Weyl semimetals are recently discovered materials where charge carriers behave as if they were massless particles moving at a slower speed of light. Therefore, the electric conduction in these materials reflects the physics of Einstein’s special theory of relativity. But special relativity also assumes an absence of gravity, which Einstein formulated as a geometry of spacetime. In this work, we propose a method on how to go beyond special relativity and simulate Einstein’s theory of general relativity. Our method provides a route to making the charge carriers move as if they were living in a curved space, providing a tabletop laboratory for simulating certain cosmological phenomena as well as the interplay between quantum physics and gravity.

By local manipulation of a Weyl semimetal, such as by strain or magnetization, it is possible to generate an artificial geometry and magnetic field experienced by the charge carriers. We dub these systems (where the low-energy dynamics is that of relativistic particles in curved space) Weyl metamaterials. We derive a mathematical connection between the local manipulation and the resulting geometry and show how the curved geometry and quantum effects lead to unique particle dynamics. As an example of the application potential, we introduce a structure called a Weyl electron lens, where the trajectories of charge carriers are focused much like beams of light in an optical lens.

Weyl metamaterials enable new types of electronic devices through geometry engineering and new possibilities in studying curved-space quantum physics in laboratories. The physics of Weyl metamaterials also has diverse connections to particle physics and cosmology.