Electron-phonon driven charge density wave and superconductivity in a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>1</mml:mn><mml:mi>T</mml:mi><mml:mtext>−</mml:mtext><mml:msub><mml:mi>TaSi</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">N</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math> monolayer

Charge-density wave (CDW) and superconductivity, as well as their interplay, are fascinating topics in condensed-matter physics. In this work, we propose a single-layer (SL) CDW material, $1T\text{\ensuremath{-}}{\mathrm{TaSi}}_{2}{\mathrm{N}}_{4}$, among synthesized two-dimensional (2D) ${\mathrm{MoSi}}_{2}{\mathrm{N}}_{4}$ family. Through first-principles simulations, its stability, vibrational properties, electronic structures, CDW, and superconductivity have been systematically scrutinized. The Ta-${\mathit{d}}_{{z}^{2}}$ orbitals occupy mainly at the Fermi level and SL $1T\text{\ensuremath{-}}{\mathrm{TaSi}}_{2}{\mathrm{N}}_{4}$ exhibits intrinsic metallic property. Besides, the CDW transition temperature (${T}_{\mathrm{CDW}}$) is estimated to be $\ensuremath{\sim}500$ K by using the temperature dependent effective potential technique. We found that it is the electron-phonon couping (EPC) that drives the CDW to form. Furthermore, its CDW orders can be manipulated by carrier doping and applying strain. At doping of 0.14 h/cell, the CDW instability is effectively suppressed and it changes to a 2D superconductor below $\ensuremath{\sim}21.84$ K. Moreover, its superconducting transition temperature ${\mathit{T}}_{c}$ under the strain of 10% is $\ensuremath{\sim}10.47$ K. Physically, the superconductivity in stabilized $1T\text{\ensuremath{-}}{\mathrm{TaSi}}_{2}{\mathrm{N}}_{4}$ monolayer is mainly contributed by the EPC between electrons from the Ta-${\mathit{d}}_{{z}^{2}}$ orbitals and phonon vibrations from the $\mathrm{Ta}\text{\ensuremath{-}}xy$ and $\mathrm{N}\text{\ensuremath{-}}z$ modes with evident soft phonon mode.