Scientists illustrated the processes in a topological insulator through the medium of dance.

Science can be challenging to explain to a broad audience. In fact, any field can be difficult to grasp even for scientists working in different areas. Explaining a theoretical concept to high school students in a way that captivates their interest without overwhelming them is a task that requires creativity.

Researchers from the University of California, San Diego (USA) successfully accomplished this. They organized a dance with high school students to visually demonstrate the nature of the properties and internal organization of topological insulators.

“The concept of a topological insulator is quite simple, but the mathematics behind the processes is much more complex. We wanted to show that intricate ideas in theoretical and experimental physics and chemistry are not as impossible to understand as they may seem,” said Professor Joel Yuen-Zhou (Joel Yuen-Zhou).

Topological insulators are a relatively new type of quantum material. They behave like an insulator within the bulk of the material but conduct electricity along the surface. This is in stark contrast to electrical wires, which are intentionally coated with an insulating layer. We frequently encounter organizational structures where the properties of the outer layer differ significantly from those of the bulk of the object. Examples include human skin and tree bark, whose outer layers consist of dead cells, or a pastry, where the outer layer is the dough.

Topological insulators can retain their properties despite certain defects and deformations. This makes them promising for quantum computing, laser development, and creating more efficient electronics.

To visually demonstrate the properties of these quantum materials, researchers recreated a topological insulator on asphalt, marking it with red and blue tape. Matthew Du (Matthew Du) developed a series of defining movements for each dancer based on the rules.

These rules were grounded in the concept of the Hamiltonian in quantum mechanics. Electrons follow the rules embedded in the Hamiltonian functions, which describe the total energy of a quantum system, including kinetic and potential energy. The Hamiltonian also defines the interactions of an electron with the potential energy of the material.

To choreograph the dance, the scientists developed an algorithm to approximate the distribution of the wave function and matched it first with real numbers and then with human movements.

Each dancer represents an electron and behaves accordingly. Dancers have a pair of flags and a number corresponding to a specific movement:

1 = waving flags with arms raised;

 0 = remaining still;

-1 = waving flags with arms lowered;

The movements of each dancer depend on what the neighboring dancer was doing and the color of the tape on the floor they were standing on. The dancer mirrored the actions of the neighbor on the blue tape but performed the opposite if the neighbor was on the red tape. Mistakes or the departure of one dancer from the dance floor do not disrupt the integrity of the dance, demonstrating the stability of topological insulators.

Matthew Du, born into a family of educators committed to the popularization of science, believes that this project has given him insight into how important it is to distill science down to its fundamentals.

“We wanted to remove the ‘mystique’ from the concept of a topological insulator in an unconventional way,” he noted.

The dance and accompanying computations have been published in the journal Science Advances.