Thursday, September 17, 2015

Desperately seeking triplet superconductors, II

Previously, I posted about the tricky problem of establishing experimentally that an unconventional superconductor that the Cooper pairs are in a spin triplet state. One basic (but far from definitive) signature is that the upper critical magnetic field is larger than the Clogston-Chandreshakar limit [this is often called the Pauli paramagnetic limit but I think that is a scientific misnomer].

I am particularly interested in this problem because of recent theoretical work showing how triplet superconductivity may arise in a particular quasi-one-dimensional metal.

A new family of materials A2Cr3As3 [A=K,Rb,Cs] is attracting significant interest because some experiments show the desired high upper critical field.

I think the "first" paper is a Phys. Rev. X article with the title Superconductivity in Quasi-One-Dimensional K2Cr3As3 with Significant Electron Correlations

I am slowly trying to work through some of the literature. Here are a few observations. I welcome comments and corrections.

Sample quality.
This is usually a big issue in newly discovered strongly correlated electron materials. Unfortunately, this does not stop the rush to publish and make bold claims.
Many of the reported measurements are on polycrystalline samples not single crystals. A "Note added" in the Phys. Rev. X article concedes that the linear in T resistivity that they observed in polycrystalline samples is not seen by other authors. Nevertheless the abstract states
A linear temperature dependence of resistivity in a broad temperature range from 7 to 300 K is observed, which suggests non-Fermi liquid behavior.

Furthermore, this preprint notes
The different low temperature behavior observed in samples which have deteriorated after being exposed to air, emphasises that it is necessary to properly handle the samples prior to being measured because the A2Cr3As3 compounds are extremely air sensitive and evidence for nodal superconductivity from penetration depth measurements is only observed in the samples which display a sharp superconducting transition.

This is subtle. The crystal structure does contain chains of Cr3As3 with C_3 symmetry. [Double walled sub-nanotubes!]
However, electronic structure calculations suggest one three-dimensional Fermi surface sheet in addition to two quasi-one-dimensional Fermi surface sheets.
Unfortunately, this is not stopping people already claiming experimental results "consistent with a Tomonaga-Luttinger liquid."

Strong correlations.
The abstract of the Phys. Rev. X article states
The material has a large electronic specific-heat coefficient of  70–75  mJ K−2 mol−1, indicating significantly strong electron correlations.
This is a weak statement. This coefficient is certainly large compared to elemental metals. However, the key issue is how large is this value compared to the value found from the density of states at the Fermi energy calculated in a "weakly correlated" band structure method such as a DFT approximation. In the text the authors report that the enhancement calculated this way is slightly larger than three. Some might say this is "moderate" rather than "strong" correlations.

Hund's rule coupling and minimal model effective Hamiltonian.
A three band model has been constructed and found to exhibit triplet p_z superconductivity at the RPA level.

NMR and spin fluctuations.
The measurements have been interpreted as evidence for Luttinger liquid behaviour,  antiferromagnetic spin fluctuations, and unconventional superconductivity. On the second, it is pity they don't have Knight shift data. Then one could have discussed the magnitude of the Korringa ratio.

Proximity to magnetism and possible parent compounds.
One might consider K2Cr3As3 as an electron doped version of  KCr3As3. The latter has been studied both experimentally (with the magnetic susceptibility exhibiting Curie-Weiss behaviour suggesting the present of antiferromagnetic magnetic moments; it remains metallic with no superconductivity) and theoretically (leading to a "spin tube" model). There are some interesting and subtle issues associated of the coupling of Cr spins, within the triangles, somewhat reminiscent of an organic system some my UQ colleagues have been studying.
Mike Norman briefly mentions K2Cr3As3 in a nice Physics article discussing the broader context of the interplay of helical magnetism and superconductivity in (three-dimensional) CrAs and MnP. Aside: They were the first Cr an Mn compounds ever found to superconduct.

Spin-locked superconductivity?
A paper reporting measurements of the anisotropic upper critical magnetic field up to 60 tesla claims that
The paramagnetically limited behavior of H∥c2(T) is inconsistent with triplet superconductivity but suggests a form of singlet superconductivity with the electron spins locked onto the direction of Cr chains.
I don't follow this at all. Surely, if you have a spin singlet there is no preferred direction for the electron spins. I must be missing something. Can someone explain?

Spin-orbit coupling
Electronic structure calculations suggest that 
Despite of the relatively small atomic numbers, the antisymmetric spin-orbit coupling splitting is sizable (≈ 60 meV) on the 3D Fermi surface sheet as well as on one of the quasi-1D sheets.
I welcome discussion as I am finding my way. 


  1. Very nice overview of this system and the remaining issues. We have a contribution from our study of single-crystals and the comparison of K- and Rb-233 basic properties. The interesting result is our finding of a strong sensitivity of the normal state transport anisotropy (i.e. field response) to the crystal structure, in particular the inter-chain distance that is controlled by the alkali metal species:

    .F. Wang et al., "Tunable electronic anisotropy in single-crystal A2Cr3As3 (A = K, Rb) quasi-one-dimensional superconductors", Phys. Rev. B 92, 020508(R) (2015)

  2. Replies
    1. Some of the differences in electronic structure between A=K,Rb,Cs and the isoelectronic compound Tl2Mo6Se6 [which also may be a triplet superconductor] is nicely discussed in the paper

      I thank Enric Canadell for bringing it to my attention.

  3. I have worked on probing the pairing symmetry of Ferromagnetic superconductors by crossed Andreev reflection, Ref. Crossed Andreev reflection as a probe for the pairing symmetry of ferromagnetic superconductors, Colin Benjamin
    Phys. Rev. B 74, 180503(R) (2006),