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Two-dimensional materials with a proper band gap and high carrier mobilityare urgently desired in the field of nanoelectronics. We propose a noveltwo-dimensional crystal monolayer $\mathrm{TlP_5}$, which is dynamically andthermodynamically stable and possesses a direct band gap of 2.02 eV with highcarrier mobilities (13960 $\mathrm{cm^2\ V^{-1}s^{-1}}$ for electrons and 7560$\mathrm{cm^2\ V^{-1}s^{-1}}$ for holes), comparable to that of phosphorene.The band gap value and band characteristics of monolayer $\mathrm{TlP_5}$ canbe adjusted by biaxial and uniaxial strains, and excellent optical absorptionover the visible-light range is predicted. These properties, especially for thebalanced high mobilities for not only the electrons but also the holes, rendermonolayer $\mathrm{TlP_5}$ an exciting functional material for futurenanoelectronics and optoelectronic applications.

$\mathrm{TlP_5}$: An unexplored direct band gap 2D semiconductor with ultra-high carrier mobility