Superconducting Gap inMgB2: Electronic Raman Scattering Measurements of Single Crystals

Abstract

Polarization-resolved Raman scattering measurements were performed on MgB(2) single crystals to determine the magnitude, symmetry, and temperature dependence of the superconducting gap. A single sharp peak due to Cooper pair breaking appears in the electronic continuum below T(c), reaching a maximum Raman shift of 105 +/- 1 cm(-1) [2 Delta(0)/k(B)T(c) = 3.96 +/- 0.09] and showing up to 5 cm(-1) anisotropy between polarized and depolarized spectra. The temperature dependence of 2 Delta follows that predicted from BCS theory, while the anisotropy decreases with decreasing temperature. It is concluded that the Raman results are consistent with a slightly anisotropic s-wave gap in a conventional BCS superconductor.

Ab initiocalculation of low-energy collective charge-density excitations inMgB2

“…In the evaluation of these curves we use a "σπ − E2g" coupling parameter ∆=17.3 meV in order to place the position of the P ⊕ mode at qc = 0 in agreement with the Raman measurements. 5,6,7 in MgB 2 feed the strength from the small q c modes into the charge density fluctuations at large (q c + G z ) in a similar fashion as occurs in the case of the higher energy mode. 25 These sine-like dispersing modes continue to have strength at momenta in subsequent BZ's and this is a direct consequence of a layered MgB 2 structure.…”

“…However, despite the tremendous progress achieved in understanding of superconductivity in MgB 2 , many of its fundamental properties related to phonons and electron-phonon (e − ph) coupling are still puzzling and remain under intense debate. Thus such important issues as, e.g., the reduced isotope effect, 2,3,4 the nature of the strong broad continuum in Raman spectra, the unusually broad linewidth of the E 2g phonon mode seen in Raman spectra, 5,6,7 the inconsistency between the results of Raman scattering and x-ray measurements, 8,9,10 and the role of non-adiabatic effects 8,11,12,13,14 have not yet found satisfactory explanations.As for the electronic part of the e−ph picture of superconductivity in MgB 2 , it has received substantially less attention than the phonon part. In particular, in all evaluations of the e−ph interaction the adiabatic approximation has been used, and even in ab initio calculations 15 of T c the dynamical Coulomb interaction has been considered in its static form.…”

Kohn Anomaly inMgB2by Inelastic X-Ray Scattering

“…Even more extreme cases of a Kohn anomaly have been considered in related materials [12]. Earlier experimental work to probe phonon structure in MgB 2 includes neutron density of states measurements on polycrystalline samples [13] and Raman scattering data [14]. The first is an integral method which does not easily allow investigation of specific modes, while the second is limited to probing phonons (and in this case only the E 2g mode) at Γ.…”

Strong interaction between electrons and collective excitations in the multiband superconductorMgB2

“…The superconductivity is believed to caused by the E 2g phonon mode at 75meV that couples strongly to the 2D σ-bands, but more weakly to the π-bands 19 , leading to two different gaps, ∆ σ = 6.5 meV and ∆ π = 1.5meV, as revealed by previous tunneling 26 and ARPES studies 27 . Inelastic neutron scattering studies have reported optical phonon modes at ∼35, 55, 75, 85 and 100 meV 28 , while Raman scattering reports a single, broad asymmetric peak at 75meV, attributed to the E 2g mode, as well as a sharp peak at 2∆ σ = 12meV due to a pair breaking excitation 29 . As a bonus, due to its multi-gap nature, MgB 2 also contains another exotic collective mode that can couple to the electrons: the Leggett mode [21][22][23][24][25] .…”