What Specifies Energy Bands in Solid?

In summary, the band index (n) and electron wave vector (k) are used to specify the energy band in Ashcroft Mermin. While k determines the boundary conditions for an elementary cell, n labels an infinite family of solutions to the Schroedinger equation within that cell. This means that for a given k, there are multiple solutions for n, making the second statement about n being the band index the correct one.
  • #1
mkbh_10
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n is the band index and k is the electron wave vector. Now is energy band specified when for each n , k runs through all the values available that specify periodic boundary conditions ?

But in Ashcroft Mermin , it is also given that for a given k , there exists an infinite family of solutions labelled by n which is the band index.

I am confused here about what specifies the band.
 
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  • #2
Look at it like this: k determines the boundary conditions for an elementary cell, namely the value of the logarithmic derivative of the wavefunktion ##\psi'/\psi (a)=\psi'/\psi(0) \exp(ika)##.
Now the Schroedinger equation in a single cell, with the boundary condition specified by k, has an infinity of solutions labelled by n.
 
  • #3
So the second one is correct ans.
 

1. What are energy bands in solid materials?

Energy bands in solid materials refer to the range of energies that electrons can occupy within a solid material. These bands are formed by the overlapping of individual energy levels of atoms in the material.

2. What determines the width of energy bands in solids?

The width of energy bands in solids is determined by the spacing between energy levels of atoms in the material. This spacing is affected by the type and arrangement of atoms, as well as external factors such as temperature and pressure.

3. How do energy bands affect the properties of solid materials?

The properties of solid materials are greatly influenced by the energy bands present. For example, materials with wider energy bands tend to be better electrical conductors, while those with narrower bands are often insulators. Energy bands also play a role in determining a material's optical and magnetic properties.

4. Can energy bands in solids be changed?

Yes, energy bands in solids can be changed through various means such as doping, applying external electric or magnetic fields, or altering the temperature or pressure. These changes can result in a shift in the position or width of energy bands, thus affecting the properties of the material.

5. How are energy bands related to the band gap in a material?

The band gap in a material refers to the energy range between the valence band (highest occupied energy band) and the conduction band (lowest unoccupied energy band). Energy bands within this range are filled with electrons, while those above or below are empty. The band gap is determined by the width and position of energy bands in the material.

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