2
votes
0answers
20 views

What is the the real world interpretation of the high dimensionality of quasicrystals?

One of the examples of the problems of 5-fold symmetry is that pentagons tiled on a 2D plane do not completely fill that plane, leaving voids. This may be solved by "folding" it into 3D space, and ...
0
votes
0answers
11 views

Symmetry of amorphous thin films

I'm wondering whether amorphous thin films have point group symmetries? Landau's Statistical Physics Vol. I writes: The highest symmetry is that of isotropic bodies (bodies whose properties are the ...
1
vote
1answer
34 views

Can someone explain LO-TO Splitting?

LO-TO splitting occurs in an ionic (i.e. polar) solid such as GaAs or NaCl. What happens is that the degeneracy of the transverse optical (TO) and longitudinal optical (LO) phonons at $k=0$ is broken ...
4
votes
1answer
96 views

Crystal Momentum in a Periodic Potential

I'm working through some basic theory on periodic potentials, and I would appreciate help in understanding the crystal momentum. Suppose we have a Bravais lattice with lattice vectors $\textbf{R}$. ...
0
votes
0answers
35 views

How to easily calculate lengths (or relative lengths) of paths between symmetry points in BZ

I am trying to easily calculate the length between special kpoints within the BZ of the 32 point groups in a crystal system. I am calculating the lengths in order to scale k point sampling along these ...
0
votes
1answer
155 views

Plotting a bandstructure along High-symmetry points when kx,ky,kz is known

Suppose you know kx,ky,kz points along with the corresponding energies. Basically, you know about the 4-D E(k) dispersion. How you do then convert that data into the bandstructure plots you commonly ...
0
votes
1answer
222 views

Overview and doubts about Bloch's theorem and the concept of partial density of states

So I have a large confusion with QM as applied to solid state. The following is a summary of what I know, what I think I know, and what I know I don't know. I hope to stir a discussion that will help ...
3
votes
1answer
158 views

Why does total spin conservation law forbid the spin wave gap in Heisenberg magnets?

What is the explanation for total spin conservation forbidding the spin wave gap in Heisenberg magnets?
1
vote
2answers
200 views

Eigenfunctions in periodic potential

For Hamiltonian $\operatorname H$ and lattice translation operator $\operatorname T$, if $$\operatorname H\psi=E\psi, \qquad \operatorname T\psi=e^{ik\cdot R}\psi,$$ and $$\operatorname ...
1
vote
0answers
43 views

Residual symmetries of the superposition of two fcc lattices

Fcc lattices are Bravais lattices and so are invariant under a set of discrete translations plus inversions over the 3 axis ($x\rightarrow -x$,$y\rightarrow -y$,$z\rightarrow -z$). When one superposes ...
3
votes
1answer
301 views

Lorentz invariance of a frequency- and wavelength- dependent dielectric tensor

Suppose we have a material described by a dielectric tensor $\bar{\epsilon}$. In frequency domain, this tensor depends on the wave frequency $\omega$ and the wave vector $\vec{k}$. Clearly not all ...
2
votes
3answers
373 views

About symmetry, and about electron density in crystals in particular

The book Introduction to Solid State Physics by Kittel says: "We have seen that a crystal is invariant under any translation of the form T [...]. Any local physical property of the crystal, such as ...