Dependence of the superconducting transition temperature of organic molecular crystals on intrinsically nonmagnetic disorder: A signature of either unconventional superconductivity or the atypical formation of magnetic moments

Abstract

We give a theoretical analysis of published experimental studies of the effects of impurities and disorder on the superconducting transition temperature, Tc, of the organic molecular crystals κ-(BEDT-TTF)2X (where X=Cu[N(CN)2]Br and Cu(NCS)2 and BEDT-TTF is bis(ethylenedithio)tetrathiafulvalene) and β-(BEDT-TTF)2X (for X=I3 and IBr2). The Abrikosov-Gorkov (AG) formula describes the suppression of Tc both by magnetic impurities in singlet superconductors, including s-wave superconductors and by non-magnetic impurities in a non-s-wave superconductor. We show that various sources of disorder (alloying anions, fast electron irradiation, disorder accidentally produced during fabrication and cooling rate induced disorder) lead to the suppression of Tc as described by the AG formula. This is confirmed by the excellent fit to the data, the fact that these materials are in the clean limit and the excellent agreement between the value of the interlayer hopping integral, t ⊥ , calculated from this fit and the value of t ⊥ found from angular-dependant magnetoresistance and quantum oscillation experiments. There are only two scenarios consistent with the current state of experimental knowledge. If the disorder induced by all of the four methods considered in this paper is, as seems most likely, non-magnetic then the pairing state cannot be s-wave. We show that published measurements of the cooling rate dependence of the magnetisation are inconsistent with paramagnetic impurities. Triplet pairing is ruled out by NMR and upper critical field experiments. Thus if the disorder is non-magnetic then this implies that l ≥ 2, in which case Occam's razor suggests that d-wave pairing is realised in both β-(BEDT-TTF)2X and κ-(BEDT-TTF)2X. However, particularly given the proximity of these materials to an antiferromagnetic Mott transition, it is possible that the disorder leads to the formation of local magnetic moments via some novel mechanism. Thus we conclude that either β-(BEDT-TTF)2X and κ-(BEDT-TTF)2X are d-wave superconductors or else they display a novel mechanism for the formation of localised moments, possibly related to the competition between the antiferromagnetic and superconducting grounds states. We suggest systematic experiments to differentiate between these two scenarios.

Chirald-wave superconductivity in doped graphene

“…Experimental results seem ambiguous with regards to if the superconducting state is fully gapped or contains nodes, see e.g. [199,195] and references therein. The interplay between antiferromagnetism, the Mott transition, and d-wave superconductivity has been studied by different theoretical methods [200,201,202].…”

Inhomogeneous superconductivity in organic conductors: the role of disorder and magnetic field

“…The rapid decrease of T c for small disorder amount is attributed to the non-s-wave part whereas the slowing down of the T c suppression is assigned to the s-wave component. However, to the best of our knowledge, there is no experimental evidence of such mixed superconducting gap in organic conductors [33].…”

“…τ is the quasi-particle lifetime due to scattering with magnetic impurities (τ = τ M ) or non-magnetic impurities (τ = τ N ). Powell and McKenzie [33] compared the experimental data obtained in β(ET) 2 X and κ(ET) 2 X with various types of disorder to the expectations of the AG formula. They found an excellent agreement using two free parameters to fit the theory.…”

“…Theoretical approaches: brief review Powell and McKenzie [33] have analyzed, in the framework of the AG law, the experimental results dealing with the effect of different types of disorder on the superconducting transition temperature T c of quasi-2D organic conductors. It is worthwhile reminding that the AG law describes the suppression of T c by magnetic impurities for s-wave pairing.…”

“…A theoretical analysis [33] of the dependence of T c on disorder in different (ET) 2 X salts has shown that the suppression of T c obeys to the Abrikozov-Gor'kov (AG) law [34] which describes the suppression of T c in the presence of either magnetic impurities or non magnetic impurities in non-s-wave superconductors. However, for large disorder, clear departure from the AG formula has been reported in several low dimensional organic superconductors [15,22,25,30].…”