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We systematically investigated the geometric, electronic and thermoelectric (TE) properties of bulk black phosphorus (BP) under strain. The hinge-like structure of BP brings unusual mechanical responses such as anisotropic Youngs modulus and negative Poissons ratio. A sensitive electronic structure of BP makes it transform among metal, direct and indirect semiconductors under strain. The maximal figure of merit $ZT$ of BP is found to be 0.72 at $800,mathrm{K}$ that could be enhanced to 0.87 by exerting an appropriate strain, revealing BP could be a potential medium-high temperature TE material. Such strain-induced enhancements of TE performance are often observed to occur at the boundary of the direct-indirect band gap transition, which can be attributed to the increase of degeneracy of energy valleys at the transition point. By comparing the structure of BP with SnSe, a family of potential TE materials with hinge-like structure are suggested. This study not only exposes various novel properties of BP under strain, but also proposes effective strategies to seek for better TE materials.
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