Topological Materials Reveal Stronger Interactions at Open Edges

A thorough investigation into the interplay between topology and charge ordering in interacting non-Hermitian systems reveals potential for new electronic devices. Sebastião dos A. Sousa-Júnior and colleagues at University of Houston, in collaboration with Uppsala University and Brazilian Centre For Research in Physics, detail how interactions sharply alter the behaviour of the Su-Schrieffer-Heeger model, especially under open boundary conditions. The study uncovers a key topological marker that precisely identifies topological phases and their breakdown, coinciding with the formation of charge density waves. Non-Hermiticity amplifies interaction effects, leading to a pronounced increase in staggered charge correlations and promoting electronic instabilities near exceptional points, thus deepening understanding of correlated topological matter

Open boundaries maximise charge ordering and topological phase detection

Staggered charge correlations increased by up to 10 times under open boundary conditions compared to periodic boundary conditions near exceptional points, a level of control previously unattainable. The amplification, observed in the non-Hermitian Su-Schrieffer-Heeger model, results from an accumulation of low-energy states, promoting electronic instabilities and strengthening tendencies towards a charge density wave (CDW) phase, a patterned arrangement of electrons. A real-space topological marker consistently diagnosed topological phases and their breakdown coinciding with CDW formation, offering a simpler alternative to methods requiring multiple boundary condition calculations. The Su-Schrieffer-Heeger (SSH) model, originally formulated for polyacetylene, describes electrons hopping between adjacent atoms in a one-dimensional chain with alternating hopping strengths. Introducing non-Hermiticity, through asymmetric hopping or gain/loss terms, fundamentally alters the band structure and gives rise to unique topological phases. These phases are characterised by the presence of edge states, which are protected from backscattering and can conduct electricity without dissipation. However, strong electronic interactions can significantly modify these topological properties, leading to complex behaviour and the emergence of correlated phases.

Electronic interactions also enlarged the region of topological phases, suppressing the non-Hermitian phase more strongly. These findings currently relate only to one-dimensional models and do not yet show a clear pathway to scalable, three-dimensional devices. Open boundary conditions amplified indicators of electron arrangement, staggered charge correlations, by up to 10 times compared to periodic boundary conditions near exceptional points, areas of unique energy behaviour. This enhancement stems from an accumulation of low-energy states, which destabilise the electronic structure and encourage the formation of a charge density wave (CDW) phase, a patterned ordering of electrons within the material. The real-space topological marker, a tool for identifying different material phases, consistently and accurately pinpointed topological phases and their breakdown as CDW formation began, simplifying analysis previously requiring multiple calculations. Exceptional points represent singularities in the non-Hermitian energy spectrum where eigenvalues and eigenvectors coalesce, leading to enhanced sensitivity to perturbations and dramatic changes in physical properties. The proximity of these points to the Fermi level plays a crucial role in driving the observed charge ordering and topological phase transitions.

Non-Hermitian topology and boundary effects in simplified material models

The study of topology, a branch of mathematics concerning properties preserved under continuous deformation, is increasingly the focus of efforts to engineer novel materials with tailored electronic behaviour. Topological insulators and semimetals, for example, exhibit robust surface states that are protected by topology and offer potential for spintronics and quantum computing. This research clarifies how interactions within non-Hermitian systems, those not adhering to conventional symmetry rules, fundamentally alter electronic behaviour, particularly when confined by open boundaries. Understanding how fundamental topological properties behave within these constrained systems provides important groundwork for tackling more complex materials. The conventional SSH model assumes that the system is Hermitian, meaning that its Hamiltonian is equal to its conjugate transpose. However, many physical systems exhibit non-Hermiticity due to dissipation, gain, or measurement processes. This non-Hermiticity can dramatically alter the topological properties of the system, leading to the emergence of new phases and phenomena.

Although these observations stem from a simplified, one-dimensional model, their importance remains significant. The demonstrated link between non-Hermitian physics, electronic interactions, and charge ordering, a redistribution of electrical density, offers a new perspective through which to view material behaviour. This investigation establishes a clear link between non-Hermitian physics and the emergence of charge density waves, patterned arrangements of electrons, within interacting systems. Employing a real-space topological marker, the team accurately tracked topological phases even with strong interactions and open boundaries, conditions where electrons are exposed at the material’s edges. Specifically, open boundaries amplify the impact of non-Hermiticity, dramatically increasing the tendency for electrons to organise into charge density waves near exceptional points, areas of unique energy behaviour. The real-space topological marker used in this study provides a local measure of the topological properties of the system, allowing for a more intuitive understanding of the phase diagram. This marker is based on the calculation of a topological invariant in real space, which can be efficiently computed even for complex systems with strong interactions. The researchers employed numerical simulations to map out the phase diagram of the interacting non-Hermitian SSH model under both periodic and open boundary conditions, carefully analysing the charge correlations and the complex many-body spectrum to identify the different phases and transitions. The observed enhancement of charge ordering under open boundary conditions suggests that edge effects play a crucial role in driving the formation of CDWs in non-Hermitian systems, potentially leading to new functionalities in nanoscale electronic devices.

Further research will need to extend these findings to higher-dimensional systems and explore the possibility of realising these effects in real materials. While the current study focuses on a theoretical model, the insights gained could inform the design of novel materials with tailored topological and charge ordering properties. The ability to control charge ordering and topological phases in non-Hermitian systems could pave the way for new electronic devices with enhanced performance and functionality, such as highly sensitive sensors and low-power transistors.

The research demonstrated that a real-space topological marker successfully identified topological phases within an interacting non-Hermitian system, even when electrons were exposed at material edges. Non-Hermiticity, a property departing from conventional physics, was found to amplify interactions and increase the formation of charge density waves, patterned arrangements of electrons. Open boundaries particularly enhanced these charge correlations near exceptional points, indicating edge effects are important in driving this process. Researchers plan to extend these findings to more complex, higher-dimensional systems and explore potential realisation in actual materials.