That’s precisely what researchers at the University of California, San Diego, did when they orchestrated a dance with students from Orange Glen High School in Escondido to explain topological insulators.

The experiment, led by former graduate student Matthew Du and UC San Diego associate professor of chemistry and biochemistry Joel Yuen-Zhou, was published in Scientific advances.

“I think the concept is simple,” Yuen-Zhou said. “But mathematics is much more difficult. We wanted to show that these complex ideas in theoretical and experimental physics and chemistry are actually not as impossible to understand as you might first think.”

Topological insulators are a relatively new type of quantum material that has insulating properties on the inside, but conducting properties on the outside. To use a Southern California staple, if the topological insulator were a burrito, the filling would be insulating and the tortilla would be conductive.

Since topological insulators are able to resist certain disorders and deformations, they can be synthesized and used in conditions where imperfections may appear. For this reason, they show promise in the fields of quantum computing and lasers, as well as in creating more efficient electronics.

To bring these quantum materials to life, the researchers created a dancefloor (topological insulator) by creating a grid with pieces of blue and red ribbon. Then, to choreograph the dance, Du created a series of rules that governed how the dancers moved.

These rules are based on what is called a Hamiltonian in quantum mechanics. Electrons obey rules given by a Hamiltonian, which represents the total energy of a quantum system, including kinetic and potential energy. The Hamiltonian encodes the interactions of the electron in the potential energy of the material.

Each dancer (electron) had a pair of flags and received a number corresponding to a movement:

• 1 = waving flags with arms pointing upwards
• 0 = stay still
• -1 = waving flags with arms pointing down

Subsequent moves were based on what a neighboring dancer was doing and the color of the tape on the floor. A dancer would imitate a neighbor with blue ribbon, but do the opposite of a neighbor with red ribbon. Individual errors or dancers leaving the floor did not disrupt the overall dance, demonstrating the robustness of topological insulators.

In addition to topology, Yuen-Zhou’s lab also studies chemical processes and photonics, and it was when thinking about light waves that they realized that the movement of a group of people also resembles a wave. This gave Yuen-Zhou the idea of ​​using dance to explain a complex topic like topological insulators. Implementing this idea seemed like a fun challenge for Du, who is currently a postdoctoral researcher at the University of Chicago and takes salsa lessons in his free time.

Du, who comes from a family of educators and is committed to science outreach, says the project allowed him to appreciate his ability to distill science into its simplest elements.

“We wanted to demystify these concepts in an unconventional and fun way,” he said. “I hope the students were able to understand that science can be made understandable and enjoyable by relating it to everyday life.”

Full list of authors: Matthew Du, Juan B. Pérez-Sánchez, Jorge A. Campos-Gonzalez-Angulo, Arghadip Koner, Federico Mellini, Sindhana Pannir-Sivajothi, Yong Rui Poh, Kai Schwennicke, Kunyang Sun, Stephan van den Wildenberg, Alec Barron and Joel Yuen-Zhou (all UC San Diego); and Dylan Karzen (Orange Glen High School).

This research was supported by a CAREER grant from the National Science Foundation (CHE 1654732).