Monolayer RhB4 : Half-auxeticity and almost ideal spin-orbit Dirac point semimetal

Structural-property relationship, the connection between materials' structures and their properties, is central to the materials research. Especially at reduced dimensions, novel structural motifs often generate unique physical properties. Motivated by a recent work reporting a novel half-auxetic effect in monolayer ${\mathrm{PdB}}₄$ with a hypercoordinated structure, here we extensively explore similar two-dimensional (2D) transition-metal boride structures $M{\mathrm{B}}₄$ with $M$ covering $3d$ and $4d$ elements. Our investigation screens out one stable candidate, the monolayer ${\mathrm{RhB}}₄$. We find that monolayer ${\mathrm{RhB}}₄$ also shows half-auxeticity, i.e., the material always expands in a lateral in-plane direction in response to an applied strain in the other direction, regardless of whether the strain is positive or negative. We show that this special mechanical character is intimately tied to the hypercoordinated structure with the $MC\text{\textcopyright{}}{\mathrm{B}}₈$ structural motif. Furthermore, regarding electronic properties, monolayer ${\mathrm{RhB}}₄$ is found to be an example of an almost ideal 2D spin-orbit Dirac-point semimetal. The low-energy band structure is clean, with a pair of fourfold degenerate Dirac points robust under spin-orbit coupling located close to the Fermi level. These Dirac points are $enforced$ by the nonsymmorphic space-group symmetry which is also determined by the lattice structure. Our work deepens the fundamental understanding of structural-property relationship in reduced dimensions. The half-auxeticity and the spin-orbit Dirac points will make monolayer ${\mathrm{RhB}}₄$ a promising platform for nanomechanics and nanoelectronics applications.