具有半子模式欧拉拓扑绝缘体的声学观测

Topological band theory has conventionally been concerned with the topology of bands around a single gap. Only recently non-Abelian topologies that thrive on involving multiple gaps were studied, unveiling a new horizon in topological physics beyond the conventional paradigm. Here, we report on the first experimental realization of a topological Euler insulator phase with unique meronic characterization in an acoustic metamaterial. We demonstrate that this topological phase has several nontrivial features:First, the system cannot be described by conventional topological band theory, but has a nontrivial Euler class that captures the unconventional geometry of the Bloch bands in the Brillouin zone.Second, we uncover in theory and probe in experiments a meronic configuration of the bulk Bloch states for the first time. Third, using a detailed symmetry analysis, we show that the topological Euler insulator evolves from a non-Abelian topological semimetal phase via. the annihilation of Dirac points in pairs in one of the band gaps. With these nontrivial properties, we establish concretely an unconventional bulk-edge correspondence which is confirmed by directly measuring the edge states via. pump-probe techniques. Our work thus unveils a nontrivial topological Euler insulator phase with a unique meronic pattern and paves the way as a platform for non-Abelian topological phenomena.

A gauge theory for two-band model of Chern insulators and induced topological defects

In this paper a gauge theory is proposed for the two-band model of Chern insulators.Based on the so-calle't Hooft monopole model,a U(1)Maxwell electromagnetic sub-field is constructed from an SU(2)gauge field,from which arise two types of topological defects,monopoles and e2 merons.We focus on the topological number in the Hall conductance σ_(xy)=e^(2)/hC,where C is the Chern number.It is discovered that in the monopole case C is indeterminate,while in the meron case C takes different values,due to a varying on-site energy m.As a typical example,we apply this method to the square lattice and compute the winding numbers(topological charges)of the defects;the C-evaluations we obtain reproduce the results of the usual literature.Furthermore,based on the gauge theory we propose a new model to obtain the high Chern numbers|C|=2,4.