Theoretical analysis of the upper critical field of two-band superconductor LaNiC2

LaNiC2 is one of ternary RNiC2 compounds, where R is a rare earth or Y. Its space group is Amm2. the symmetry along the c-axis of the crystal structure lacks inversion symmetry along the c-axis. In 2009, Hillier et al. performed the muon spin relaxation experiment (upSR) which implied that time-reversal symmetry is broken in LaNiC2. As a weak correlation noncentrosymmetric superconductor, LaNiC2 has attracted wide research interest in recent years. Though a lot of theoretical and experimental studies have been carried out, the order parameter of this compound remains highly controversial. The measurements of specific heat and nuclear quadrupole relaxation suggest that LaNiC2 is normally BCS-like, which is further supported by theoretical calculations. But recently another study showed that the London penetration depth depends on T2 below 0.4 Tc indicative of nodes in the energy gap. Evidence of possible nodal superconductivity can also be inferred from the early measurements of specific heat given by Lee et al. However, the experimental results obtained by Chen et al. supported the existence of two-gap superconductivity in LaNiC2.Based on the above case, the two-band Ginzburg-Landau theory is used to study the temperature dependence of the upper critical field for the superconductor LaNiC2 in this paper. Choosing the Ginzburg-Landau theory for calculating the upper critical field is just because Ginzburg-Landau theoretical model is simple, easy to understand, low-calculation, and the clear physical meanings of the parameters. The theoretical results in this paper accord with the experimental data very well in the whole temperature range. The curve of Hc2 (T) has an obvious positive curvature near the critical temperature, which is typical feature of multi-gap superconductor. Therefore, our results show strong evidence that two-gap scenario is better to account for the superconductivity of LaNiC2, consistent with the results of Chen Jian et al. The influences of two different energy bands on the upper critical field are also studied. It is found that the relatively small coherent length has a grester influence on the upper critical magnetic field of LaNiC2. So if we want to improve the upper critical field of LaNiC2, reducing the relatively small coherence length can be achieved in theory.