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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.