MIT OpenCourseWare http ocw mit edu 8 512 Theory of Solids II Spring 2009 For information about citing these materials or our Terms of Use visit http ocw mit edu terms 1 Lectures 11 E ect of Disorder on Superconductors We discuss the e ect of disorder on the electromagnetic response of a superconductor and show that the Meissner e ect survives in the presence of disorder The method we use is called the exact eigenstate method where we work with the exact eigenstate of the one body Hamiltonian including the random potential The pairing theory can proceed on this basis An important outcome is the Anderson theorem which states that the energy gap and Tc are una ected by nonmagnetic impurities as long as localization e ects can be ignored On the other hand disorder has a strong e ect on the super uid density This e ect can be calculated quantitatively by recognizing that the matrix elements also appear in the expression for the normal state conductivity For 1 1 where 1 is the impurity scattering rate ns n 1 and is greatly reduced from the total electron density This can be understood from the fact that by opening up an energy gap a piece of width is cut out of the Drude conductivity Lorentzian with width 1 of the normal metal and goes into the delta function in the superconductor The weight of the delta function is ns m Equation 1 follows from the conductivity sum rule Reading de Gennes Superconductivity of Metals and Alloys Chapters 5 2 and 5 3 Lecture 12 Quasiparticles and Coherence Factors In the calculation of the super uid density in the last chapter coherence factors appear which are typical in the expression for many properties of superconductors Famous examples are ultrasonic attenuation and nuclear spin relaxation rate The latter shows a peak just below Tc due to the singular density of states of the superconductor while the former does not show such a peak due to cancellation by the coherence factors Reading Schrie er Theory of Superconductivity Chapters 3 2 3 5
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