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Anomalous topological pumping in hyperbolic lattices.

Hao Yuan1, Weixuan Zhang1, Na Sun1

  • 1Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education, Beijing Institute of Technology, Beijing 100081, China; Beijing Key Laboratory of Nanophotonics & Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing 100081, China.

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We discovered novel topological pumping phenomena in hyperbolic lattices, a non-Euclidean geometry. This research reveals 2D hyperbolic systems can mimic 8D quantum Hall physics, with dynamics controlled by boundary conditions.

Keywords:
Hyperbolic latticesQuantum Hall physicsTime-varying circuit networksTopological pumping

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Area of Science:

  • Condensed Matter Physics
  • Topology
  • Non-Euclidean Geometry

Background:

  • Hyperbolic lattices, non-Euclidean tilings with negative curvature, offer unique platforms for topological phenomena.
  • Current research primarily explores static hyperbolic systems, leaving the dynamics of time-modulated topology in curved spaces largely uninvestigated.

Purpose of the Study:

  • To investigate topological pumping in hyperbolic lattices.
  • To explore novel topological phenomena arising from the interplay of curvature and time modulation.
  • To understand the influence of boundary conditions on topological dynamics in hyperbolic systems.

Main Methods:

  • Theoretical study of topological pumping in hyperbolic lattices.
  • Analysis of pumping trajectories using Chern numbers and periodic boundary condition (PBC) configurations.
  • Experimental validation using time-modulated hyperbolic circuits.

Main Results:

  • Discovered anomalous topological pumping phenomena absent in Euclidean analogs.
  • Demonstrated that 2D hyperbolic pumping can emulate 8D quantum Hall physics, surpassing dimensional limitations.
  • Identified that specific PBCs induce periodic topological oscillations and recurrent cycles of quantized transport collapse.
  • Experimentally validated high-dimensional quantum Hall signatures and PBC-dependent topological dynamics in hyperbolic circuits.

Conclusions:

  • Pioneered the study of topological pumping in hyperbolic lattices.
  • Showcased the significant impact of non-Euclidean geometry on topological phenomena.
  • Opened new avenues for exploring curvature-driven topological physics and its potential applications.