Enhancing the Superconducting Transition Temperature of ${\mathrm{BaSi}}_2$ by Structural Tuning

We present a joint experimental and theoretical study of the superconducting phase of the layered binary silicide ${\mathrm{BaSi}}_2$. Compared with the ${\mathrm{AlB}}_2$ structure of graphite or diboridelike superconductors, in the hexagonal structure of binary silicides the $s{p}^3$ arrangement of silicon atoms leads to corrugated sheets. Through a high-pressure synthesis procedure we are able to modify the buckling of these sheets, enhancing the superconducting transition temperature from 6 to 8.9 K when the silicon planes flatten out. By performing ab initio calculations based on density-functional theory we explain how the electronic and phonon properties are strongly affected by changes in the buckling. This mechanism is likely present in other intercalated layered superconductors, opening the way to the tuning of superconductivity through the control of internal structural parameters.

Figure 1

Variation of the total energy of trigonal ${\mathrm{BaSi}}_2$ per unit cell as a function of the buckling parameter $z$, calculated at 0 K. The low-buckled regime $0.545\lesssim z\lesssim 0.575$ corresponds to the values of $z$ that can be explored experimentally. Inset: (left) Layered structure of ${\mathrm{BaSi}}_2$ (${\mathrm{EuGe}}_2$-type, $P\mathrm{\text{−}}3m1$ space group). (right) Projection of the crystal structure onto the (a),(b) plane. The large green (or gray) spheres represent Ba and the small yellow (or light gray) spheres represent Si atoms.

Figure 2

Left panel: Temperature dependence of the ZFC dc-magnetic susceptibility measured at 20 Oe of two trigonal samples of ${\mathrm{BaSi}}_2$ marked by their $z$ coordinate. For convenience, we plot the ratio $[\chi (T)-\chi (10\mathrm{K})]/|[\chi (2\mathrm{K})-\chi (10\mathrm{K})]|$. The arrows indicate the values of $T_c$ obtained at the first point that satisfies the condition $\chi (T)-\chi (10\mathrm{K})<-{10}^{-5}\mathrm{emu}/\mathrm{mol}$. Right panel: initial magnetization curve as a function of the applied magnetic field measured at 2 K in the trigonal phase with $z=0.546(3)\AA$. The upper critical field $H_{c2}$ has been estimated to be 7 kOe, by measuring the magnetic field at which the $M\mathrm{\text{−}}H$ reverse legs merge at high magnetic field using the criterion $|\Delta M|<{10}^{-5}\mathrm{emu}/\mathrm{mol}$.

Figure 3

(a) Fermi surface of trigonal ${\mathrm{BaSi}}_2$ [27]. (b) and (c) two-dimensional cuts of the Fermi surface perpendicular to the [001] direction for $z=0.55$ and 0.58. The increase of the Fermi surface when the structure flattens out (smaller $z$) is evident. (d) Electronic density of states as a function of $z$.

Figure 4

Bottom: Eliashberg spectral function ${\alpha }^{2}F(\omega )$ (inset: EP coupling constant $\lambda$) as a function of $z$. Top: $T_c$ in K calculated with the McMillan formula. The shaded area shows the $T_c$ values when ${\mu }^{*}$ varies from 0.06 to 0.125. The squares are the experimental values of $T_c$.