Two-dimensional nature of superconductivity in the intercalated layered systems Li_xHfNCl and Li_xZrNCl: Muon spin relaxation and magnetization measurements

We report muon spin relaxation (μSR) and magnetization measurements, together with synthesis and characterization, of the Li-intercalated layered superconductors Li_xHfNCl and Li_xZrNCl with/without cointercalation of THF (tetrahydrofuran) or propylene carbonate. The three-dimensional superfluid density n_s/m* (superconducting carrier density/effective mass) as well as the two-dimensional superfluid density n_s2D/m*_ab [two-dimensional (2D) area density of superconducting carriers/ab-plane effective mass] have been derived from the μSR results of the magnetic-field penetration depth λ _ab observed with external magnetic field applied perpendicular to the 2D honeycomb layer of HfN/ZrN. In a plot of T_c versus n _s2D/m*_ab, most of the results lie close to the linear relationship found for underdoped high-T_c cuprate (HTSC) and layered organic BEDT (bis(ethylenedithio)) superconductors. In Li _xZrNCl without THF intercalation, the superfluid density and T _c for x = 0.17 and 0.4 do not show much difference, reminiscent of μSR results for some overdoped HTSC systems. Together with the absence of dependence of T_c on average interlayer distance among ZrN/HfN layers, these results suggest that the 2D superfluid density n_s2D/m* _ab is a dominant determining factor for T_c in the intercalated nitride-chloride systems. We also report μSR and magnetization results on depinning of flux vortices, and the magnetization results for the upper critical field H_c2 and the penetration depth λ. A reasonable agreement was obtained between μSR and magnetization estimates of λ. We discuss the two-dimensional nature of superconductivity in the nitride-chloride systems based on these results.