Abstract
With the discovery of the quantum Hall effect and topological insulators,
there has been an outpouring of ideas to harness topologically knotted
band-structures in the design of state-of-the art, disorder-insensitive
materials. From studies of exotic quantum many- body phenomena to applications
in spintronics and quantum information processing, topological materials are
poised to revolutionize the condensed matter frontier. Here we demonstrate, for
the first time, a circuit that behaves as a time-reversal invariant topological
insulator for RF photons. In this meta-material, composed of capacitively
coupled high-Q inductors, we observe a gapped density of states consistent with
a modified Hofstadter spectrum at a flux per plaquette of \phi=\pi/2.
In-situ probes further reveal time-resolved, spin-dependent edge-transport. We
leverage the unique flexibility of our materials to investigate, for the first
time, features of topological insulators on manifolds such as the Möbius
strip. This new approach elucidates the fundamental ingredients essential to
topologically active materials, whilst providing a powerful laboratory to study
topological physics and a promising route to topological quantum science.
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