Nodeless superconductivity in Lu$_{5-x}$Rh$_6$Sn$_{18+x}$ with broken time reversal symmetry

TL;DR

This study investigates the superconducting properties of Lu$_{5-x}$Rh$_6$Sn$_{18+x}$, revealing nodeless, fully gapped superconductivity with broken time reversal symmetry, supported by neutron diffraction, penetration depth measurements, and band structure calculations.

Contribution

It provides the first evidence of nodeless superconductivity in Lu$_{5-x}$Rh$_6$Sn$_{18+x}$ with broken TRS, challenging previous theories predicting nodal states based on band structure.

Findings

Superconductivity is fully gapped and consistent with an s-wave model.

Neutron diffraction shows a composition with Sn occupying Lu sites.

Band calculations suggest TRS breaking states should have nodes, contrary to observations.

Abstract

Evidence for broken time reversal symmetry (TRS) has been found in the superconducting states of the $R_5$Rh$_6$Sn$_{18}$ (R = 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 $R$=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 nominal Lu sites in the Lu$_5$Rh$_6$Sn$_{18}$ structure is occupied by Sn, yielding a composition Lu$_{5-x}$Rh$_6$Sn$_{18+x}$ ($x=1$). The low temperature penetration depth shift $\Delta\lambda(T)$ exhibits an exponential temperature dependence below around $0.3T_c$, 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 constrast to the observations.