Plane waves and sites distance in a lattice

In summary, the conversation discusses the effects of a lattice defect on a plane wave. It is determined that the defect will cause a phase shift and partial reflection of incident waves. The individual is seeking to justify the introduction of a global phase factor in the S-matrix and suggests that the lattice defect may help, but it is determined that this is not the case. They ask for suggestions on how to introduce a global phase in the scattering matrix.
  • #1
AdeBlackRune
9
0
Hi, i would ask you an opinion about a (maybe stupid) doubt.
Let us think of a 1D lattice whose sites distant from each other "a"; a plane wave
in the lattice is given by [itex]e^{ikja}[/itex] where k is the momentum and j an
integer label for each site. Now, we modify the lattice in this way: between sites j
and j+1 we put a distance that is a+c (instead of a). Then, what is the effect of this
alteration on the plane wave? It is right to say that the only effect is a shift in the
phase of the wave before and after the sites j,j+1?
 

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  • #2
no one has a little suggestion ç_ç?
 
  • #3
You've introduced a lattice defect. As you say, there will be a phase shift added to waves on the right.

Now consider a wave incident from the left. When it gets to the defect, it will have a problem. The only way to satisfy the matching conditions (both ψ and ψ' continuous) is to add another wave traveling to the left. Thus the defect will cause incident waves to be partially transmitted and partially reflected.
 
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  • #4
Thanks! So such a defect introduce a non zero reflection amplitude and unlukily it is not the answer i hoped to hear :(
The real problem I'm trying to resolve is to physically justify the introduction of a global phase factor in the S-matrix. I hoped that such a defect could help me but, as you say, I'm wrong. Do you know any way to introduce a global phase in a scattering matrix?
 

What are plane waves in a lattice?

Plane waves in a lattice refer to the propagation of a wave through a regular arrangement of points in space, such as atoms in a crystal lattice. These waves have a constant phase and amplitude and can be described using mathematical equations.

How is the distance between sites in a lattice determined?

The distance between sites in a lattice is determined by the lattice constant, also known as the lattice parameter. This is the distance between two adjacent points in the lattice and can be measured using techniques such as X-ray diffraction.

What is the significance of plane waves and lattice distance in materials science?

Plane waves and lattice distance play a crucial role in understanding the properties of materials. The interaction between waves and the lattice structure can affect the mechanical, electrical, and thermal properties of a material, making it an essential consideration in materials science.

How do plane waves and lattice distance affect the behavior of electrons?

Plane waves and lattice distance can affect the behavior of electrons in a material, specifically in the electronic band structure. The periodicity of the lattice can cause constructive or destructive interference of the electron waves, leading to energy bands and band gaps.

Can the distance between sites in a lattice be altered?

Yes, the distance between sites in a lattice can be altered by changing the lattice constant. This can be achieved through various methods, such as applying external pressure or strain, doping with impurities, or modifying the composition of the lattice. These alterations can have a significant impact on the properties of the material.

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