  Second order quantum phase transitions, with well-known features such as
long-range entanglement, symmetry breaking, and gap closing, exhibit quantum
enhancement for sensing at criticality. However, it is unclear which of these
features are responsible for this enhancement. To address this issue, we
investigate phase transitions in free-fermionic topological systems that
exhibit neither symmetry-breaking nor long-range entanglement. We analytically
demonstrate that quantum enhanced sensing is possible using topological edge
states near the phase boundary. Remarkably, such enhancement also endures for
ground states of such models that are accessible in solid state experiments. We
illustrate the results with 1D Su-Schrieffer-Heeger chain and a 2D Chern
insulator which are both experimentally accessible. While neither
symmetry-breaking nor long-range entanglement are essential, gap closing
remains as the major candidate for the ultimate source of quantum enhanced
sensing. In addition, we also provide a fixed and simple measurement strategy
that achieves near-optimal precision for sensing using generic edge states
irrespective of the parameter value. This paves the way for development of
topological quantum sensors which are expected to also be robust against local
perturbations.
