Multiple superconducting transitions in Yb$_{3+x}$Co$_4$Sn$_{13-x}$

Abstract of the accompanying article: In the Yb-Co-Sn system a Remeika phase Yb $3+ x$ Co $4$ Sn $13− x$ is found with solid solution extending within $0≤ x ≤0.5$ . All these compounds crystallize with primitive cubic [space group $P m 3¯ n$ , $a ≈9.54$ \AA] strongly disordered Sc $3$ Ir $4$ Si $13+ x$ type. Stoichiometric Yb $3$ Co $4$ Sn $13$ is a superconductor with critical temperature $T c =3.1(2)$ ,K, lower- [ $B c 1 =1.90(2)$ ,mT] and upper [ $B c 2 =2.16(5)$ ,T] critical fields. The specific heat jump $Δ c p / γ T c =1.72(9)$ together with the fact that $B c 2 (T c)$ dependence is described by the Werthamer-Helfand-Hohenberg (WHH) model hint towards a conventional mechanism with a weak electron-phonon coupling. Although a more precise analysis is hampered by the presence of multiple superconducting transitions observed in the specific heat of this Remeika phase, the non-stoichiometric Yb $3.2$ Co $4$ Sn $12.8$ reveals $T c =2.4(2)$ ,K and $B c 2 =4.79(9)$ ,T exceeding the classical Pauli limit. Strong electron-phonon coupling in this superconductor is confirmed by the high value of the $λ AD =0.92(2)$ parameter determined from the Allen-Dynes formula. However, the electronic specific heat of Yb $3.2$ Co $4$ Sn $12.8$ follows the exponential law [ $c el (T)∝ e − Δ (0) / k B T$ ] and can be described by the $α$ -model [ $α ≡ Δ (0) / k B T c =2$ ] indicating this stannide to be a conventional BCS-superconductor. Both Yb $3+ x$ Co $4$ Sn $13− x$ ( $x =0,0.2$ ) compounds reveal complex phonon spectra with possible `rattling' behavior. They are also found to be metallic systems, some aspects of which can be described by a free electron gas model.