Understanding the Density of States Diagram in Insulators and Superconductors

[nicola_gao]

The Density of States diagram gives gaps sometime. As I know, if the band is filled up to the gap, then the material is an insulator.
However, it seems to me, that superconductors also open a gap in their density of states diagram, as BCS theory says.

If my understanding is correct, I am a little confused here, so how can you tell the difference between an insulator and an superconductor?

Thanks a lot for whom could give me some help

 

[ZapperZ]

The Density of States diagram gives gaps sometime. As I know, if the band is filled up to the gap, then the material is an insulator.
However, it seems to me, that superconductors also open a gap in their density of states diagram, as BCS theory says.

If my understanding is correct, I am a little confused here, so how can you tell the difference between an insulator and an superconductor?

Thanks a lot for whom could give me some help

One type of gap is not the same as other gap.

The "gap" in insulators and semiconductors are BAND GAPS. The gap in a superconductor is not a band gap - it is the gap in the single particle spectrum. This is the energy that you need to break up a Cooper pair. This is not a band gap.

Furthermore, the gap size in an insulator/semiconductor does not change in size with temperature other than thermal broadening. The gap size in a superconductor does change with temperature, getting smaller with increasing temperature. In addition, the conductivity in a superconductor is due to the supercurrent, i.e. a 2-particle state, rather than a single-particle state.

So not all gaps are the same.

Zz.

 

[charng]

I can provide some clarification on the density of states diagram and its implications for insulators and superconductors.

Firstly, the density of states diagram is a plot that shows the number of energy states available to electrons in a material at different energy levels. In insulators and superconductors, this diagram shows a gap in energy levels, indicating that there are no available states for electrons to occupy within that energy range.

In insulators, this gap is typically a large one, meaning that there are a limited number of energy states available for electrons to move through and conduct electricity. As you correctly stated, if the band is filled up to the gap, the material is an insulator.

In superconductors, the gap in the density of states diagram is much smaller. This is due to the phenomenon of superconductivity, where electrons can pair up and move through the material without resistance. This pairing process creates a gap in the density of states diagram, but it is a much smaller one compared to insulators.

So, to answer your question, the main difference between an insulator and a superconductor is the size of the gap in the density of states diagram. In insulators, the gap is large and the material does not conduct electricity well, while in superconductors, the gap is smaller and the material can conduct electricity without resistance.

I hope this helps clarify any confusion you may have had about the density of states diagram and its implications for insulators and superconductors. Keep exploring and learning about these fascinating materials!