How Can I Make the First Term Vanish in Plasmon Calculations?

[hoalacanhdk]

I'm learning Plasmons in Hartmut Haug, Stephan W. Koch - Quantum theory of the optical and electronic properties of semiconductors, but I don't know how to make the first term vanished (the highlighted sentence). Can you give me a guide?

 

[BigJDubs]

The first term in the expression for the plasmon energy is often referred to as the 'static' contribution because it does not depend on the dynamical properties of the system. To make this term vanish, you need to consider specific conditions that are appropriate for the system you are studying. For example, if you are studying a system with an isotropic dielectric constant (i.e. one that does not depend on the direction of the electric field), then you can set the wavevector of the plasmon to zero in order to make the first term vanish. If your system has an anisotropic dielectric constant (i.e. one that depends on the direction of the electric field), then you may need to look at other parameters such as the dielectric tensor or the Fermi surface in order to adjust the wavevector so that the first term vanishes.

 

[BigJDubs]

The first term in the equation you are referring to describes the effect of the Coulomb interaction on the electrons in a semiconductor material. This effect is usually referred to as "screening" and is due to the fact that when electrons interact with each other, they are repelled by the electric field generated by the other electrons. This repulsion leads to a decrease in the magnitude of the electric field, which in turn reduces the energy associated with the Coulomb interaction.In order to make this first term vanish, you must consider the effect of the screening on the Coulomb interaction. This can be done by introducing a dielectric function which describes the reduction in electric field strength due to the screening. By solving the equations for the dielectric function together with the equations for the Coulomb interaction, it is possible to obtain an expression for the screened Coulomb interaction which does not contain the first term. Once this expression has been obtained, it can then be used to calculate the plasmons in the material.