The team constructed hyperbolic {8,8} lattices with constant negative curvature and introduced electromagnetic fields to create the first topological pumping framework in non-Euclidean space. Theoretical calculations confirmed the ground-state band carries topological invariants equivalent to 8D quantum Hall physics. When adiabatically modulated, wavepackets showed quantized transport velocities matching predictions for eight-dimensional systems.
"This breaks dimensional constraints," said co-senior author Xiangdong Zhang, professor at Beijing Institute of Technology. "A physical 2D system can now emulate quantum phenomena that mathematically require eight dimensions in flat space."
Crucially, transport behavior depends on periodic boundary conditions (PBCs) - a unique feature of hyperbolic geometry. Under one PBC configuration, wavepackets quantum-jump between unit cells. Under alternative PBCs, they exhibit periodic "topological oscillations" by returning to their origin after each pump cycle.
"This boundary-sensitive control is unprecedented," said co-senior author Weixuan Zhang. "The non-Abelian nature of hyperbolic translation groups creates transport rules that simply don't exist in Euclidean materials."
To verify these predictions, researchers built a 512-node electronic circuit network that precisely emulates the hyperbolic lattice. Voltage measurements confirmed both the 6D quantum Hall trajectories and boundary-dependent pumping/oscillation effects - marking the first experimental observation of hyperbolic topological pumping.
The discovery opens pathways for high-dimensional quantum simulation platforms and fault-tolerant topological devices.
This work received support from the National Key R&D Program of China and the National Natural Science Foundation of China.
Science Bulletin
Experimental study