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Unformatted text preview: Physics 880.06: Problem Set 4 This problem set is due by BEGINNING OF CLASS on Tuesday, May 10, 2011. This problem set consists of just a single problem, which is worth 25 points. 1. The BCS equation for the gap function k at temperature T = 0 is k =- 1 2 summationdisplay k k V k , k radicalBig 2 k + 2 k , (1) where k = k- E F , and k is the energy of a non-interacting electron of wave vector k . (a). Show that if V k , k =- A k A k , where A k is a specified function of k , then the above equation is solved by a gap function of the form k = A k , where is independent of k , and find an equation for . (b). Now suppose specifically that our superconductor is two-dimensional, and that A k has the form A k = A cos(2 ) (2) if | k- E F | < h c , and A k = 0 (3) otherwise. Here h c is a cutoff energy, k = h 2 k 2 / (2 m ), and we have written k = ( k cos ,k sin ). Obtain an integral expression which de- termines in this case, but you need not solve this to obtain ex-...
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This note was uploaded on 07/28/2011 for the course PHYSICS 880.06 taught by Professor Stroud during the Fall '10 term at Ohio State.
- Fall '10