Related papers: Dynamically characterizing topological phases by high-order topological charges

Dynamically characterizing topological phases by high-order topological charges

URL: http://arxiv.org/abs/2012.13494v1
Date: Fri, 25 Dec 2020 02:51:21 GMT
Title: Dynamically characterizing topological phases by high-order topological charges
Authors: Wei Jia, Lin Zhang, Long Zhang, and Xiong-Jun Liu
Abstract summary: We propose a new theory to characterize equilibrium topological phase with non-equilibrium quantum dynamics. We show that the bulk topology of post-quench Hamiltonian can be detected through a high-order dynamical bulk-surface correspondence.
Score: 10.846336976807514
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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.

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