Southeast University Team Uncovers Inert Term’s Topology Role

Researchers at Southeast University in Nanjing, China, have revealed a surprising role for a component of physics typically considered inconsequential. The team demonstrates that an identity term in the Hamiltonian, conventionally regarded as spectrally inert and therefore negligible, can actively drive a specific type of topology known as Non-Hermitian topology. This discovery challenges established criteria for understanding these systems, as the identity term deforms the generalized Brillouin zone under non-Hermitian skin pumping. By achieving an exact analytical solution with a Hatano-Nelson chain incorporating spin-orbit coupling, the researchers have established a rigorous benchmark for testing topological invariants in systems with momentum-dependent identity terms, opening new avenues for exploring topology beyond symmetry protection.

Non-Hermitian Physics and Recent Discoveries

A component within physics, the identity term, is now revealed to be a key driver of topological behavior in non-Hermitian systems, a finding that challenges long-held assumptions about these materials. This deformation alters established criteria for understanding topology, which previously relied on fixed complex contours. By introducing spin-orbit coupling into a Hatano-Nelson chain, the researchers present an exact analytical solution for the non-Hermitian eigensystem under open boundary conditions. Their solution reveals that inter-cell spin-orbit coupling, working with the momentum-dependent identity term, induces topological edge states even without chiral symmetry, a common requirement for topological protection in many materials. An identity term in the Hamiltonian is conventionally regarded as spectrally inert, it shifts energies but does not alter eigenstate topology.

This work establishes an exactly solvable paradigm for non-Hermitian topology beyond symmetry protection and provides a rigorous benchmark for testing topological invariants in systems with momentum-dependent identity terms. The research, originating from the Key Laboratory of Quantum Materials and Devices of Ministry of Education at Southeast University, Nanjing 211189, China, is a crucial step toward predicting and controlling topological phenomena in systems lacking the simplifying constraints of chiral symmetry.

Recent advances in non-Hermitian physics have revealed a range of unusual phenomena, including the non-Hermitian skin effect (NHSE) and non-Bloch topological phases, expanding beyond traditional Hermitian frameworks. The NHSE, where bulk eigenstates concentrate at system boundaries, necessitates the use of the generalized Brillouin zone (GBZ) to accurately describe topology in one-dimensional systems. This non-Bloch band theory has found applications in diverse platforms, from cold atoms to photonic lattices. Much of this progress relies on models possessing simplifying symmetries like chiral or particle-hole symmetry. Researchers are now addressing the more complex scenario of non-chiral systems lacking these symmetries. Existing analytical approaches often require Hamiltonians expressible in a two-band form, limiting their applicability. A key challenge arises when a momentum-dependent identity term is present in the Hamiltonian, actively deforming the GBZ and invalidating established topological criteria based on fixed contours. The work shows that this assumption fails under non-Hermitian skin pumping, as the identity term actively reshapes the GBZ.

While previous analytical progress largely focused on two-band models, this work tackles the more complex scenario of a momentum-dependent identity term within the Hamiltonian, a feature that complicates the generalized Brillouin zone and renders traditional topological criteria unreliable. An identity term in the Hamiltonian is conventionally regarded as spectrally inert, it shifts energies but does not alter eigenstate topology. The research demonstrates that under non-Hermitian skin pumping, this understanding fails: a momentum-dependent identity term actively deforms the generalized Brillouin zone, thereby challenging established topological criteria that rely on fixed complex contours. The result reveals how this interplay induces topological edge states and robust zero modes, even without symmetry protection, establishing a new paradigm for understanding non-Hermitian topology.

Applications of Non-Bloch Band Theory Across Platforms

The utility of non-Bloch band theory extends beyond foundational studies, now impacting the design of diverse physical platforms. While initial explorations focused on understanding fundamental topological phenomena, researchers are increasingly leveraging these principles for practical applications, ranging from manipulating cold atoms to engineering novel photonic devices. An identity term in the Hamiltonian is conventionally regarded as spectrally inert, it shifts energies but does not alter eigenstate topology. The research shows that under non-Hermitian skin pumping, this understanding fails: a momentum-dependent identity term actively deforms the generalized Brillouin zone, thereby challenging established topological criteria that rely on fixed complex contours. Here, by introducing spin-orbit coupling into a Hatano-Nelson chain, the researchers present an exact analytical solution for the entire non-Hermitian eigensystem under open boundary conditions.

Their solution reveals how inter-cell spin-orbit coupling, working with this non-trivial identity term, induces topological edge states and robust zero modes in the complete absence of chiral symmetry. This work establishes an exactly solvable paradigm for non-Hermitian topology beyond symmetry protection and provides a rigorous benchmark for testing topological invariants in systems with momentum-dependent identity terms. Electric circuits, mechanical metamaterials, and photonic lattices are among the platforms where these concepts are being actively implemented, enabling the creation of robust and tunable devices.

Conventional understandings of topological systems often rely on the presence of protecting symmetries, such as chiral or particle-hole symmetry, simplifying the analysis of edge states. However, a growing number of real-world materials lack these features, presenting a significant hurdle for both theoretical prediction and experimental verification of non-Hermitian topology. Existing analytical approaches have largely focused on two-band models, establishing non-Bloch topological invariants even in non-chiral systems, but these methods falter when confronted with momentum-dependent identity terms within the Hamiltonian. The introduction of spin-orbit coupling into a non-Hermitian Hatano-Nelson chain, a system known to exhibit the non-Hermitian skin effect, is central to this work. This analytical control is crucial, as it moves beyond case-by-case numerical computations of the generalized Brillouin zone, which can become computationally intractable for complex systems.

The pursuit of understanding non-Hermitian topology has largely focused on systems with simplifying symmetries, but researchers at Southeast University have now demonstrated a pathway to analyze systems lacking these protections. This deformation complicates established topological criteria, necessitating new analytical tools. Previously, probing these systems relied heavily on computationally intensive GBZ calculations, limiting the ability to predict behavior in complex scenarios.

The exploration of non-Hermitian physics has rapidly expanded in recent years, revealing phenomena like the non-Hermitian skin effect and novel topological phases in systems ranging from cold atoms to photonic lattices.

This analytical control is particularly valuable given the difficulties in probing these systems numerically. Existing methods often rely on computationally intensive GBZ calculations, which become intractable with complex geometries. This work has been published on arXiv.