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Strong-Coupling Superconductivity with $T_c$ $\sim$ 10.8 K Induced by P Doping in the Topological Semimetal Mo$_5$Si$_3$

By performing P doping on the Si sites in the topological semimetal Mo$_5$Si$_3$, we discover strong-coupling superconductivity in Mo$_5$Si$_{3-x}$P$_x$ (0.5 $\le$ $x$ $\le$ 2.0). Mo$_5$Si$_3$ crystallizes in the W$_5$Si$_3$-type structure with space group of $I4/mcm$ (No. 140), and is not a superconductor itself. Upon P doping, the lattice parameter $a$ decreases while $c$ increases monotonously. Bulk superconductivity is revealed in Mo$_5$Si$_{3-x}$P$_x$ (0.5 $\le$ $x$ $\le$ 2.0) from resistivity, magnetization, and heat capacity measurements. $T_c$ in Mo$_5$Si$_{1.5}$P$_{1.5}$ reaches as high as 10.8 K, setting a new record among the W$_5$Si$_3$-type superconductors. The upper and lower critical fields for Mo$_5$Si$_{1.5}$P$_{1.5}$ are 14.56 T and 105 mT, respectively. Moreover, Mo$_5$Si$_{1.5}$P$_{1.5}$ is found to be a fully gapped superconductor with strong electron-phonon coupling. First-principles calculations suggest that the enhancement of electron-phonon coupling is possibly due to the shift of the Fermi level, which is induced by electron doping. The calculations also reveal the nontrivial band topology in Mo$_5$Si$_3$. The $T_c$ and upper critical field in Mo$_5$Si$_{3-x}$P$_x$ are fairly high among pseudobinary compounds. Both of them are higher than those in NbTi, making future applications promising. Our results suggest that the W$_5$Si$_3$-type compounds are ideal platforms to search for new superconductors. By examinations of their band topologies, more candidates for topological superconductors can be expected in this structural family.