Nonlinear terahertz phononics in the Dirac semimetal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Cd</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>As</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></m

The coherent lattice dynamics in the three-dimensional (3D) Dirac semimetal <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msub><a:mi>Cd</a:mi><a:mn>3</a:mn></a:msub><a:msub><a:mi>As</a:mi><a:mn>2</a:mn></a:msub></a:mrow></a:math> is investigated in the nonperturbative regime of light-matter interaction using coherent two-dimensional terahertz (THz) spectroscopy, as a function of time delay and field strength. The phase-resolved nonlinear signal reveals a coherent phonon mode at 1.48 THz, corresponding to the <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msub><b:mi>B</b:mi><b:mrow><b:mn>2</b:mn><b:mi>g</b:mi></b:mrow></b:msub></b:math> Raman-active mode, characterized by the periodic motion of two cadmium atoms in the substructure toward and away from two cadmium-vacant sites. The interaction of a strong THz electric field with the 3D Dirac semimetal <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:msub><c:mi>Cd</c:mi><c:mn>3</c:mn></c:msub><c:msub><c:mi>As</c:mi><c:mn>2</c:mn></c:msub></c:mrow></c:math> leads to transient charge carrier imbalance via tunneling ionization, which results in a displacive force that drives the lattice dynamics of a noninteracting Raman-active mode. The selective excitation of otherwise inaccessible phonon modes enables precise control over the material's properties at the atomic level, opening new pathways to manipulate its topological characteristics.