Something that's taken my attention recently has been the presence of the energy bands particularly of the form of the dispersion relation, i.e. expression of energy wrt wavevector.
Transport properties, such as the conductivity tensor, current density and the Onsager relation, have expressions in terms of the energy.
Something I fund a little unsettling is why the energy holds such significance? As in, what is the physical significance of the energy?
I can see that the wavevector could be taken as an independent variable as the wavevector is related to the momentum of electrons, hence could be controlled by input energy or voltage.
I suppose this energy is the response to electron behaviour?
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Well, when you consider that energy is pretty much what the universe is made of, it makes sense to consider thee universe in terms of it. With energy playing such a fundamental role (conservation of energy etc...) the idea of relating things to energy makes is easy to relate different aspects of theories. Thoughts?
ReplyDeleteThere should not be too much of a surprise here. Even in the Sommerfeld model energy was written in terms of the wave vector albeit its simple form and the velocity of the electrons can be found from the dispersion relationship. There are many reasons why many quantities written in terms of energy. Only electrons that contribute to the dynamics are those near the Fermi energy surface. Surfaces of constant energy are often important. It is better to write things in terms of energy than let say momentum cause crystal momentum is no longer the physical momentum but energy is still the same quantity. The only difference in the Bloch model is that it that the dispersion relation is more complicated cause it already includes the periodic potential/interaction of ions with electrons.
ReplyDeleteI guess it makes sense, the transport properties have to be somehow related how much energy the electrons can move around with and distribute the energy i.e. realise thermal equilibrium. I think it's pretty cool how the Lorentz ratio and Onsager conditions explain why good conductors are often bad insulators just because the electrons are free to move around.
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