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A thin film of nickel oxide, tens of nanometers thick, is like a sheet of paper folded hundreds of times thinner. At room temperature, it conducts electricity, but cool it slightly and it becomes an insulator. This metal-insulator transition has been known for a long time, but how heat behaves during it remained a mystery.

Conventional methods couldn't measure the thermal conductivity of such a thin film because the substrate contributed too much. The authors used frequency-domain thermoreflectance (FDTR): a laser heats the surface, and the reflected light reveals how quickly heat dissipates into the material. This allowed them to see that at the metal-insulator transition, thermal conductivity across the film changes sharply and with almost no hysteresis.

The difference in behavior along and across is linked to nanodomains — regions where metallic and insulating phases coexist. When the film thickness approaches the domain size, percolation along the layer is hindered, but across it is not. It's like a crowd trying to pass through a narrow corridor: movement along the corridor gets stuck, but across it flows freely.