Physics Letters A 373 (2009) 3392–3394 Contents lists available at ScienceDirect Physics Letters A www.elsevier.com/locate/pla On σ – anticorrelation in high-temperature superconductors A.M. Gulian a,∗ , A.R. Harutyunyan b a Physics Art Frontiers, Ashton, MD 20861, USA b Honda Research Institute USA, Inc., Columbus, OH 43212, USA article info abstract Article history: Received 28 June 2009 Received in revised form 12 July 2009 Accepted 13 July 2009 Available online 21 July 2009 Communicated by V.M. Agranovich PACS: 74.20.Fg 74.50.+r 74.70.-b Keywords: Superconductivity mechanisms Tunneling spectroscopy Normal conductivity BCS model High-T c superconductors Recently, the application of the BCS-type pairing mechanism to a Bi-cuprate system has been questioned based on the experimentally observed anticorrelation between the values of the superconducting gap  and normal conductivity σ . Here we analyze similar data available for the lead-based alloys Pb 1−x Bi x (x ≪ 1), which definitely belong to the BCS-type superconductors. Our analysis reveals exactly same kind of anticorrelation. In view of our results, the anticorrelation arguments against the applicability of the BCS-type model to the cuprate high-T c superconductors should be relaxed.  2009 Elsevier B.V. All rights reserved. 1. Introduction Since the discovery of high-temperature superconductivity pos- sible mechanisms leading to this phenomenon have been a sub- ject of controversy and debates. Despite more than two decades of intense research summarized in many voluminous encyclopedic monographs (see, e.g., Refs. [1–3]), a satisfactory level of clarity has not yet been achieved in this important area (for current status of debates see, for example, the article [4] and references therein). However, noticeable progress in experimentation with these mate- rials yields good hope that all these controversies will be resolved and the desired clarity achieved. Electron tunneling spectroscopy is regarded as a powerful an- alytical tool potentially able to spread a light on microscopic mechanisms of superconductivity (see for example, Chapter 8 in Vol. 1 of Ref. [1]). Recently, using lattice tracking tunneling spectroscopy, Pasupathy et al. [5] reported very interesting data on the tunneling conductance vs. the superconducting gap in overdoped and optimally doped Bi 2 Sr 2 CaCu 2 O 8+δ superconductors. Their high-spatial resolution technique allowed the tracking of in- * Corresponding author. Tel.: +1 202 247 7996; fax: +1 301 570 2212. E-mail address: gulian@superconducting.org (A.M. Gulian). homogeneities in the 2D-mapped samples. Measurements in the similar regions above and well-below of the transition temperature T c provided an opportunity to correlate the values of the normal- state electric conductance at the Fermi-level, dI /dV (0), with the low-temperature value of the superconducting energy gap,  0 (Fig. 1). As claimed in Ref. [5], this decrease of differential conductance with increasing values of the superconducting gap  0 contradicts the BCS-mechanism of superconductivity. However, we will show below that this contradiction is the result of tacit suggestions and oversimplifications. 2. Microscopic origins of σ – correlation In the electron Fermi-liquid theory of metals the conductivity σ is proportional to N(0), the density of states at the Fermi energy E F [6]: σ = 1 3 e 2 v 2 F τ N(0) ≡ e 2 DN(0). (1) Here v F is the velocity of electrons on the Fermi-surface, τ is the transport relaxation time, D is the diffusion coefficient. The proportionality to N(0) is also valid for dimensionless electron- phonon coupling constant λ = N(0) g 2 , where g is the Fröhlich 0375-9601/$ – see front matter  2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2009.07.036