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Electronic structure and superconductivity of the non-centrosymmetric Sn$_4$As$_3$

In a superconductor that lacks inversion symmetry, the spatial part of the Cooper pair wave function has a reduced symmetry, allowing for the mixing of spin-singlet and spin-triplet Cooper pairing channels and thus providing a pathway to a non-trivial superconducting state. Materials with a non-centrosymmetric crystal structure and with strong spin-orbit coupling are a platform to realize these possibilities. Here, we report the synthesis and characterisation of high quality crystals of Sn$_4$As$_3$, with non-centrosymmetric unit cell ($R3m$). We have characterised the normal and superconducting state using a range of methods. Angle-resolved photoemission spectroscopy shows a multiband Fermi surface and the presence of two surface states, confirmed by Density-functional theory calculations. Specific heat measurements reveal a superconducting critical temperature of $T_c\sim 1.14$ K and an upper critical magnetic field of $H_c\gtrsim 7$ mT, which are both confirmed by ultra-low temperature scanning tunneling microscopy and spectroscopy. Scanning tunneling spectroscopy shows a fully formed superconducting gap, consistent with conventional $s$-wave superconductivity.