Graphene Plasmonic Crystals Exhibit Topological Bands and Phase Transitions with Quantized Geometric Phase

The behaviour of light interacting with specially structured materials holds immense promise for future technologies, and recent research explores how to harness this interaction in graphene. André Octávio Soares from University of Minho, Christos Tserkezis from University of Southern Denmark, and N. M. R. Peres investigate topological plasmons within graphene structures, specifically examining how light waves behave in a periodically patterned sheet placed on a metallic surface. This work reveals the existence of robust, topologically protected bands of light, meaning these waves are remarkably stable and resistant to disruption, and demonstrates the emergence of unique edge states within the material. By establishing a theoretical framework for understanding these effects, the team extends the possibilities for designing and engineering two-dimensional materials with precisely controlled optical properties, potentially leading to advances in areas like sensing and data transmission.

Robust Topological Plasmons in Graphene Crystals

Researchers investigate topological plasmons in graphene plasmonic crystals, structures created by periodically patterning graphene sheets. They explore how the arrangement of these patterns influences plasmon behaviour, aiming to control their properties for nanophotonic applications. The study demonstrates the existence of robust, topologically protected plasmon modes less susceptible to defects in the graphene structure. The approach involves theoretical modelling and numerical simulations to analyse the electromagnetic response of these crystals. Scientists employ a theoretical model to describe graphene’s electronic structure, coupled with classical electrodynamics to calculate plasmon propagation.

They systematically vary the geometry of the crystal to map the energy levels of the plasmon modes, identifying topological features and understanding environmental effects. Specific contributions include demonstrating a shift in plasmon frequency due to environmental effects and observing a change in the topological state as environmental strength varies. The team reveals that strong environmental effects can suppress edge states crucial for propagating topologically protected plasmons, establishing a clear relationship between geometry, environment, and topological properties. Researchers study topological effects in a one-dimensional plasmonic crystal formed by screened plasmons emerging in a periodically modulated graphene sheet on a metallic substrate. They develop a theory to quantify these screened plasmons, appropriate for graphene with specific electrical properties. Analysing the resulting energy levels, they show the crystal sustains unique energy bands with a quantized geometric phase, and that finite structures exhibit edge states undergoing a change in topological state and merging with other energy levels.

Graphene Plasmons Demonstrate Strong Non-Local Effects

This research delves into plasmonics, topological photonics, and quantum effects in graphene. Graphene is an excellent material for supporting tunable plasmons. The research emphasizes considering non-local effects in describing graphene plasmons, meaning the electron response isn’t instantaneous and depends on spatial distribution. Graphene plasmons exhibit long-range interactions, making them suitable for waveguiding and signal propagation. The text explores engineering analogous behaviour to topological insulators in photonic and plasmonic systems.

A crucial concept is the Zak phase, a geometric phase characterizing energy levels in periodic systems, used to identify topological phases and characterize edge states. The goal is to create systems with topologically protected edge states robust against defects, enabling robust waveguiding and information transfer. The Su-Schrieffer-Heeger model, originally developed for a different material, provides a framework for understanding topological behaviour in one-dimensional plasmonic systems, and Wilson loops characterize topology. The text explores observing quantum effects in plasmonic systems, such as entanglement and non-classical light generation.

Graphene plasmons are proposed as a source of entangled photons essential for quantum information processing, with potential as qubits and for building quantum circuits. Observing quantum interference effects in plasmonic circuits is also highlighted. The Berry phase, a geometric phase arising from the evolution of quantum states, is key to understanding topological properties. A tight-binding model describes the electronic structure of materials, and the transfer matrix method calculates wave transmission and reflection through periodic structures. Bloch’s theorem describes electron behaviour in periodic potentials. This research paints a picture of a rapidly evolving field where the intersection of plasmonics, topology, and quantum mechanics promises new functionalities for light manipulation, information processing, and quantum technologies.

Topological Plasmons and Mid-Gap Edge States

This research presents a theoretical framework for understanding light behaviour within specifically designed layered materials, focusing on the quantum properties of plasmons. Scientists developed a method to analyse plasmon behaviour when material properties are periodically altered, demonstrating the formation of unique energy bands. Crucially, the analysis reveals these plasmonic bands exhibit non-trivial topological properties, possessing characteristics distinguishing them from conventional materials and defined by a quantized geometric phase. The team demonstrated a direct link between the material’s topological state and the emergence of mid-gap edge states localized at the material’s boundaries, confirming the principle of bulk-boundary correspondence. Numerical analysis of a finite material slab confirmed the existence of these exponentially localized edge states. This work establishes a pathway for manipulating light using graphene-based plasmonic crystals and lays the groundwork for exploring quantum optical phenomena within these structures.