We study the nonequilibrium driven dynamics at topologically nontrivial quantum critical points (QCPs) and find that topological edge modes at criticality give rise to anomalous dynamical scaling behavior. By analyzing the driven dynamics of bulk and boundary order parameters at topologically distinct QCPs in quantum spin chains, we demonstrate that, while the bulk dynamics remain indistinguishable and follow standard Kibble-Zurek (KZ) scaling, the anomalous boundary dynamics are unique to topological criticality, obeying modified scaling relation beyond the traditional KZ framework. To elucidate the unified origin of this anomaly, we further study the dynamics of defect production at topologically distinct QCPs in free-fermion models and demonstrate similar anomalous scaling exclusive to topological criticality. These findings establish the existence of anomalous dynamical scaling arising from the interplay between topology and driven dynamics, challenging standard paradigms of quantum critical dynamics.

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• Critical phenomena
• Nonequilibrium statistical mechanics
• Quantum criticality
• Quantum quench
• Symmetry protected topological states
• Topological phase transition
• Quantum spin models
• Topological insulators
• Topological materials
• Finite-size scaling