Fermi Surface Instability in Solid States: Explained

[mavipranav]

Hi

Can somebody explain the meaning of the following sentence which is from Wikipedia: "Solids with a large density of states at the Fermi level become unstable at low temperatures and tend to form ground states where the condensation energy comes from opening a gap at the Fermi surface e.g. superconductors, Jahn-Teller distortion"? I know what a Fermi surface is, but the sentence above is not clear.

Thanks,
Mavi

 

[stephenhky]

I don't know about superconductivity and Jahn-Teller distortion, but since the Wikipedia entry talks about ferromagnetism and I feel like I want to use it as an example.

At higher temperatures, there is no ferromagnetism and the number of up and down spins in the metal are the same, including the levels around the Fermi surface. At lower temperatures, the spin-up particles outnumber the spin-down particles, causing the Fermi surfaces of particles with different spins to depart from each other. It is what it means by the Wikipedia entry that at low temperatures, the Fermi-level becomes unstable and a ground state that opens a gap at the Fermi-surface is formed.

It is called condensation probably in the context of superconductivity, where the electrons form Cooper pairs which are bosonic, and they formed a condensate at low temperatures.

 

[mavipranav]

causing the Fermi surfaces of particles with different spins to depart from each other.

What do you mean by Fermi surfaces of particles with different spins? Fermi surface applies to the entire solid and not for individual particles.

 

[rizzodex]

What do you mean by Fermi surfaces of particles with different spins? Fermi surface applies to the entire solid and not for individual particles.

It's called spin polarization. A phenomenon relevant to ferromagnetism and spintronics.

 

[stephenhky]

Yes I referred to Fermi surface for different particles.

I checked some papers that the Fermi surface does distort in ferromagnetism, but I think someone who is more expert in this can explain how this distortion comes out.

 

[mavipranav]

rizzodex/stephenhky

Can you explain the mechanism as to how the Fermi surface of different spin sites depart from each other, thus opening up a gap?

 

[rizzodex]

rizzodex/stephenhky

Can you explain the mechanism as to how the Fermi surface of different spin sites depart from each other, thus opening up a gap?

In paramagnetic materials, the density of states for spin up and spin down electrons are the same. So there is no spin polarization.
In ferromagnetic materials, their DOS are different. So, they are spin polarized. One is majority and the other is minority carrier.
In half-metallic ferromagnets, the DOS of the minority carrier vanishes which opens up a gap at the Fermi level for minority band, where as the majority band is metallic. That's why it's called semi-metallic.

 

[mavipranav]

Right that makes sense; I guess its something similar to a p-n junction where the Fermi levels between the p and n sides develop a gap between each other.

 

[stephenhky]

i agree with you rizzodex
it is this difference in DOS so that the numbers of spins in different spins are different, so that we have ferromagnets

 

[gesheften]

The large density of states (DOS) refers to the DOS of a non-interacting many-body system. At low temperatures this system will arrange in a Fermi sea, where all states in momentum space are occupied up to some Fermi momentum. Now when adding interactions, one finds that the interaction energy is not necessarily minimized by the Fermi sea configuration (actually usually not...), and the kinetic and interaction energy compete. When the DOS is large it means that changes in the particle numbers, i.e. changes in the configurations in momentum space entail a minor change in the kinetic energy and therefore the system can satisfy the interaction term without "paying" a lot of kinetic energy.

These states where the configuration that minimizes the interaction becomes preferable over the standard Fermi sea configuration are called strongly correlated phases, examples are superconductivity, ferromagnetic, fractional quantum hall effect and Jahn-Teller effect in solids...

 

[asheg]

The large density of states (DOS) refers to the DOS of a non-interacting many-body system. At low temperatures this system will arrange in a Fermi sea, where all states in momentum space are occupied up to some Fermi momentum. Now when adding interactions, one finds that the interaction energy is not necessarily minimized by the Fermi sea configuration (actually usually not...), and the kinetic and interaction energy compete. When the DOS is large it means that changes in the particle numbers, i.e. changes in the configurations in momentum space entail a minor change in the kinetic energy and therefore the system can satisfy the interaction term without "paying" a lot of kinetic energy.

These states where the configuration that minimizes the interaction becomes preferable over the standard Fermi sea configuration are called strongly correlated phases, examples are superconductivity, ferromagnetic, fractional quantum hall effect and Jahn-Teller effect in solids...

Beautiful description.
I want to add that in ferromagnetism and superconductivity the ground state of energy differs from fermi sea. i.e. in superconductors electrons near fermi surface go beyond fermi surface and each 2 of them make a pair. despite this increases their kinetic energy but the total energy decreases because of attractive pair interaction. this phenomena occurs just near fermi surface and when density of states be high there, the opportunity for such phase transition increases

 

[gesheften]

moreover, these states do not have a well defined particle number, they are a coherent state, i.e. an eigen state of the destruction operator.