experiments have shown that the frequency of the E 2g mode in single crystals at room temperature is around 79 meV 5,6 whereas theoretical calculations systematically underestimate this value by about 10 meV 3,8 . It has been suggested that if the E 2g band around the Γ-point is anharmonic then the E 2g mode frequency is increased by the missing amount to match the experimentally observed value 13,14 . In addition, the experimenta...

Electronic Raman scattering studies on MgB2 single crystals as a function of excitation and polarization have revealed three distinct superconducting features: a clean gap below 37 cm −1 and two coherence peaks at 109 cmand 78 cm −1 which we identify as the superconducting gaps in π-and σ-bands and as the Leggett's collective mode arising from the fluctuation in the relative phase between two superconducting condensates residing on corresponding bands. The temperature and field dependencies of the superconducting features have been established. A phononic Raman scattering study of the E2g boron stretching mode anharmonicity and of superconductivity induced self-energy effects is presented. We show that anharmonic two phonon decay is mainly responsible for the unusually large linewidth of the E2g mode. We observe ∼ 2.5% hardening of the E2g phonon frequency upon cooling into the superconducting state and estimate the electron-phonon coupling strength associated with this renormalization.

Polarized Raman scattering has been performed on CaC 6 superconductor. We identify two of the three Raman-active E g phonon modes at 440 and 1508 cm −1 expected for the R3m space group of CaC 6 . These first-order scattering modes appear along with the D and G bands around 1300 and 1600 cm −1 that are similar in origin to the corresponding bands in plain graphite. The intensities of the D and G bands in CaC 6 correlate with degree of disorder. The D band arises from the double resonant Raman-scattering process; its frequency shifts as a function of excitation energy with ϳ35 cm −1 / eV. The double resonant Raman scattering probes phonon excitations with finite wave vector q. We estimate the characteristic spacing of structural defects to be on the scale of about 100 Å by comparing the intensity of the D band and the 1508 cm −1 E g mode in CaC 6 to calibrated intensity ratio of analogous bands in disordered graphites. A sharp superconducting coherence peak at 24 cm −1 is observed below T c .

Semiconductor strain engineering has become a critical feature of high-performance electronics because of the significant device performance enhancements that it enables. These improvements, which emerge from strain-induced modifications to the electronic band structure, necessitate new ultra-sensitive tools to probe the strain in semiconductors. Here, we demonstrate that minute amounts of strain in thin semiconductor epilayers can be measured using electronic Raman scattering. We applied this strain measurement technique to two different semiconductor alloy systems using coherently strained epitaxial thin films specifically designed to produce lattice-mismatch strains as small as 10−4. Comparing our strain sensitivity and signal strength in AlxGa1−xAs with those obtained using the industry-standard technique of phonon Raman scattering, we found that there was a sensitivity improvement of 200-fold and a signal enhancement of 4 × 103, thus obviating key constraints in semiconductor strain metrology.