Excitonic properties of two-dimensional (2D) crystals are of broad interest for luminescent devices. In 2D inversion-symmetry-breaking tetragonal crystals, a robust linear scaling holds between exciton binding energy ($E_{\mathrm{b}}$) and quasiparticle band gap ($E_{\mathrm{QP}}$), namely, $E_{\mathrm{b}}=3/8E_{\mathrm{QP}}$. However, how the built-in potential difference in 2D inversion-symmetry-breaking tetragonal crystals affects the scaling coefficient and the exciton radiative lifetimes remains unclear. Therefore, we systematically investigate excitonic properties and carrier mobility in such crystals using k·p perturbation theory, the screened hydrogen model, high-precision $G_0{W}_0$, and the Bethe-Salpeter equation (BSE). Our results indicate that the built-in potential difference weakens electron-hole coupling, reducing both $E_{\mathrm{QP}}$ and $E_{\mathrm{b}}$, and leading to a slightly shorter exciton radiative lifetime. Importantly, the exciton lifetime (up to 2.15 ps) remains significantly larger than in 2D hexagonal crystals, and the linear scaling between $E_{\mathrm{b}}$ and $E_{\mathrm{QP}}$ persists in the inversion-symmetry-breaking tetragonal crystals. Furthermore, all the materials exhibit high carrier mobility, which is more than two orders of magnitude higher than that of ${\mathrm{MoS}}_2$ and ${\mathrm{WS}}_2$. Our findings not only deepen the fundamental understanding of exciton properties in 2D tetragonal crystals but also suggest a viable strategy for exploring high-performance optoelectronic devices.

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• Excitons
• First-principles calculations
• Lifetimes & widths
• Electronic structure
• Layered semiconductors
• Semiconductor compounds
• Charge
• Density functional theory
• GW method