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

TL;DR

This paper defends the universality of a non-zero density of states in 2D disordered d-wave superconductors, showing it holds across different disorder distributions and is not dependent on specific tail behaviors.

Contribution

It establishes that the non-zero density of states result is generic for a broad class of disorder distributions, countering claims that it depends on Lorentzian-specific properties.

Findings

Non-zero lower bound for DOS is proven without tail dependence.

Gaussian and Lorentzian disorders belong to the same universality class.

The result is robust across different disorder models.

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.