# Superconductivity or insulation at 0 K ?

1. Dec 16, 2005

### omul_b

Hy! I made a bet with a friend. He said that at absolute zero, there is no movement so a conductor becomes an insulator (remember, it's about conductors, not semi-conductors). I say the exact opposite: because at temperatures near absolute zero a conductor becomes a super-conductor there is no logic that at 0 K things should be any different. So, which is it, is there no conductivity or super-conductivity. The really annoying part is that the net is very vague about this and they only discuss about temperatures NEAR absolute zero. That's why it's sooo hard. Please help. Thanks !

2. Dec 16, 2005

### ZapperZ

Staff Emeritus
You win the bet, but not for the reason you have described.

If you look at the conductivity of an ordinary metal, and you measure this conductivity as a function of temperature, as the temperature drops, the conductivity increases. [Conductivity is the reciprocal of resistivity.] Now unless your friend can explain why this is so and then suddenly there is a discontinuity where the conductivity goes immediately to zero right at T=0, then there's no reason to expect that the conductivity to continue to increase, maybe even reaching a very high value at T=0.

There is a good explanation for this. "Resistivity" is due to the collision of charge carriers with itself, with the vibrating lattice ions, and with impurities. In most cases, the collision with the vibrating lattice ions dominates. As temperature decreases, the lattice ions vibrates less, thus resistivity decreases and consequently conductivity increases. At T=0, in principle, the lattice ions have "extremely low vibrations" (notice I didn't say zero vibrations), and thus the conductivity is maximum here.

Is this a superconductor? NO! Not all metals can become a superconductor. Having zero resistivity, even in principle, is not the only criteria of a superconductor (even this is dubious because almost every metals have residual resistivity even as T approaches 0K).

Zz.

3. Dec 16, 2005

### abszero

To expand, in some materials where there are impurities you can have resistivity spike to very high values at zero temperatures due to something called the Kondo effect, in which the magnetic scattering cross section of impurity elements diverges. This causes the charge carriers to scatter randomly off impurities at all distances, and thus it breaks up any coherence in the motion of the charge carriers, thus no current.

4. Dec 17, 2005

### ZapperZ

Staff Emeritus
We need to be clear that they're talking about your ordinary, non-exotic metals. The Kondo effect, which really is a higher order scattering with magnetic impurities, would not be something that they would be considering here.

Zz.

5. Dec 18, 2005

### Pieter Kuiper

All metals in the normal state have residual resistivity at 0 K.

I would not say that omul_b won the bet.

6. Dec 18, 2005

### ZapperZ

Staff Emeritus
But having a residual resistivity at 0K does not mean the material is an insulator. An "insulating behavior" implies that a plot of resisitivity versus temperature has a negative slope. This is the typical behavior of semiconductors. A "metallic behavior" on the other hand has a positive slope, meaning the resistivity increases with increasing temperature. [See Valla et al. Nature v.417, p.627 (2002)] This behavior is described within the Fermi Liquid theory, the "bad metals" description, and even Varma's "Marginal Fermi Liquid".

In any case, even with a residual resistivity, the material certainly isn't an insulator.

Zz.

Last edited: Dec 18, 2005