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

We report muon spin relaxation $(\ensuremath{\mu}\mathrm{SR})$ and magnetization measurements, together with synthesis and characterization, of the Li-intercalated layered superconductors ${\mathrm{Li}}_{x}\mathrm{HfNCl}$ and ${\mathrm{Li}}_{x}\mathrm{ZrNCl}$ 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 ${n}_{s2\mathrm{D}}{/m}_{\mathrm{ab}}^{*}$ [two-dimensional (2D) area density of superconducting carriers/ab-plane effective mass] have been derived from the $\ensuremath{\mu}\mathrm{SR}$ results of the magnetic-field penetration depth ${\ensuremath{\lambda}}_{\mathrm{ab}}$ observed with external magnetic field applied perpendicular to the 2D honeycomb layer of HfN/ZrN. In a plot of ${T}_{c}$ versus ${n}_{s2\mathrm{D}}{/m}_{\mathrm{ab}}^{*},$ 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 ${\mathrm{Li}}_{x}\mathrm{ZrNCl}$ without THF intercalation, the superfluid density and ${T}_{c}$ for $x=0.17$ and 0.4 do not show much difference, reminiscent of $\ensuremath{\mu}\mathrm{SR}$ 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 ${n}_{s2\mathrm{D}}{/m}_{\mathrm{ab}}^{*}$ is a dominant determining factor for ${T}_{c}$ in the intercalated nitride-chloride systems. We also report $\ensuremath{\mu}\mathrm{SR}$ and magnetization results on depinning of flux vortices, and the magnetization results for the upper critical field ${H}_{c2}$ and the penetration depth $\ensuremath{\lambda}.$ A reasonable agreement was obtained between $\ensuremath{\mu}\mathrm{SR}$ and magnetization estimates of $\ensuremath{\lambda}.$ We discuss the two-dimensional nature of superconductivity in the nitride-chloride systems based on these results.