In 2001 a new superconductor, the simple intermetallic alloy MGB2 with critical temperature T. = 39 K, was discovered. This was the highest T. for a non-ceramic superconductor and thus attracted much interest. a) What are the two main phenomena associated with superconductivity (i.e. two basic property of superconductivity)? b) Explain the following two concepts: (i) coherence length , (ii) penetration depth c) In the Bardeen-Cooper-Schrieffer theory of superconductivity the critical temperature is given by the semi-empirical McMillan formula 1.04(1+ 1) 2-H (1+0.621) ho, T. 1.45k, -exp 2>0.2 where op is the Debye frequency, 2 is the effective electron-phonon coupling constant, and 4 is the repulsive Coulomb interaction parameter which is = 0.15 for all superconductors. Assuming 4 is constant, how whould you change the remaining parameters to maximize T? d) Figure shows the phonon density of states for MGB2 at 295 K. Estimate the Debye frequency and the effective electron-phonon coupling constant of MGB2. e) Let us assume that you can engineer the electron-phonon coupling without affecting other parameters. Could MgB, in this case be engineered to be a room temperature superconductor? 0.30 MgB, 0.25T=295K 0.20 0.15 0.10 0.05 0.00 O 20 40 60 80 Energy (mev) 100 Density of phonon modes as a function of phonon energy in MgB,at 295 K. f) Following figure shows a scanning electron microscope image of the superconductor NbSe, at 0.2 K and an applied magnetic field H. Explain the pattern of bright dots shown in the figure. Explain what you would expect to see in the scanning electron microscope if the applied magnetic field is (i) below the lower critical field, H < Hej, (ii) above the upper critical field H > H,2. 1000 A GDOS (arb. units) 8 8