states and energy of paired electrons in BCS

zhanhai

Hello, everyone:

My question is about the states of paired electrons in BCS Theory.

According to Tinkham's book (pages 70-71), electron states in the superconducting gap (SG) in normal state are push up to above the upper edge of the SG in superconducting state; on the other hand, it seems that electrons on these pushed up states actually have energy lower than the lower edge of SG. Is this understanding correct?

How can an electron on a state above SG be said to have an energy lower than SG? An electron on an energy state should have the energy of that state?

Thank.

ZapperZ

Er.. you need to understand the difference between the density of states, and the actual states that an electron occupy.

When the gap opens, the states ABOVE the superconducting gap are EMPTY states, at least in the ground state! They are unoccupied. The occupied states are the ones below the lower edge of the superconducting gap.

Zz.

zhanhai

The gap opens as the states originally in the gap are "pushed up" to above the gap, but some of these "pushed up" states are originally occupied in normal state(?); then, where the electrons originally on these "pushed up" states go?

The states below the lower edge of the superconducting gap are originally occupied in normal state.

Does BCS say the electrons originally on these "pushed up" states condensate to some of the states below the lower edge of the superconducting gap as bosons? In that sense, what's the difference between such a superconducting gap and a (forbidden) gap in a semiconductor or an insulator?

ZapperZ

Er.. no. The states are piled up on BOTH sides, i.e. the lower energy edge and the upper energy edge of the gap. If you integrate over all states, the TOTAL number of states are essentially conserved. Look at Fig. 7 at this link:

http://web.mit.edu/physics/hudson/Re...Background.htm

Notice that both upper edge and lower edge of the gap have high density of states. But at low temperatures, only the states BELOW the gap are occupied!

This is not true for a semiconductor because there are no piled-up states. There were no states originally in the gap that has to be "pushed out".

Zz.