A Numerical Study of the Effect of Disorder on Optical Conductivity in Inhomogeneous Superconductors

Long He, Jian Sun, Cunjun Yang, Yun Song

Department of Physics, Beijing Normal University, Beijing, China.

DOI: 10.4236/jmp.2013.46A004                

Abstract

We present the effect of disorder on the optical conductivity of two-dimensional inhomogeneous superconductors by applying the kernel polynomial method to solve the Bogoliubov-de Gennes equations. By means of the lattice size scaling of the generalized inverse participation ratio, we find that the localization length of the quasiparticle decreases significantly with the increase of the disorder strength. Meanwhile, the weak disorder can readily restrain the Drude weight, while the superconducting gap has the tendency to suppress the low-energy optical conductivity. We also employ the Lanczos exact diagonalization method to study the competition between the on-site repulsive interactions and disorder. It is shown that the screening effect of repulsive interactions significantly enhances the Drude weight in the normal phase.

Keywords

Inhomogeneous Superconductor; Disorder Effect; Anderson Localization; Kernel Polynomial Method; Lanczos Method

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	P. A. Lee, Reports on Progress in Physics, Vol. 71, 2008, Article ID: 012501. doi:10.1088/0034-4885/71/1/012501
[2]	A. N. Pasupathy, A. Pushp, K. K. Gomes, C. V. Parker, J. S. Wen, Z. J. Xu, et al., Science, Vol. 320, 2008, pp. 196-201. doi:10.1126/science.1154700
[3]	K. Chatterjee, M. C. Boyer, W. D. Wise, T. Kondo, T. Takeuchi, H. Ikuta and E. W. Hudson, Nature Physics, Vol. 4, 2008, pp. 108-111. doi:10.1038/nphys835
[4]	P. G. de Gennes, “Superconductivity of Metals and Alloys,” Addison-Wesley, Boston, 1989.
[5]	W. A. Atkinson, P. J. Hirschfeld and A. H. MacDonald, Physical Review Letters, Vol. 85, 2000, pp. 3922-3925. doi:10.1103/PhysRevLett.85.3922
[6]	A. Garg, M. Randeria and N. Trivedi, Nature Physics, Vol. 4, 2008, pp. 762-765. doi:10.1038/nphys1026
[7]	H. Alloul, J. Bobroff, M. Gabay and P. J. Hirschfeld, Reviews of Modern Physics, Vol. 81, 2009, pp. 45-108.
[8]	L. Covaci, F. M. Peeters and M. Berciu, Physical Review Letters, Vol. 105, 2010, Article ID: 167006. doi:10.1103/PhysRevLett.105.167006
[9]	A. Weiße, G. Wellein, A. Alvermann and H. Fehske, Reviews of Modern Physics, Vol. 78, 2006, pp. 275-306. doi: 10.1103/RevModPhys.78.275
[10]	A. Ghosal, M. Randeria and N. Trivedi, Physical Review B, Vol. 65, 2001, Article ID: 014501. doi:10.1103/PhysRevB.65.014501
[11]	A. Punnoose and A. M. Finkel’stein, Science, Vol. 14, 2005, pp. 289-291. doi:10.1126/science.1115660
[12]	Y. Song, H. K. Song and S. P. Feng, Journal of Physics: Condensed Matter, Vol. 23, 2011, Article ID: 205501. doi:10.1088/0953-8984/23/20/205501
[13]	N. C. Murphy, R. Wortis and W. A. Atkinson, Physical Review B, Vol. 83, 2011, Article ID: 184206. doi:10.1103/PhysRevB.83.184206
[14]	E. Dagotto, Reviews of Modern Physics, Vol. 66, 1994, pp. 763-840. doi:10.1103/RevModPhys.66.763
[15]	Y. Song, S. Bulut, R. Wortis and W. A. Atkinson, Journal of Physics: Condensed Matter, Vol. 21, 2011, Article ID: 385601. doi:10.1088/0953-8984/21/38/385601