Wenbu Duan | Searcharxiv

arXiv2024

Non-Hermitian Topology and Boundary Jordan Chains with Generalized Chiral Symmetry

We study a generalization of chiral symmetry applicable to non-Hermitian systems and its topological consequences on one-dimensional chains. We find a rich family of topological phases characterized not by a single winding number, but a vector of them. More importantly, we uncover a novel type of bulk-boundary correspondence, where the vector of winding numbers in the bulk corresponds to the set of Jordan chains of various length at the boundary. This in turn leads to highly unconventional chiral-charge distributions on both edges. Our work extends the topological classification of the non-Hermitian AIII class along a new axis.

cond-mat.mes-hall↗

arXiv2023

Topological Phases on Quantum Trees

In this work, we present a theory for topological phases for quantum systems on tree graphs. Conventionally, topological phases of matter have been studied in regular lattices, but also in quasicrystals and amorphous settings. We consider specific generalizations of regular tree graphs, and explore their topological properties. Unlike conventional systems, infinite quantum trees are not finite-dimensional, allowing for novel phenomena. We find a proliferation of topological zero modes present throughout the entire system, indicating that the bulk also acts as a boundary. We then go on to show that only three symmetry classes host stable topological phases in contrast to the usual five symmetry classes per dimension. Finally, we introduce what we call the Su-Schrieffer-Heeger tree which is topologically non-trivial even in the absence of inner degrees of freedom and does not possess any gapped trivial phases. We realize this system in an electronic circuit and show that our theory matches with experiments.

cond-mat.mes-hall↗