Fig. 13 JO. Optical reflectivity spectra in the infrared range at several temperatures (below and above Tc) for (a) KjC«, and (b) Rb3Cal. Also shown in the figure is the Hagen-Rubens extrapolation for the Kramers-Kronig analysis of the 5?(c<j) reflectivity data at low frequencies in (a) for the 25 K data, and in (b) for the 25 K and 40 K data [13.151], temperature above Tc and another below Tc (6 K) for both K3C60 (a) and Rb3C 60 (b). In the superconducting ground state, (rx(w) - 0 for hw < 2A, where 2A is the superconducting gap. Thus the cr,(w) data in Fig. 13.31 indicate that 2A= 48 cm-1 (K3C60) and 60 cm_1(Rb3C60). Normalizing these values to Tc yields 2A/khTc = 3.6 (K3C60) and 2.98 (Rb3C60) [13.151], in good agreement with the weak-coupling Bardeen-Cooper-Schrieffer (BCS) value 2&/kTc = 3.52.
To satisfy the conductivity sum rule, the oscillator strength associated with the area A in Fig. 13.31 between the <x,(m) curves in the normal
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