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aaaa202
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Why can't electrons move inside the valence band? Is that the Pauli exclusion principle - and is it true that the electrons can't move even when the valence band is only partially filled?
aaaa202 said:Why can't electrons move inside the valence band? Is that the Pauli exclusion principle
- and is it true that the electrons can't move even when the valence band is only partially filled?
aaaa202 said:Okay I thought it might be the Pauli exlusion principle. So each band has only a finite number of energy and when all these are filled the electrons cannot move unless the next band is close.
But I must admit that there is one thing I really don't understand about all this. We are using the eigenstates to determine which states an electron can occupy. But this is quantum mechanics! Superposition of eigenstates are possible state to leading to almost infinite combinations of possible states. Why are these not relevant for solid state theory? I think I am misunderstanding something completely.
How does this symmetry arise? Why most the electrons move so as to cancel out any net current?DrDu said:Looking at it from another angle, electrons in the valence band can always move. However, electrons near the top of the valence band move in the opposite direction to electrons near the bottom of the valence band, so that in a full band no net current arises.
The problem is not that I don't know how to distinguish between them. The problem is the whole statistical approach where it only seems that the eigenstates are relevant for the statistics when in reality there exists an infinite amount of superpositions of eigenstates for the many particle Hamiltonian, which the many-particle system could be in. https://www.physicsforums.com/showthread.php?t=715106You have to distinguish between eigenstates of a one particle hamiltonian and eigenstates of a many particle hamiltonian. If you consider but a single electron, all these superpositions of Bloch states are relevant. However in solid state theory, we are interested in systems containing many electrons.
There we use the Bloch one electron states only to build up a convenient basis for the many particle hamiltonian, e.g. via antisymmetrized Slater determinants.
aaaa202 said:How does this symmetry arise? Why most the electrons move so as to cancel out any net current?
The valence band and conduction band are two bands of energy levels in a solid material. The valence band represents the highest energy level occupied by electrons in a material at absolute zero temperature. The conduction band, on the other hand, represents the lowest energy level that free electrons can occupy to move freely and conduct electricity.
The number of valence electrons in a material determines whether its valence band is full or empty. A full valence band means that all the available energy levels are occupied by electrons, and there is no room for them to move and conduct electricity. An empty valence band means that there are unoccupied energy levels, and electrons can move freely to conduct electricity.
The properties of a material, such as its electrical conductivity and ability to absorb or emit light, are determined by the energy levels in the valence and conduction bands. Materials with a small energy gap between the two bands are good conductors, while those with a large energy gap are insulators. Semiconductors have a moderate energy gap and can be manipulated to behave as either conductors or insulators.
At higher temperatures, some electrons in the valence band may gain enough energy to jump to the conduction band, creating free electrons that can conduct electricity. This is known as thermal excitation. The temperature also affects the energy gap between the two bands, with higher temperatures causing the gap to decrease and allowing for more conduction.
Yes, in certain materials, the valence band and conduction band can overlap, creating a continuous band of energy levels. This is seen in metals, which have a high number of free electrons that can easily move between the two bands. As a result, metals have high electrical conductivity and can absorb and emit light at various wavelengths.