Superconductivity in gallium-substituted ${\mathrm{Ba}}_8{\mathrm{Si}}_{46}$ 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 ${\mathrm{Ba}}_8{\mathrm{Si}}_{46-x}{\mathrm{Ga}}_x$, with different values of $x$. We show that ${\mathrm{Ba}}_8{\mathrm{Si}}_{40}{\mathrm{Ga}}_6$ is a bulk superconductor, with an onset at $T_C\approx 3.3\mathrm{K}$. For $x=10$ and higher, no superconductivity was observed down to $T=1.8\mathrm{K}$. This represents a strong suppression of superconductivity with increasing Ga content, compared to ${\mathrm{Ba}}_8{\mathrm{Si}}_{46}$ with $T_C\approx 8\mathrm{K}$. 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 $s{p}^3$-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 ${\mathrm{Ba}}_8{\mathrm{Si}}_{40}{\mathrm{Ga}}_6$ to be a type-II superconductor. The critical magnetic fields were measured to be $H_{C1}\approx 35\mathrm{Oe}$ and $H_{C2}\approx 8.5\mathrm{kOe}$. We deduce the London penetration depth $\lambda \approx 3700\mathrm{\AA }$ and the coherence length ${\xi }_c\approx 200\mathrm{\AA }$. Our estimate of the electron-phonon coupling reveals that ${\mathrm{Ba}}_8{\mathrm{Si}}_{40}{\mathrm{Ga}}_6$ is a moderate phonon-mediated BCS superconductor.

Figure 1

(Color online) X-ray refinement for ${\mathrm{Ba}}_8{\mathrm{Si}}_{40}{\mathrm{Ga}}_6$. Upper curve: data and fit, with difference plot below. Ticks show peaks indexed according to the type-I clathrate structure. Right inset: the type-I clathrate structure, built from a regular arrangement of a combination of ${\mathrm{Si}}_{20}$ $\left(I_h\right)$ and ${\mathrm{Si}}_{24}$ $\left(D_{6d}\right)$ cages. Left inset: lattice parameters of ${\mathrm{Ba}}_8{\mathrm{Si}}_{46-x}{\mathrm{Ga}}_x$ ($x=6$, 10, and 16), showing an increasing trend with $x$. The lattice parameter for Ga-free ${\mathrm{Ba}}_8{\mathrm{Si}}_{46}$ clathrate was taken from Ref. 16.

Figure 2

(Color online) Upper figure: Electron diffraction patterns from the clathrate structure along the [111] (a), [112] (b), and [113] (c) axis. Lower figure: Comparison of EDS spectra from samples ${\mathrm{Ba}}_8{\mathrm{Si}}_{40}{\mathrm{Ga}}_6$ (solid curve), ${\mathrm{Ba}}_8{\mathrm{Si}}_{36}{\mathrm{Ga}}_{10}$ (long-dashed curve), and ${\mathrm{Ba}}_8{\mathrm{Si}}_{30}{\mathrm{Ga}}_{16}$ (short-dashed curve). The intensities are normalized to the lowest-energy Ba peak to reveal the variation of the Si-Ga ratio.

Figure 3

ac and dc magnetic susceptibility of ${\mathrm{Ba}}_8{\mathrm{Si}}_{40}{\mathrm{Ga}}_6$ vs temperature. Main plot: temperature dependence of the in-phase $\left({\chi }^{\prime }\right)$ and out-of-phase $\left({\chi }^{″}\right)$ ac susceptibility, measured in zero dc field. Inset: dc susceptibility for conditions of zero-field cooling (ZFC) and field cooling (FC) in the measurement field of $3\mathrm{Oe}$. The onset superconducting transition is observed at $3.3\mathrm{K}$ as shown.

Figure 4

Resistance of ${\mathrm{Ba}}_8{\mathrm{Si}}_{40}{\mathrm{Ga}}_6$ versus temperature at $H=0$ and $70\mathrm{kOe}$. Inset: magnified view of the low-temperature region, for clarity. The onset superconducting transition is observed at $3.3\mathrm{K}$.

Figure 5

(Color online) FC susceptibility under different fields for ${\mathrm{Ba}}_8{\mathrm{Si}}_{40}{\mathrm{Ga}}_6$. Inset: Meissner superconducting volume $\left(V_{\mathit{sup}}\right)$ decreasing with external field according to log-linear behavior, with the fitted curve ${\log }_{10}{V}_{\mathit{sup}}=a+b$ ${\log }_{10}H$.

Figure 6

(Color online) (a) $M\text{−}H$ hysteresis of ${\mathrm{Ba}}_8{\mathrm{Si}}_{40}{\mathrm{Ga}}_6$ at $1.8\mathrm{K}$. (b) Initial magnetization curve at $T=1.8$ and $2\mathrm{K}$, respectively. The lower critical field $H_{C1}$ is determined from the departure from linearity at low field, which occurs at an applied field of approximately $21\mathrm{Oe}$ corresponding to $1.8\mathrm{K}$. (c) $M\text{−}H$ reverse legs merge at high field. The upper critical field $H_{C2}$ was estimated to be $8.5\mathrm{kOe}$ at $1.8\mathrm{K}$.

Figure 7

(Color online) Band structures and density of states for (a) ${\mathrm{Ba}}_8{\mathrm{Si}}_{40}{\mathrm{Ga}}_6$ and (b) ${\mathrm{Ba}}_8{\mathrm{Si}}_{30}{\mathrm{Ga}}_{16}$. Density of states is calculated using $0.1\mathrm{eV}$ Gaussian broadening of the band structure. The Fermi levels are denoted by broken horizontal lines.

Figure 8

(Color online) Contour maps of the valence electron densities of (a) ${\mathrm{Ba}}_8{\mathrm{Si}}_{40}{\mathrm{Ga}}_6$ and (b) ${\mathrm{Ba}}_8{\mathrm{Si}}_{30}{\mathrm{Ga}}_{16}$ on the (100) plane.

Figure 9

(Color online) Contour maps of the electron densities at the Fermi level of ${\mathrm{Ba}}_8{\mathrm{Si}}_{40}{\mathrm{Ga}}_6$ (upper) and ${\mathrm{Ba}}_8{\mathrm{Si}}_{30}{\mathrm{Ga}}_{16}$ (lower) on the (100) plane.