Superconductivity in gallium-substituted Ba₈Si₄₆ clathrates

We report a joint experimental and theoretical investigation of superconductivity in Ga-substituted type-I silicon clathrates. We prepared samples of the general formula Ba₈Si_46−xGa_x, with different values of x. We show that Ba₈Si₄₀Ga₆ is a bulk superconductor, with an onset at T_C≈3.3 K. For x=10 and higher, no superconductivity was observed down to T=1.8 K. This represents a strong suppression of superconductivity with increasing Ga content, compared to Ba₈Si₄₆ with T_C≈8 K. Suppression of superconductivity can be attributed primarily to a decrease in the density of states at the Fermi level, caused by a reduced integrity of the sp³-hybridized networks as well as the lowering of carrier concentration. These results are corroborated by first-principles calculations, which show that Ga substitution results in a large decrease of the electronic density of states at the Fermi level, which explains the decreased superconducting critical temperature within the BCS framework. To further characterize the superconducting state, we carried out magnetic measurements showing Ba₈Si₄₀Ga₆ to be a type-II superconductor. The critical magnetic fields were measured to be H_C1≈35 Oe and H_C2≈8.5 kOe. We deduce the London penetration depth λ≈3700 Å and the coherence length ξ_c≈200 Å. Our estimate of the electron-phonon coupling reveals that Ba₈Si₄₀Ga₆ is a moderate phonon-mediated BCS superconductor.