Superconducting Open-Framework Allotrope of Silicon at Ambient Pressure

Diamond Si is a semiconductor with an indirect band gap that is the basis of modern semiconductor technology. Although many metastable forms of Si were observed using diamond anvil cells for compression and chemical precursors for synthesis, no metallic phase at ambient conditions has been reported thus far. Here we report the prediction of pure metallic Si allotropes with open channels at ambient pressure, unlike a cubic diamond structure in covalent bonding networks. The metallic phase termed $P6/m\text{−}{\mathrm{Si}}_6$ can be obtained by removing Na after pressure release from a novel Na-Si clathrate called $P6/m\text{−}{\mathrm{NaSi}}_6$, which is predicted through first-principles study at high pressure. We identify that both $P6/m\text{−}{\mathrm{NaSi}}_6$ and $P6/m\text{−}{\mathrm{Si}}_6$ are stable and superconducting with the critical temperatures of about 13 and 12 K at ambient pressure, respectively. The prediction of new Na-Si and Si clathrate structures presents the possibility of exploring new exotic allotropes useful for Si-based devices.

Figure 1

Formation enthalpies of stable and metastable configurations for ${\mathrm{Na}}_{1-x}{\mathrm{Si}}_x$ with various composition ratios at pressures of 10 GPa (top) and 20 GPa (bottom). The configurations on the convex hull are marked by solid symbols and connected by red lines.

Figure 2

(a) Top and side views of the atomic structures of $P6/m\text{−}{\mathrm{NaSi}}_6$ (left) and $P6/m\text{−}{\mathrm{Si}}_6$ (right) clathrates. In $P6/m\text{−}{\mathrm{NaSi}}_6$, the open channels filled with Na atoms are embedded in the metallic bonding networks of Si atoms that are exactly the same as that of a simple hexagonal lattice except for the open channels. The green and yellow spheres represent Na and Si atoms, respectively. (b) Relative enthalpies ($\mathrm{\Delta }H$) of various clathrate structures with respect to a mixture of Zintl and CD-Si as a function of pressure.

Figure 3

(a) Phonon spectra, phonon densities of states (PDOS in arb. unit), Eliashberg spectral functions ${\alpha }^{2}F(\omega )$, and electron-phonon couplings $\lambda (\omega )$ for $P6/m\text{−}{\mathrm{NaSi}}_6$ (top) and $P6/m\text{−}{\mathrm{Si}}_6$ (bottom) at 15 GPa. The magnitude of $\lambda (\omega )$ is indicated by the thickness of the red curves. (b) Band structures and electronic densities of states (DOS in arb. unit) of $P6/m\text{−}{\mathrm{NaSi}}_6$ (top) and $P6/m\text{−}{\mathrm{Si}}_6$ (bottom) at 15 GPa, with the Fermi level set to zero.

Figure 4

(a) Pressure dependences of $T_c$ and $\lambda$ for $P6/m\text{−}{\mathrm{NaSi}}_6$ and $P6/m\text{−}{\mathrm{Si}}_6$. (b) Pressure variation of the low-frequency modes of $P6/m\text{−}{\mathrm{Si}}_6$ along the $\mathrm{\Gamma }\text{−}A\text{−}L$ line in the BZ. The balls represent the Si atoms around the open channels and the arrows stand for the displacements of the TA mode at the $A$ point. (c) Energy vs volume curves of various Si phases.