Protective layer enhanced the stability and superconductivity of tailored antimonene bilayer

For two-dimensional superconductors, the high stability in ambient conditions is critical for experiments and applications. Few-layer antimonene can be nondegradative over a couple of months, which is superior to the akin black phosphorus. Based on the anisotropic Migdal-Eliashberg theory and maximally-localized Wannier functions, this work predicts that electron-doping and Ca-intercalation can transform $\beta$-Sb bilayer from a semimetal to a superconductor. However, the stability of antimonene bilayer in air trends to be decreased due to the electron doping. To overcome this drawback, two kinds of protective layers (graphene and $h$-BN) are proposed to enhance the stability. Interestingly, the superconducting transition temperature will also be enhanced to $9.6\mathrm{K}$, making it a promising candidate as nanoscale superconductor.

Figure 1

Side and top views of atomic structures of $\beta$-Sb bilayer with different stacking configurations. (a) A-B CG; (b) A-A CG.

Figure 2

Projected electronic band structures of $\beta$-Sb bilayer with different stacking. (a) A-B CG; (b) A-A CG.

Figure 3

$\beta$-Sb bilayer with 1.0 electron/cell doping concentration. (a) Electronic band structure. (b) Phonon dispersion. The red circles indicate the strength of electron-phonon coupling.

Figure 4

(a) Phonon density of states (PDOS) $F\left(\omega \right)$, Eliashberg-spectral function ${\alpha }^{2}F\left(\omega \right)$, and electron-phonon coupling $\lambda \left(\omega \right)$ with 1.0 electron/cell doping concentration. (b) Electron-phonon coupling constant $\lambda$ and superconducting $T_{\mathrm{C}}$ under different doping concentration.

Figure 5

Side view of atomic structures of $\beta$-Sb bilayer with Ca doping. (a) AB-I CG and (b) AB-III CG.

Figure 6

Electronic structure of $\beta$-Sb bilayer without [(a),(b)] and with Ca intercalation [(c),(f)]. (c) and (e) Electronic band structures and DOS's of AB-I CG without/with SOC. The violet circles indicate those states with more than $50\%$ of density contributed by Ca. (d) and (f) The corresponding Fermi surfaces.

Figure 7

Results for $\beta$-Sb bilayer with Ca intercalation. (a) Electron density difference (between the pristine $\beta$-Sb bilayer and the Ca-intercalated one) viewed along the (001) direction for AB-I CG. (b) Electron localization function along the [001] direction for AB-I CG. Violet: Sb; Yellow: Ca. (c) Phonon density of states [PDOS, $F\left(\omega \right)]$, Eliashberg-spectral function ${\alpha }^{2}F\left(\omega \right)$, and electron-phonon coupling $\lambda \left(\omega \right)$ for AB-I CG. (d) Superconducting gap for AB-I CG. The red curve is the fitting result. (e) Normalized quasiparticle density of states for AB-I in the superconducting and normal state.

Figure 8

Phonon spectrum and electron-phonon coupling of AB-I CG. The orange circles are proportional to the magnitude of electron-phonon couplings ${\lambda }_{\mathbf{q}\nu }$.

Figure 9

MD simulated process of ${\mathrm{O}}_2$ adsorption on the AB-I CG surface without energy barrier. The $d_{\mathrm{int}}$ indicates the interlayer distance between ${\mathrm{O}}_2$ and AB-I CG surface.

Figure 10

(a) Side and (b) top views of atomic structure of AB-I CG with the protective layers.

Figure 11

Electronic band structures, phonon density of states $\mathrm{[}\mathrm{PDOS},F\left(\omega \right)]$, Eliashberg-spectral function ${\alpha }^{2}F\left(\omega \right)$, and electron-phonon coupling $\lambda \left(\omega \right)$ of AB-I CG with two kinds of covered layers. The red circles indicate those states with more than $60\%$ of density contributed by covered layers. (a),(c) The graphene covered bilayer. (b)(d) The $h$-BN covered bilayer.