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Composite topological phases with intriguing topology like M${\"o}$biusstrips emerge in sublattice symmetric non-Hermitian systems due to spontaneousbreaking of time-reversal symmetry at some parameter regime. While these phaseshave been characterized by nonadiabatic complex geometric phases of multipleparticipating complex bands, the physical properties of these phases largelyremain unknown. We explore the dynamical response of these phases by studyingLoschmidt echo from an initial state of the Hermitian Su-Schrieffer-Heeger(SSH) model, which is evolved by a non-Hermitian SSH Hamiltonian after a suddenquench in parameters. Topology-changing quenches display non-analyticaltemporal behavior of return rates (logarithm of the Loschmidt echo) for thenon-Hermitian SSH Hamiltonian in the trivial, M${\"o}$bius and topologicalphase. Moreover, the dynamical topological order parameter appears only at oneside of the Brillouin zone for the M${\"o}$bius phase case in contrast to bothsides of the Brillouin zone for quench by the trivial and topological phase ofthe non-Hermitian SSH model. The last feature is a dynamical signature ofdifferent symmetry constraints on the real and imaginary parts of the complexbands in the M${\"o}$bius phase.

Anomalous dynamical response of non-Hermitian topological phases