Nodeless superconductivity in Lu 5 − x Rh 6 Sn 18 + x with broken time reversal symmetry

Evidence for broken time reversal symmetry (TRS) has been found in the superconducting states of the ${R}_{5}{\mathrm{Rh}}_{6}{\mathrm{Sn}}_{18}$ ($R=\text{Sc}$, Y, Lu) compounds with a centrosymmetric caged crystal structure, but the origin of this phenomenon is unresolved. Here, we report neutron diffraction measurements of single crystals with $R=\text{Lu}$, as well as measurements of the temperature dependence of the magnetic penetration depth using a self-induced tunnel-diode-oscillator (TDO)-based technique, together with band structure calculations using density functional theory. Neutron diffraction measurements reveal that the system crystallizes in a tetragonal caged structure, and that one of the nominal Lu sites in the ${\mathrm{Lu}}_{5}{\mathrm{Rh}}_{6}{\mathrm{Sn}}_{18}$ structure is occupied by Sn, yielding a composition ${\mathrm{Lu}}_{5\ensuremath{-}x}{\mathrm{Rh}}_{6}{\mathrm{Sn}}_{18+x}$ ($x=1$). The low temperature penetration depth shift $\mathrm{\ensuremath{\Delta}}\ensuremath{\lambda}(T)$ exhibits an exponential temperature dependence below around $0.3{T}_{c}$, giving clear evidence for fully gapped superconductivity. The derived superfluid density is reasonably well accounted for by a single-gap $s$-wave model, whereas agreement cannot be found for models of TRS breaking states with two-component order parameters. Moreover, band structure calculations reveal multiple bands crossing the Fermi level, and indicate that the aforementioned TRS breaking states would be expected to have nodes on the Fermi surface, in contrast to the observations.