LaNiC2: triplet pairing via reversed quantum criticality

Just as 2014 was drawing to a close, two experimental papers from different groups in Japan appeared that significantly advance our understanding of LaNiC2. The first paper provides fresh evidence of the non-unitary triplet pairing scenario we proposed back in 2009. The second paper offers tantalising hints that a quantum critical point is behind the pairing mechanism in this system, but that the critical point had been hidden from sight because it is “reversed”: the order parameter is suppressed as the pressure is reduced towards, rather than increased away from, room pressure.

The first of these papers [1], by Sumiyama et al., was published online on 9 December and reports the observation of a bulk, spontaneous magnetisation that appears on crossing the superconducting critical temperature, Tc. This observation is consistent with the theoretical prediction we made back in 2012 that magnetisation is a sub-dominant order parameter in any non-unitary triplet pairing instability of a paramagnetic normal state.

Our theory was based on symmetry arguments, which demand, in the case of a non-unitary triplet pairing, a term in the Ginzburg-Landau free energy that couples the pairing order parameter to magnetisation. A bit more recently, but independently, Kazumasa Miyake has developed, with Sr2RuO4 in mind this time, a more microscopic theory of non-unitary triplet pairing that makes the same prediction. The experimental observation of such magnetisation in LaNiC2 is strong evidence for the non-unitary triplet pairing state that we originally proposed for this system in view of the enhanced muon spin relaxation rate and which we then predicted on the basis of a detailed symmetry analysis of its crystal structure.

This latest, additional evidence for triplet pairing in LaNiC2 leaves a very important question unanswered: where do the strong correlations come from?

The second paper [2], by Susumu Katano et al., appeared on 15 December and provides an important hint towards answering the above question. It provides evidence for an unexpected quantum critical point that might be driving the superconducting instability in this carbometalate.

The standard scenario for the emergence of unconventional superconductivity from a pressure-driven quantum critical point (a) in contrast to a “reversed” scenario, where the non-superconducting ordered phase is accessed by increasing pressure and the non-Fermi liquid behaviour is not apparent at ambient pressure (b). Recent experiments by Katano and co-workers suggest that LaNiC2 is our first example of the latter.

Pressure can be used to drive the critical temperature of an ordered, non-superconducting phase, such as an antiferromagnetic or charge-ordered phase, to zero temperature, thus creating a quantum critical point (QCP). Near the QCP, electron-electron interactions are heavily renormalised, and out of the resulting, strongly-correlated state a dome of unconventional superconductivity often emerges [see Figure, panel (a)]. Indeed, taking a non-superconducting system with a spin- or charge-ordered ground state at room pressure and applying high pressures to supress the corresponding critical temperature is one of the best ways to find an unconventional superconductor, usually with a non-Fermi liquid (NFL) non-superconducting state. This is now well-established after the systematic work carried out by Gil Lonzarich and his co-workers, in Cambridge, and other groups around the world (see Sec. VI.C of the review of quantum criticality by Lohneysen et al.)

Until now, LaNiC2 seemed not to fit the above picture: the superconductivity occurs at room pressure and, in spite of the evidence pointing to an unconventional superconducting state mentioned above, other features of the system seemed quite conventional. Crucially, the normal state appeared to be a very good, paramagnetic Fermi liquid, with no evidence of any nearby magnetic or charge-ordered phases or a quantum critical point. What Katano et al.’s high-pressure work has revealed is that the superconductivity seen at room pressure in LaNiC2 is, indeed, part of a dome growing around a QCP – however, the critical temperature of the corresponding non-superconducting ordered phase is suppresed by reducing presure, rather than by increasing it. As a result, the part of the dome that we see at room pressure is what would normally correspond to the region of the phase diagram beyond the QCP, where FL behaviour is usually restored. This explains the apparent contradiction between the exotic nature of superconductivity in LaNiC2 and the seemingly conventional normal state, and constitutes an example of the quantum critical paradigm of unconventional superconductivity seen “in reverse”: first we discovered that a certain superconductor was unconventional and then the corresponding QCP was found. This could have important implications, for example, for the cuprates, where a hidden QCP has been hypothesised. In the case of LaNiC2, the exact nature of the ordered non-superconducting phase is as yet unknown.

In my opinion, these two papers represent two very exciting developments in the unfolding LaNiC2 story. Taken together, they place this material firmly as one of the most exciting superconductors being researched today.

[1] Sumiyama, A. et al. Spontaneous Magnetization of Non-centrosymmetric Superconductor LaNiC 2. Journal of the Physical Society of Japan 84, 013702 (2015). DOI: 10.7566/JPSJ.84.013702

[2] Katano, S. et al. Anomalous pressure dependence of the superconductivity in noncentrosymmetric LaNiC2: Evidence of strong electronic correlations. Physical Review B 90, (2014). DOI: 10.1103/PhysRevB.90.220508

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