Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe Bulk-boundary Correspondence in Non-Hermitian Hopf-link Exceptional Line Semimetals
185
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We consider a 3-dimensional (3D) non-Hermitian exceptional line semimetal model and take open boundary conditions in x, y, and z directions separately. In each case, we calculate the parameter regions where the bulk-boundary correspondence is broken. The breakdown of the bulk-boundary correspondence is manifested by the deviation from unit circles of generalized Brillouin zones (GBZ) and the discrepancy between spectra calculated with open boundary conditions (OBC) and periodic boundary conditions (PBC). The consistency between OBC and PBC spectra can be recovered if the PBC spectra are calculated with GBZs. We use both unit-circle Brillouin zones (BZ) and GBZs to plot the topological phase diagrams. The systematic analysis of the differences between the two phase diagrams suggests that it is necessary to use GBZ to characterize the bulk-boundary correspondence of non-Hermitian models.
rate research
Read More
We study a new class of non-Hermitian topological phases in three dimension in the absence of any symmetry, where the topological robust band degeneracies are Hopf-link exceptional lines. As a concrete example, we investigate the non-Hermitian band structures of nodal line semimetals under non-Hermitian perturbations, where the Fermi surfaces can transit from 1d nodal lines to 2d twisting surfaces with Hopf-link boundaries when the winding number defined along the nodal line is $pm 1$. The linking numbers of these linked exceptional line phases are also proposed, based on the integral of Chern-Simons form over the Brillouin zone.
Bulk-boundary correspondence, a central principle in topological matter relating bulk topological invariants to edge states, breaks down in a generic class of non-Hermitian systems that have so far eluded experimental effort. Here we theoretically predict and experimentally observe non-Hermitian bulk-boundary correspondence, a fundamental generalization of the conventional bulk-boundary correspondence, in discrete-time non-unitary quantum-walk dynamics of single photons. We experimentally demonstrate photon localizations near boundaries even in the absence of topological edge states, thus confirming the non-Hermitian skin effect. Facilitated by our experimental scheme of edge-state reconstruction, we directly measure topological edge states, which match excellently with non-Bloch topological invariants calculated from localized bulk-state wave functions. Our work unequivocally establishes the non-Hermitian bulk-boundary correspondence as a general principle underlying non-Hermitian topological systems, and paves the way for a complete understanding of topological matter in open systems.
Bulk-boundary correspondence, connecting the bulk topology and the edge states, is an essential principle of the topological phases. However, the bulk-boundary correspondence is broken down in general non-Hermitian systems. In this paper, we construct one-dimensional non-Hermitian Su-Schrieffer-Heeger model with periodic driving that exhibits non-Hermitian skin effect: all the eigenstates are localized at the boundary of the systems, whether the bulk states or the zero and the $pi$ modes. To capture the topological properties, the non-Bloch winding numbers are defined by the non-Bloch periodized evolution operators based on the generalized Brillouin zone. Furthermore, the non-Hermitian bulk-boundary correspondence is established: the non-Bloch winding numbers ($W_{0,pi}$) characterize the edge states with quasienergies $epsilon=0, pi$. In our non-Hermitian system, a novel phenomenon can emerge that the robust edge states can appear even when the Floquet bands are topological trivial with zero non-Bloch band invariant, which is defined in terms of the non-Bloch effective Hamiltonian. We also show that the relation between the non-Bloch winding numbers ($W_{0,pi}$) and the non-Bloch band invariant ($mathcal{W}$): $mathcal{W}= W_{0}- W_{pi}$.
We provide a systematic and self-consistent method to calculate the generalized Brillouin Zone (GBZ) analytically in one dimensional non-Hermitian systems, which helps us to understand the non-Hermitian bulk-boundary correspondence. In general, a n-band non-Hermitian Hamiltonian is constituted by n distinct sub-GBZs, each of which is a piecewise analytic closed loop. Based on the concept of resultant, we can show that all the analytic properties of the GBZ can be characterized by an algebraic equation, the solution of which in the complex plane is dubbed as auxiliary GBZ (aGBZ). We also provide a systematic method to obtain the GBZ from aGBZ. Two physical applications are also discussed. Our method provides an analytic approach to the spectral problem of open boundary non-Hermitian systems in the thermodynamic limit.
Bulk-boundary correspondence is the cornerstone of topological physics. In some non-Hermitian topological system this fundamental relation is broken in the sense that the topological number calculated for the Bloch energy band under the periodic boundary condition fails to reproduce the boundary properties under the open boundary. To restore the bulk-boundary correspondence in such non-Hermitian systems a framework beyond the Bloch band theory is needed. We develop a non-Hermitian Bloch band theory based on a modified periodic boundary condition that allows a proper description of the bulk of a non-Hermitian topological insulator in a manner consistent with its boundary properties. Taking a non-Hermitian version of the Su-Schrieffer-Heeger model as an example, we demonstrate our scenario, in which the concept of bulk-boundary correspondence is naturally generalized to non-Hermitian topological systems.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
