Abstract
We show that weak static random potentials have pronounced effects on the quasiparticle states of a 2Dd-wave superconductor close to a node. We prove that the vertex correction coming from the simplest crossed diagram is important even for a nonmagnetic potential. The leading frequency and momentum dependent logarithmic singularities in the self-energy are calculated exactly to second order in perturbation theory. The self-energy corrections lead to a modified low energy density of states which depends strongly on the type of random potential and which can be measured in experiments. There is an exceptional case for a potential with extremely local scatterers and opposite nodes separated by (π, π) where an exact cancelation takes place eliminating the leading frequency dependent singularity in the simplest crossed diagram. A comparison of the perturbative results with a self-consistent CPA (coherent potential approximation) for the nonmagnetic disorder reveals qualitative differences in the self-energy at the smallest energies which are due to the neglectance of vertex corrections in CPA.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Wollman, D.A., et al.: Phys. Rev. Lett.71, 2134 (1993); Iguchi, I., Wen, Z.: Phys. Rev. B49, 12388 (1994); C.C. Tsuei, C.C., et al.: Phys. Rev. Lett.73, 593 (1994); Brawner, D.A., Ott, H.R.: Phys. Rev. B50, 6530 (1994); Mathai, A., et al.: preprint (1994); Kirtley, J.R., et al.: preprint (1994).
Chen, L., Tremblay, A.-M.S.: J. Phys. Chem. Solids54, 1381 (1993); Mahan, G.D.: Phys. Rev. Lett.71, 4277 (1993).
Radtke, R.J. et al.: Phys. Rev. B48, 653 (1993); Fehrenbacher, R., Norman, M.R.: Phys. Rev. B50, 3495 (1994).
Gor'kov, L.P., Kalugin, P.A.: Pis'ma v ZhETP41, 208 (1985), [JETP Lett.41, 253 (1985)]; Ueda, K., Rice, T.M.: inTheory of Heavy Fermions and Valence Fluctuation, ed. by T. Kazuya. Berlin, Heidelberg, New York: Springer 1985.
Lee, P.A.: Phys. Rev. Lett.71, 1887 (1993).
Pethick, C.J., Pines, D.: Phys. Rev. Lett.57, 118 (1986); Monien, H., Scharnberg, K., Walker, D.: Sol. St. Comm.63, 263 (1987); Hirschfeld, P.J., Wölfle, P., Einzel, D.: Phys. Rev. B37, 83 (1988); Preosti, G., Kim, H., Muzikar, P.: Phys. Rev.B 50, 1259 (1994); Balatsky, A.V., Salkola, M.I., Rosengren, A.: preprint (1994).
Bonn, D.A., et al.: Phys. Rev. B50, 4051 (1994).
I thank A. V. Balatsky for pointing out this difference to me.
Nersesyan, A.A., Tsvelik, A.M., Wenger, F.: Phys. Rev. Lett.72, 2628 (1994); Nersesyan, A.A., Tsvelik, A.M., Wenger, F.: submitted to Nucl. Phys. B. (1994).
Rokhsar, D.S.: Phys. Rev. Lett.70, 493 (1993); Laughlin, R.B.: preprint (1994).
Wenger, F., Östlund, S.: Phys. Rev. B47, 5977 (1993).
Elliot, R.J., Krumhansl, J.A., Leath, P.L.: Rev. Mod. Phys.46, 465 (1974); Thouless, D.J.: Phys. Rep.13, 93 (1974).
Rickayzen, G.:Green's function and Condensed Matter. London, San Diego, Academic Press 1980.