Symmetry classes of dissipative topological insulators with edge dark state
Abstract
We classify the dissipative topological insulators (TIs) with edge dark states (EDS) by using the 38-fold way of non-Hermitian systems in this paper. The dissipative dynamics of these quadratic open fermionic systems is captured by a non-Hermitian single-particle matrix which contains both the internal dynamics and the dissipation, refereed to as damping matrix $X$. And the dark states in these systems are the eigenmodes of $X$ which the eigenvalues' imaginary part vanishes. However, there is a constraint on $X$, namely that the modes in which the eigenvalues' imaginary parts are positive are forbidden. In other words, the imaginary line-gap of $X$ is ill-defined, so the topological band theory classifying the dark states can not be applied to $X$. To reveal the topological protection of EDS, we propose the double damping matrix $\tilde{X} = \text{diag}\left( X, X^* \right)$, where the imaginary line-gap is well defined. Thus, the 38-fold way can be applied to $\tilde{X}$, and the topological protection of the EDS is uncovered. Different from previous studies of EDS in purely dissipative dynamics, the EDS in the dissipative TIs are robust against the inclusion of Hamiltonians. Furthermore, the topological classification of $\tilde{X}$ not only reflects the topological protection of EDS in dissipative TIs but also provides a paradigm to predict the appearance of EDS in other open free fermionic systems.
Read the paper
Related studies
- The Matrisome: In Silico Definition and In Vivo Characterization by Proteomics of Normal and Tumor Extracellular Matrices
- The Escherichia coli MG1655 in silico metabolic genotype: Its definition, characteristics, and capabilities
- In silico pharmacology for drug discovery: methods for virtual ligand screening and profiling
- In silico prediction of splice-altering single nucleotide variants in the human genome
- In silico clinical trials: how computer simulation will transform the biomedical industry
- In silico optimization of a guava antimicrobial peptide enables combinatorial exploration for peptide design
Go deeper in Evidence Hub
Evidence Hub adds a study data sheet (design, sample size, evidence level, key numbers), an AI summary and a chat grounded in the paper's text.