HKBU Professor Ma Guancong advances understanding of exceptional deficiency

Traditional exceptional points in non-Hermitian systems involve the coalescence of isolated eigenvectors alongside degenerate complex energies. While these unique singularities have enabled advanced applications such as high-precision sensing, accessing them typically demands delicate parameter tuning. Furthermore, any related physical phenomena are intrinsically restricted to a very narrow bandwidth. To address and overcome these fundamental limitations, Professor Ma Guancong (Chair Professor in Physics and Metamaterials) led a research team that developed a profound generalisation of the conventional exceptional point concept, known as an exceptional deficiency. 

This advanced framework shifts the focus from individual vectors to entire eigenspaces. An exceptional deficiency features the complete coalescence of entire eigenspaces possessing identical, arbitrarily large dimensions, accompanied by the coincidence of entire spectral continua. Rather than occurring at isolated points in the complex spectrum, defective states emerge broadly across continuous bands. This structural transformation hinges on block-triangular matrices where invariant subspaces allow high-dimensional spaces to align completely, even when the constituent diagonal blocks comprise different Hermitian and non-Hermitian matrices. 

Anomalous skin effects and dynamics

“When applied to physical structures such as one-dimensional double-chain lattices, exceptional deficiency produces unexpected behaviour that transcends established topological bulk-edge correspondence,” said Professor Ma. Systems governed by this phenomenon can exhibit the anomalous absence or presence of the non-Hermitian skin effect, a localisation mechanism where states in continuous bands normally cling exclusively to open boundaries. By arranging a Hermitian chain and a non-Hermitian chain with one-way coupling, researchers observe synergistic skin-propagative dynamics. 

Depending on the specific direction of interchain hopping, wave packets can undergo remarkable phenomena such as skin-effect-amplified propagation or a propagation-enhanced skin effect. In these scenarios, localised boundary tendencies combine dynamically with bulk transport. Rather than remaining trapped at an edge, waves can experience directional amplification while simultaneously escaping through robust propagative channels provided by non-defective subspaces. 

Experimental realisation and future applications

These theoretical concepts have been successfully validated using active mechanical lattices outfitted with programmable electronic feedback control. “By adjusting the natural frequencies and coupling parameters of individual mechanical oscillators, researchers can experimentally map out steady-state frequency responses and time-dependent wave evolution”, said Professor Ma. The physical measurements confirm that extended modes and skin modes can coexist in massive quantities. Moreover, by introducing a constant offset to the spectra, the ratio of these distinct modes can be flexibly tuned, offering a reliable route to controlling wave localisation and propagation. 

The experimental verification of exceptional deficiency opens up fresh perspectives across multiple branches of physics. Because exceptional deficiency involves continuous spectra rather than isolated points, it provides a viable solution to the narrow-band constraints that have traditionally hindered conventional exceptional point devices. This broadband capability is particularly advantageous for practical engineering tasks, paving the way for the development of ultra-sensitive sensors featuring large dynamic ranges, alongside valuable advancements in modal control and lasing technologies. 

Full article on Nature Physics: https://www.nature.com/articles/s41567-026-03259-7
Professor Ma’s research profile: https://scholars.hkbu.edu.hk/en/persons/PHGCMA

Professor Ma Guancong

Faculty of Science and Technology