d-Wave-like nodal superconductivity in the organic conductor (TMTSF)2ClO4

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Abstract

We suggest theoretical explanation of the high upper critical magnetic field, perpendicular to conducting chains, Hc2b, experimentally observed in the superconductor (TMTSF)2ClO4, in terms of singlet superconducting pairing. In particular, we compare the results of d-wave-like nodal, d-wave-like node-less, and s-wave scenarios of superconductivity. We show that, in d-wave-like nodal scenario, superconductivity can naturally exceed both the orbital upper critical magnetic field and Clogston–Shandrasekhar paramagnetic limit as well as reach experimental value, Hc2b6T, in contrast to d-wave-like node-less and s-wave scenarios. In our opinion, the obtained results are strongly in favor of d-wave-like nodal superconductivity in (TMTSF)2ClO4, whereas, in a sister compound, (TMTSF)2PF6, we expect either the existence of triplet order parameter or the coexistence of triplet and singlet order parameters.

Introduction

High magnetic field properties of (TMTSF)2X (X=ClO4, PF6, etc.) organic materials have been intensively studied [1] since the discovery of superconductivity in (TMTSF)2PF6 conductor [2]. From the beginning, it was clear that superconductivity in the above-mentioned materials was unconventional. Indeed, early experiments [3], [4] showed that the Hebel–Slichter peak was absent in the NNR measurements [3] and that superconductivity is destroyed by non-magnetic impurities [4]. These facts were strong arguments that superconducting order parameter changed its sign on the quasi-one-dimensional (Q1D) Fermi surfaces (FS) of (TMTSF)2X material. The main results of both experiments [3], [4] were recently confirmed in a number of publications (see, for example, Refs. [5], [6]). It is important that the above-mentioned experiments did not contain information about spin part of superconducting order parameter and could not distinguish between singlet and triplet superconducting pairings.

The first measurements of the Knight shift in (TMTSF)2PF6 conductor [6], [7] showed that it was not changed in superconducting phase, which was interpreted in favor of triplet superconductivity [6], [7]. On the other hand, the more recent Knight shift measurements [8] in superconductor (TMTSF)2ClO4 have shown a clear change of the Knight shift in superconducting phase at relatively low magnetic fields, H1T, and have been interpreted as evidence of singlet superconductivity [8]. Another argument in favor of singlet order parameter is the fact that the upper critical magnetic field, parallel to conducting axis, Hc2a [9], is paramagnetically limited [10]. Moreover, very recently the Larkin–Ovchinnikov–Fulde–Ferrell phase [11], [12], which appears for singlet superconducting pairing, has been experimentally discovered [13], [14] in (TMTSF)2ClO4 and theoretically interpreted [15].

Section snippets

Goal

In such situation, where support of singlet superconducting pairing in (TMTSF)2ClO4 material is increasing, it is important to reinvestigate theoretically high experimental upper critical magnetic fields, Hc2b [13], [14], [16], observed for a magnetic field, perpendicular to conducting chains. For many years, large values of Hc2b have been considered as a consequence of triplet superconducting pairing. Our goal is to show that we can naturally explain large values of Hc2b within singlet

Results

Let us consider Q1D spectrum of (TMTSF)2ClO4 conductor in tight binding model [1],ϵ(p)=2tacos(pxa/2)2tbcos(pyb)2tccos(pzc),in a magnetic field, perpendicular to its conducting chains,H=(0,H,0),A=(0,0,Hx),where tatbtc are electron hoping integrals along a-, b-, and c-axes, respectively. Electron spectrum (1) can be linearized near two slightly corrugated sheets of Q1D FS asδϵ±(p)=±vx(py)[pxpF(py)]2tccos(pzc),where + (−) stands for right (left) sheet of Q1D FS.

We represent electron

Conclusion

We have suggested explanation of high values of the upper critical magnetic fields, experimentally observed in (TMTSF)2ClO4 conductor [13], [14], [16], using d-wave-like nodal scenario of superconductivity. On the other hand, we anticipate that, for explanation of very high values of the upper critical magnetic fields [33], [34] in a sister compound, (TMTSF)2PF6, in mixed superconducting-antiferromagnetic phase [34], [35], it is necessary to consider either triplet superconducting pairing [10],

Acknowledgments

We are thankful to N.N. Bagmet, S.E. Brown, and Y. Maeno for useful discussions. This work was supported by the NSF under Grants No DMR-0705986 and DMR-1104512.

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