Researchers Sanghoon Lee, Tilen Cadez, and Kyoung-Min Kim, affiliated with institutions in South Korea and Slovenia, have published new findings in the journal Physical Review B that shed light on the behavior of certain complex systems, with potential implications for understanding energy transport and electronic properties in materials used in the energy sector.
The study focuses on a phenomenon called “mobility edges” in one-dimensional quasiperiodic systems. Mobility edges are points in a system’s energy spectrum that separate regions where particles (such as electrons) are localized (confined to a small region) from regions where they are delocalized (free to move throughout the system). These edges are crucial for understanding how energy and charge can be transported in materials, which is vital for designing efficient energy technologies.
The researchers found that the positions of these mobility edges are not arbitrary but are constrained by a fundamental relationship between different quasiperiodic systems. They demonstrated this using a specific model called the bichromatic Aubry–André model, which serves as a minimal setting to study these phenomena. The constraints on mobility edge positions arise from an exact identity involving Lyapunov exponents, which describe the rate of separation of nearby trajectories in a dynamical system. This identity is derived from the Thouless formula, a well-known result in the theory of disordered systems.
One of the key findings is that the mobility edge positions are restricted to a reduced set of energies, meaning that not all energies are possible locations for these edges. In the special case where the system is self-dual (a situation where the system’s properties are symmetric under a certain transformation), the mobility edges coincide at a single point, marking a transition between localized and delocalized states. This structural constraint leads to a specific scaling behavior of the Lyapunov spectrum near the self-dual point, which the researchers confirmed through numerical simulations.
The critical exponent they observed is consistent with the standard value for the Aubry–André model, which is ν=1. However, they also discovered a novel, non-universal energy-dependent prefactor, indicating that while the scaling behavior is consistent, the details can vary depending on the energy level.
For the energy sector, understanding mobility edges and localization-delocalization transitions can help in the design of materials for energy storage, conversion, and transport. For example, materials with controlled electronic properties can be used in solar cells, batteries, and other energy technologies. The insights gained from this research could contribute to the development of more efficient and effective energy materials.
This research was published in the journal Physical Review B, a leading journal in the field of condensed matter and materials physics.
This article is based on research available at arXiv.