There isn't a single material that is *both* a perfect conductor and a perfect insulator at the same time. This is because the fundamental properties that make a material a good conductor (free electrons) are the opposite of the properties that make a material a good insulator (bound electrons).

However, there are materials that can act as both conductors and insulators depending on the conditions. Here are some examples:

* Semiconductors: These materials have a conductivity between that of a conductor and an insulator. Their conductivity can be changed by factors like temperature, impurities, and electric fields. Silicon and germanium are common examples.

* Conducting polymers: These are polymers with conjugated double bonds that allow for electrical conductivity. They can act as insulators in their pure state, but become conductive when doped with certain elements.

* Metal-insulator transitions: Some materials can switch between a conducting and insulating state depending on factors like temperature, pressure, or applied voltage. Vanadium dioxide (VO2) is a well-known example.

Ultimately, the concept of a "perfect" conductor or insulator is an idealization. All materials have some degree of conductivity, even those considered insulators. Similarly, all materials will exhibit some resistance to current flow, even those considered conductors.