Space and space-time topologies in a type-II hyperbolic lattice

Area of Science:

• Condensed Matter Physics
• Non-Euclidean Geometry
• Topological Materials

Background:

• Topological phases of matter are typically studied in Euclidean spaces.
• Previous research on hyperbolic lattices focused on static states at single edges.
• Dynamic transfer and spatiotemporal phenomena in hyperbolic systems are underexplored.

Purpose of the Study:

• To establish space and space-time topologies in a type-II hyperbolic lattice.
• To experimentally realize and manipulate hyperbolic topological states.
• To propose a novel hyperbolic space-time crystal.

Main Methods:

• Experimental realization using electric circuits.
• Observation of chiral edge states (CESs) in a type-II hyperbolic Chern insulator.
• Dynamic modulation of coupled counterpropagating CESs.
• Proposal of a (2+1)-dimensional hyperbolic space-time crystal.

Main Results:

• Observed degenerate chiral edge states of opposite chirality at inner and outer edges.
• Demonstrated arbitrary-proportion dynamic transfer of CESs.
• Proposed a hyperbolic space-time crystal with intertwined spatial and temporal topological numbers.
• Discovered a unique space-time topological string state.

Conclusions:

• This work expands hyperbolic topological physics into spatiotemporal dynamics.
• The findings pave the way for dynamic manipulation of hyperbolic topological states.
• The proposed space-time crystal offers a new platform for exploring complex topological phenomena.