We investigate dynamical quantum phase transitions (DQPTs) in generic Dirac Hamiltonians following a sudden quench. By deriving an exact analytical expression for the Loschmidt amplitude (LA), we establish a universal criterion for DQPTs in this broad class of systems. We introduce first- and second-order dynamical topological order parameters (DTOPs) to characterize DQPTs. Geometrically, the second-order DTOPs track the evolution of (d-2)-dimensional topological defects on a special (d-1)-dimensional surface dictated by the universal criterion. In the short-time regime, we uncover a direct link between three distinct phenomena: the reconfiguration of topological defects, the emergence of van Hove singularities in the density of LA zeros, and non-analyticities in the rate function. In the long-time limit, the defects coalesce into a dense domain-wall structure on the (d-1)-dimensional surface. We show that this critical surface is inherent to both the time-averaged pseudospin polarization and the Hamiltonian. Our general framework is validated through its application to a three-dimensional four-band Dirac model. These results provide a theoretical foundation for studying DQPTs in topological systems, particularly in higher dimensions. The developed methodology is directly extendable to other quench protocols and to non-Hermitian generalizations of Dirac Hamiltonians.

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• Dynamical phase transitions
• Geometric & topological phases
• Topological phase transition
• Topological insulators
• Tight-binding model