http://www.sciencealert.com/physicists-have-found-a-metal-that-conducts-electricity-but-not-heat
"Researchers have identified a metal that conducts electricity without conducting heat - an incredibly useful property that defies our current understanding of how conductors work."
An Explanation from Reddit
Awesome! Finally something where my PhD in theoretical solid-state physics can contribute a bit of explanation :)
A lot of the "laws" we have for metals are based on "simple" metals, those where electron-electron interaction plays a very muted role in regards to material properties. In metals such as aluminum, you can sweep all the interaction effects under the rug by just giving the electron a different mass, and then treat it as if they were non-interacting. In that case, if a material is good at conduction electricity, it means each individual electron is free to move through the material as it pleases. But that automatically also makes it a good conductor for heat.
But with transition metals such as Vanadium, you can't really do that any more, because the 3d orbitals (which are the relevant orbitals there) are very close to the nucleus and thus putting more than one electron in that orbital incurs huge Coulomb energy. Thus the field of strongly-interacting systems is a very interesting and important one. Lots of things break down there. For example, Chemists will be familiar with Density Functional Theory to compute electron levels for materials. But that doesn't work for a lot of the transition metal oxides. It'd predict that Nickle Oxide would be a conductor when really it's an insulator, due to the strong on-site Coulomb repulsion between the electrons.
Here's an analogy for the principle at work: Imagine a narrow but straight staircase, where each step has just enough room for one person. There'll be a strong on-site repulsion: You don't want two people on the same step. Now, the only way you guys are able to move is by collectively moving the same way. Either ya'll moving up or ya'll moving down. That'd be electricity: Applying an external field compels you all to move in the same direction, and there's no problem here as long as everyone keeps moving. Heat, on the other hand, would involve everyone trying to move randomly. But that won't work because you'd just get everyone bumping into each other and effectively staying put.
I see the biggest application for this in thermoelectrics: Turning waste heat from, e.g., a car motor, into electricity. The effect exists, but useful commercial applications were hindered by the Wiedemann-Franz law: A temperature difference can generate an electric current, but that current would also carry the heat and thus ruin your temperature difference. With this newly discovered property of Vanadium Oxide, you could get the current while maintaining the heat difference.