The free-fermion topological phases with Z2 invariants cover a broad range of topological states,includ-ing the time-reversal invariant topological insulators,and are defined on the equilibrium ground states.Whether such equilibrium topological phases have universal correspondence to far-from-equilibrium quantum dynamics is a fundamental issue of both theoretical and experimental importance.Here we uncover the universal topological quench dynamics linking to these equilibrium topological phases of dif-ferent dimensionality and symmetry classes in the tenfold way,with a general framework being estab-lished.We show a novel result that a generic d-dimensional topological phase represented by Dirac type Hamiltonian and with Z2 invariant defined on high symmetry momenta can be characterized by topology reduced to certain arbitrary discrete momenta of Brillouin zone called the highest-order band-inversion surfaces.Such dimension-reduced topology has unique correspondence to the topological pat-tern emerging in far-from-equilibrium quantum dynamics by quenching the system from trivial phase to the topological regime,rendering the dynamical hallmark of the equilibrium topological phase.This work completes the dynamical characterization for the full tenfold classes of topological phases,which can be partially extended to even broader topological phases protected by lattice symmetries and in non-Dirac type systems,and shall advance widely the research in theory and experiment.

Lin Zhang;Wei Jia;Xiong-Jun Liu

International Center for Quantum Materials and School of Physics,Peking University,Beijing 100871,China;Collaborative Innovation Center of Quantum Matter,Beijing 100871,China;CAS Center for Excellence in Topological Quantum Computation,University of Chinese Academy of Sciences,Beijing 100190,China;Institute for Quantum Science and Engineering and Department of Physics,Southern University of Science and Technology,Shenzhen 518055,China

科学通报（英文版）

[1]Lin Zhang;Wei Jia;Xiong-Jun Liu-.Universal topological quench dynamics for Z2 topological phases)[J].科学通报（英文版）,2022(12):1236-1242

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