Topological properties of the high-pressure hydride superconductor bismuth dihydride <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>BiH</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math>

Topological properties and topological superconductivity in real materials have attracted intensive experimental and theoretical attentions recently. The topological electronic properties of pressure-induced superconductors ${\mathrm{BiH}}_{2}$ have been studied based on first-principles electronic structure calculations. Recent experiments have revealed that ${\mathrm{BiH}}_{2}$ exhibits five distinct phases under high pressure, our studies show that $Cmcm\text{\ensuremath{-}}{\mathrm{BiH}}_{2}, Pnma\text{\ensuremath{-}}{\mathrm{BiH}}_{2}, Pnnm\text{\ensuremath{-}}{\mathrm{BiH}}_{2}$, and $P{2}_{1}/m\text{\ensuremath{-}}{\mathrm{BiH}}_{2}$ are all topological metals defined on curved Fermi levels, while the $P{2}_{1}{2}_{1}{2}_{1}\text{\ensuremath{-}}{\mathrm{BiH}}_{2}$ holds Weyl points near the Fermi level. The topological surface states (TSSs) and Fermi arcs of ${\mathrm{BiH}}_{2}$ right cross the Fermi level and hold helical spin textures. Considering the fact that the ${\mathrm{BiH}}_{2}$ exhibit high superconducting transition temperatures (${T}_{c}$) of $\ensuremath{\sim}70$ K under pressure confirmed by recent experiments, the superconducting bulks will induce superconductivity in the TSSs via the proximity effect. Thus, the hydride superconductors ${\mathrm{BiH}}_{2}$ may provide a promising platform for exploring topological superconductivity and Majorana zero modes.