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arXiv:cond-mat/9703048

Reply to the Comment by A.A. Nersesyan and A.M. Tsvelik on the "Non--Zero Fermi Level Density of States for a Disordered d-Wave Superconductor in Two Dimensions" (PRL 77, 3013 (1996)) by K. Ziegler, M.H. Hettler and P.J. Hirschfeld

K. Ziegler, Matthias H. Hettler, P. J. Hirschfeld

Published Mar 5, 1997• 0 citations
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Abstract

In a recent Comment (cond-mat/9701197) on our Letter (PRL 77, 3013 (1996), cond-mat/9604176) Nersesyan and Tsvelik questioned the relevance of our exact calculation of the density of states (DOS) of a 2D d-wave superconductor using a Lorentzian disorder distribution, claiming ``that models with Lorentzian and Gaussian disorder belong to different universality classes'', on grounds of a comparison with a straightforward perturbation expansion in the disorder potential. We showed in a very recent paper (cond-mat/9703047) that a rigorous nonzero lower bound for DOS can be established without relying on the tails of the disorder distribution, i.e. both the Gaussian and Lorentzian distributions belong to a large class of distributions which give a nonzero lower bound for the DOS. This proves that the result of our Letter is generic.

DOI
10.48550/arxiv.cond-mat/9703048

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In a recent Comment (cond-mat/9701197) on our Letter (PRL 77, 3013 (1996), cond-mat/9604176) Nersesyan and Tsvelik questioned the relevance of our exact calculation of the density of states (DOS) of a 2D d-wave superconductor using a Lorentzian disorder distribution, claiming ``that models with Lorentzian and Gaussian disorder belong to different universality classes'', on grounds of a comparison with a straightforward perturbation expansion in the disorder potential. We showed in a very recent paper (cond-mat/9703047) that a rigorous nonzero lower bound for DOS can be established without relying on the tails of the disorder distribution, i.e. both the Gaussian and Lorentzian distributions belong to a large class of distributions which give a nonzero lower bound for the DOS. This proves that the result of our Letter is generic.
We consider a disordered ddd-wave superconductor in two dimensions. Recently, we have shown in an exact calculation that for a lattice model with a Lorentzian distributed random chemical potential the quasiparticle density of states at the Fermi level is nonzero. As the exact result holds only for the special choice of the Lorentzian, we employ different methods to show that for a large class of distributions, including the Gaussian distribution, one can establish a nonzero lower bound for the Fermi-level density of states. The fact that the tails of the distributions are unimportant in deriving the lower bound shows that the exact result obtained before is generic.
We reply to the comment on our published paper `` Universal Fluctuations in Correlated Systems'',Phys. Rev. Lett. Vol; 84, p3744 (2000), by B. Zheng and S. Trimper, cond-mat/0109003. We argue that their results confirm our conjecture, that the probability distribution for order parameter fluctuations in the 2D and 3D Ising models at a temperature T∗(L)T^{\ast}(L)T∗(L) slightly below TCT_CTC​ for the infinite, system approximates the universal functional form of the 2D-XY model in its low temperature phase. We discuss the relevance of the temperature interval TC−T∗T_C-T^{\ast}TC​−T∗, considered to be large by Zheng and Trimper and explain why the observed phenomena is a critical phenomena.
We reply to the critique of our results raised by Aleiner, Altshuler and Gershenzon (AAG) in cond-mat/9808078 and cond-mat/9808053. We demonstrate that our path integral analysis fully reproduces the results of AAG if analyzed on a perturbative level. This should settle the issue of "missing diagrams" in our calculation. We, furthermore, demonstrate that our approach allows us to proceed beyond the Golden-rule-type perturbation theory employed by AAG. This explains the difference between our and AAG's results. We also comment on the comparison of our results with the experiments presented by AAG.
We present a numerical study of the quasi-particle density of states (DoS) of two-dimensional d-wave superconductors in the presence of smooth disorder. We find power law scaling of the DoS with an exponent depending on the strength of the disorder and the superconducting order parameter in quantitative agreement with the theory of Nersesyan et al. (Phys.Rev.Lett. 72, 2628 (1994)). For strong disorder a transition to a constant DoS occurs. Our results are in contrast to the case of short-ranged disorder.