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Ba$_2$phenanthrene is the main component in the Ba-doped phenanthrene sample

We systematically investigate the crystal structure of Ba-doped phenanthrene with various Ba doping levels by the first principle calculation method combining with the X-ray diffraction (XRD) spectra simulation. The optimized lattice parameters and the simulated XRD spectra of Ba$_2$phenanthrene are in good agreement with the experiment ones, and the strength difference of a few of XRD peaks can be explained by the existence of undoped phenanthrene in the experimental sample. Although the stoichiometry ratio of Ba atom and phenanthrene molecule is 1.5:1, the simulated XRD spectra, space group symmetry and the optimized lattice parameters of Ba$_{1.5}$phenanthrene are not consistent to the measured values. The sample of Ba-doped phenanthrene is deduced to be the mixture of Ba$_2$phenanthrene and some amount of undoped phenanthrene, instead of uniform Ba$1.5$phenanthrene. Our calculations indicate that Ba$_2$phenanthrene is a semiconductor with a small energy gap less than 0.05 eV. Our findings provide the fundamental information of crystal structure and electronic properties of Ba-doped phenanthrene superconductor.