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

Two-dimensional materials with a proper band gap and high carrier mobility are urgently desired in the field of nanoelectronics. We propose a novel two-dimensional crystal monolayer $\mathrm{TlP_5}$, which is dynamically and thermodynamically stable and possesses a direct band gap of 2.02 eV with high carrier 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 $\mathrm{TlP_5}$ can be adjusted by biaxial and uniaxial strains, and excellent optical absorption over the visible-light range is predicted. These properties, especially for the balanced high mobilities for not only the electrons but also the holes, render monolayer $\mathrm{TlP_5}$ an exciting functional material for future nanoelectronics and optoelectronic applications.