Tuesday 08 April 2025
The quest for new topological materials has led researchers to explore unconventional geometries, and a recent study has made significant progress in this area by creating a type of material that exists only in hyperbolic space.
Topological materials are known for their unique properties, such as being resistant to defects or able to conduct electricity without resistance. However, these properties are typically found in materials with specific symmetries, like crystals with three-dimensional periodic structures. The new study, published in a recent issue of the journal Science, demonstrates that it’s possible to create topological materials with different types of symmetry.
The researchers used a type of lattice called a hyperbolic lattice, which is constructed by tessellating the Poincaré disk, a mathematical object that represents the surface of a sphere. This lattice has a unique property: its geometry is curved in such a way that it’s impossible to draw a straight line on its surface.
The team created a type-II hyperbolic Chern insulator (HCI) by discretizing the Poincaré ring, which is a two-dimensional object obtained by wrapping and gluing together the edges of the Poincaré disk. This material has both inner and outer chiral edge states (CESs), which are topological properties that can be used to create novel devices.
The researchers then demonstrated two mechanisms for dynamically transferring CESs between the inner and outer edges of the type-II HCI: anti-parity-time phase transition (APT) and Landau-Zener single-band pumping. The APT mechanism involves modulating the material’s parameters in a way that creates an effective two-level anti-parity-time systematic, which allows the CESs to be transferred by crossing an exceptional point.
The Landau-Zener mechanism is based on adiabatic evolution along a single band, where the material’s parameters are slowly changed to pump the CESs from one edge to another. This approach avoids nonadiabatic transitions and ensures that the CESs remain localized at the edges.
The study’s findings have significant implications for the development of topological materials and devices. By exploring unconventional geometries like hyperbolic space, researchers can create new types of materials with unique properties that could be used in a wide range of applications, from electronics to optics.
The ability to dynamically transfer CESs between different edges of the type-II HCI also opens up new possibilities for designing novel devices, such as topological insulators and superconductors.
Cite this article: “Unlocking Topological Secrets in Hyperbolic Lattices: A New Frontier in Quantum Physics”, The Science Archive, 2025.
Topological Materials, Hyperbolic Space, Lattice Geometry, Chern Insulator, Chiral Edge States, Anti-Parity-Time Phase Transition, Landau-Zener Pumping, Adiabatic Evolution, Exceptional Points, Topological Devices.
