ps7 - Physics 880.06: Problem Set 7 Due Tuesday, May 31,...

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Unformatted text preview: Physics 880.06: Problem Set 7 Due Tuesday, May 31, 2011 at 11:59 P. M. 1. (20 pts.) As stated in class, the anisotropic Ginzburg-Landau free en- ergy density is given by the following expression: f = f n + | | 2 + 2 | | 4 + 1 2 m ab vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle parenleftBigg i h e A c parenrightBigg vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle 2 + + 1 2 m c vextendsingle vextendsingle vextendsingle vextendsingle parenleftbigg i h z e A z c parenrightbigg vextendsingle vextendsingle vextendsingle vextendsingle 2 + | B | 2 8 . (1) Here and are scalar coefficients, is the complex scalar order parameter, f is the free energy per unit volume, f n is the normal state free energy density, A is the vector potential, B is the magnetic induction, and m ab and m c are the effective masses. We also assume that the coefficient has the temperature dependence = [ T/T c (0) 1] , (2) where is a positive constant and T c (0) is the superconducting tran- sition temperature at zero field. The two Ginzburg-Landau equations obtained from this free energy are + | | 2 + 1 2 m ab parenleftBigg i h e A c parenrightBigg 2 + + 1 2 m c parenleftbigg i h z e A z c parenrightbigg 2 = 0 (3) and J = e 2 m ab bracketleftBigg parenleftBigg i h e A c parenrightBigg + c.c. bracketrightBigg + + e 2 m c bracketleftbigg parenleftbigg i h z e A z c parenrightbigg + c.c. bracketrightbigg z. (4) (a). (10 pts.) By linearizing Eq. 3 with respect to , and finding the energy of the lowest Landau level, find the transition temperature 1 T c ( B ) for (i) B parallel to the z axis; (ii) B parallel to the x axis....
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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.

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ps7 - Physics 880.06: Problem Set 7 Due Tuesday, May 31,...

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