It seems inevitable that the manipulation of light and sound with metamaterials1,2,3 — in which the 'atoms' are themselves artificial composites of other materials — should lead sooner or later to notions of manipulating heat. These are of course not equivalent — the heat equation is not the wave equation — but there are evident analogies. In particular, the key to controlling the flow of energy in each case is anisotropy. If transmission differs in different directions, then a prescribed path for the flow can be engineered with a suitable arrangement of materials. It is this, for example, that has enabled optical invisibility shields to be manufactured from simple, suitably shaped birefringent crystals4.

Credit: PHILIP BALL

The possibility of using a gradient in thermal properties to produce counterintuitive heat flows, including a flow from cold to hot (that is, apparent negative thermal conductivity) was first adduced by Fan and co-workers5. Now such notions have been experimentally realized by Narayana and Sato, who have made metamaterial composites that can guide heat flux along all manner of non-intuitive paths, including a reversal of the heat current6.

The basic design element used by Narayana and Sato is a tube of metamaterial embedded in a slab of host material through which heat passes from a hot to a cold side. The tube is designed to generate a particular heat profile in the interior. The metamaterial is conceptually simple: a multilayer of two alternating materials with different (isotropic) thermal conductivities. The thermal properties of the composite are different parallel and perpendicular to the layers.

First, then, a thermal shield. Of course, crude thermal insulation — lagging a pipe, say — is already a kind of shield. But not only does this provide, at best, only partial insulation from the thermal gradient outside, it tends also to significantly perturb the external temperature profile. In contrast, the thermal shield described by Narayana and Sato actively equalizes the internal temperature by rerouting heat flow, while leaving the external profile untouched. It's the same distinction as between an opaque box and a true invisibility cloak.

The shield is a series of concentric cylinders of latex rubber and a silicone elastomer with ceramic particles dispersed in it. These materials are chosen for thermal conductivities that minimize the contrast with that of the host material, a block of agar gel. Meanwhile, layers arranged radially rather than concentrically in the tube wall act as a 'thermal concentrator' that creates a central region of enhanced, but uniform, energy density.

Finally, and most dramatically, when the layers are arranged in spirals, they twist the heat flux into a 'yin–yang' form so as to invert the thermal gradient in the inner region.

Reversing the flow of heat sounds like reversing the second law of thermodynamics — a manifestation of Maxwell's demon. But of course it is not, any more than a negative refractive index violates the laws of optics. Rather, this is another demonstration that creative arrangements of materials can seem to transcend their own fundamental limitations: a reminder that the laws of physics mustn't be confused with their apparent consequences.