Unconventional superconductivity in Li-intercalated layered nitride Li x ZrNCl M. Hiraishi a, * , R. Kadono a,b , M. Miyazaki a , S. Takeshita b , A. Koda a,b , Y. Taguchi c , Y. Kasahara d , T. Takano d , T. Kishiume d , Y. Iwasa d a Department of Materials Structure Science, The Graduate University for Advanced Studies, Tsukuba, Ibaraki 305-0801, Japan b Institute of Materials Structure Science, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan c Cross-Correlated Materials Research Group (CMRG), ASI, RIKEN, Wako 351-0198, Japan d Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan article info Article history: Accepted 28 October 2009 Available online 31 October 2009 Keywords: Li x ZrNCl Anisotropic order parameter lSR abstract It is inferred from the temperature and magnetic field dependence of superfluid density that the gap parameter ð2D=k B T c Þ in Li x ZrNCl exhibits decrease with increasing x, suggesting development of aniso- tropic order parameter that leads to the reduction of D as a mean value. This observation is quantitatively in line with the d þ id pairing predicted by recent theory based on the Hubbard model considering dis- connected Fermi surfaces on a honeycomb lattice. Ó 2009 Elsevier B.V. All rights reserved. Layered nitride, Li x ZrNCl, which is discovered by Yamanaka et al. [1,2], is drawing much interest as it has relatively high super- conducting transition temperature (T c  15 K). It exhibits anoma- lous behavior that is not explained by the conventional BCS theory. For example, T c is independent of doping for x P 0:15, while it exhibits steep increase below x ’ 0:12, reaching a maximum T c ’ 15:2 K at x ¼ 0:06, then, suddenly becomes zero associated with metal-to-insulator transition below x ¼ 0:05 [3]. Moreover, contrary to the expectation that the electronic specific heat coefficient ðcÞ is roughly proportional to the applied field (as it must be proportional to the number of flux lines, so that c / H=U 0 ’ c n H=H c2 , where H c2 is the upper critical field, and U 0 is the flux quantum), it is reported for Li x ZrNCl with x ¼ 0:12 that c increases steeply with field and becomes close to the normal state value c n around a field much lower than the upper critical field ðH c2 ’ 5TÞ [4]. This strongly suggests occurrence of field-in- duced quasiparticle excitation that is not expected for conventional superconductors. In order to clarify the origin of these anomalies, we investigated the behavior of superfluid density n s using muon spin rotation (lSR) technique. Fig. 1 shows examples of transverse field (TF)–lSR time spectra with x ¼ 0:21 (a) and 0.12 (b) under TF = 0.15 and 0.3 T, respec- tively, which was measured on the M15 and M20 beamlines at TRI- UMF, Canada. Positron decay asymmetry AðtÞ above T c shows a slow Gaussian damping due to nuclear magnetic moments, while faster relaxation due to flux line lattice (FLL) is observed below T c . Additionally, we found a fast relaxation component (2 MHz) in samples with x ¼ 0:08, 0.10, and 0.12. This signal may come from muoniums formed by muons stopped in the insulating Cl bilayers. Considering a signal coming from the sample holder, we analyzed these time spectra by the following equation, AðtÞ¼ expðr 2 n t 2 Þ A s exp  r 2 s t 2 2   þ A f exp Kt ð Þ   cosðx 0 t þ /Þ þ A BG exp r 2 BG t 2   cos x BG t þ / ð Þ; ð1Þ where r n is the depolarization rate due to nuclear magnetic mo- ments, A s is the partial asymmetry for superconducting fraction with r s denoting the depolarization rate in the FLL state, A f is that for the component related with muonium formation showing depo- larization at a rate K; A BG is for the background (60.01), and x 0 and x BG are the central frequencies in respective components with / being the initial phase. Fig. 2 shows temperature dependence of r s ð/ n s Þ. Solid curves are the best fit assuming the conventional BCS theory for s-wave symmetry [5,6] with varying gap ratio ð2D=k B T c Þ. Since electron- phonon coupling plays a minor role in these compounds [4], we interpret that the reduction of the ratio with increasing x reflects development of anisotropic order parameter leading to the reduc- tion of D as a mean value. In order to stress this situation, we de- note D as D. The deduced gap ratio 2 D=k B T c is shown in inset of Fig. 2. It suggests greater anisotropy with increasing x. To verify an effect of the anisotropic order parameter in x ¼ 0:12, following analysis using the phenomenological double-gap model for s-wave symmetry was applied. 0921-4534/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2009.10.130 * Corresponding author. E-mail address: hiramasa@post.ket.jp (M. Hiraishi). Physica C 470 (2010) S723–S724 Contents lists available at ScienceDirect Physica C journal homepage: www.elsevier.com/locate/physc