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In disordered materials, such as organic semiconductors or inks made from two-dimensional materials, electrons don't move smoothly like water through a pipe. Instead, they hop from one spot to another, like a ball bouncing across a rough surface. This kind of motion is called hopping transport.

At different temperatures, electrons hop in different ways. At low temperatures, they prefer to jump farther but to sites with similar energy: this is known as variable-range hopping. At high temperatures, hops are short, only to the nearest sites. Scientists created a computer program that simulates these hops in a material. The program takes into account how the hopping sites are arranged and what their energies are. It turns out that these very properties determine which hopping regime dominates. The program was tested against real experiments: it accurately reproduces the transitions between regimes and the behavior in one, two, and three dimensions.

Now researchers have a tool to predict in advance how a new material will conduct electricity. This will speed up the development of flexible electronics, solar cells, and sensors.