Dynamically characterizing topological phases by high-order topological charges

Abstract

We propose a new theory to characterize equilibrium topological phase with non-equilibrium quantum dynamics by introducing the concept of high-order topological charges, with novel phenomena being predicted. Through a dimension reduction approach, we can characterize a $d$-dimensional ($d$D) integer-invariant topological phase with lower-dimensional topological number quantified by high-order topological charges, of which the $s$th-order topological charges denote the monopoles confined on the $(s-1)$th-order band inversion surfaces (BISs) that are $(d-s+1)$D momentum subspaces. The bulk topology is determined by the $s$th order topological charges enclosed by the $s$th-order BISs. By quenching the system from trivial phase to topological regime, we show that the bulk topology of post-quench Hamiltonian can be detected through a high-order dynamical bulk-surface correspondence, in which both the high-order topological charges and high-order BISs are identified from quench dynamics. This characterization theory has essential advantages in two aspects. First, the highest ($d$th) order topological charges are characterized by only discrete signs of spin-polarization in zero dimension (i.e. the $0$th Chern numbers), whose measurement is much easier than the $1$st-order topological charges that are characterized by the continuous charge-related spin texture in higher dimensional space. Secondly, a more striking result is that a first-order high integer-valued topological charge always reduces to multiple highest-order topological charges with unit charge value, and the latter can be readily detected in experiment. The two fundamental features greatly simplify the characterization and detection of the topological charges and also topological phases, which shall advance the experimental studies in the near future.

13 pages, 7 figures

References in corpus (15)

• Many-Body Physics with Ultracold Gases
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Topological Insulators with Inversion Symmetry
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Crystalline Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Emergent topology under slow non-adiabatic quantum dynamics

Cited by in corpus (10)

• Universal competitive spectral scaling from the critical non-Hermitian skin effect
• Unified characterization for higher-order topological phase transitions
• Quantum quenches in a pseudo-Hermitian Chern insulator
• Generic theory of characterizing topological phases under quantum slow dynamics
• Unveiling Higher-Order Topology via Polarized Topological Charges
• Unconventional hybrid-order topological insulators
• Characterizing Floquet topological phases by quench dynamics: A multiple-subsystem approach
• Dynamical detection of mean-field topological phases in an interacting Chern insulator
• Generic reduction theory for Fermi sea topology in metallic systems
• Full investigation of nonadiabatic dynamical characterization in arbitrary quenching process