Circuit implementation of a four-dimensional topological insulator.

Area of Science:

• Condensed Matter Physics
• Quantum Materials
• Topological Matter

Background:

• Topological insulators are materials with unique electronic properties.
• Theoretical classifications predict high-dimensional topological phases beyond three spatial dimensions.
• Real materials are typically limited to three or fewer spatial dimensions, hindering experimental exploration of these higher-dimensional phases.

Purpose of the Study:

• To experimentally realize and investigate a four-dimensional (4D) topological lattice.
• To explore topological phenomena in dimensions higher than typically found in solid-state materials.
• To demonstrate the potential of electric circuits as a platform for studying high-dimensional topological physics.

Main Methods:

• Implementation of a 4D topological lattice using electric circuit connections.
• Experimental observation of topological surface states on the 3D surface of the 4D lattice.
• Characterization of topological properties using Chern numbers (second Chern number nonzero, first Chern numbers vanishing).

Main Results:

• Successfully constructed and experimentally verified a 4D topological lattice using electric circuits.
• Observed distinct topological surface states with characteristics of a 4D topological insulator.
• Confirmed the lattice belongs to symmetry class AI (time-reversal-invariant, spinless, no special spatial symmetry).

Conclusions:

• The study demonstrates the feasibility of using electric circuits to create and study high-dimensional topological phases.
• This work provides experimental evidence for topological insulators in 4D for symmetry class AI, where such phases are non-trivial.
• The electric circuit approach opens new avenues for exploring complex topological phenomena in higher dimensions.