Samarium hexaboride exists simultaneously as both a metal, and an insulator. As such, it can both allow the smooth flow of electrons, and stop their movement and free passage.
Although this material has been known for quite some time. It wasn't until Suchitra Sebastian and Beng Tan "failed" at an experiment for his doctoral thesis that they discovered its duality.
Contamination (a likely cause) has already been tested for, and in fact the experiments have already been replicated. So where does that leave us? How exactly is this possible?
You can read the full article at http://www.wired.com/2015/07/paradoxical-crystal-baffles-physicists/ or the actual paper at Science.
And if you have any theories, feel free to comment below.