  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 Young's
modulus and negative Poisson's 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.
