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Weyl semimetals (WSMs) are realized when non-degenerate bands cross at isolated points in the Brillouin zone. Consider the simplest example of a time-reversal symmetry broken WSM modeled by the hamiltonian $$H = t' \sin{k_x} \sigma_x + t'' \sin{k_y} \sigma_y + t (\cos{k_x} + \cos{k_y}+ \cos{k_z} - M) \sigma_z.$$ This hamiltonian admits 2 bands ($\sigma_j$ ...

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The assumption behind the question is that materials have finite conductivity due to electron scattering from impurities and the imperfections of the crystal lattice. This is not quite the case. Firstly, the scattering from impurities and crystal imperfections is coherent scattering, so, in principle, it doesn't cause any dissipation, unless combined with an ...

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Conductivity is infinite in the sense that if you apply an electric field for a short time and, as a result, displace the electron distribution in k-space from its equilibrium distribution, and then switch the field off, there will be no mechanism to bring the electrons back to equilibrium distribution. Therefore, you will have a current forever without any ...

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Fundamentally, you need to somehow fit a parabola to the conduction band minimum and find the second derivative of the parabola. How you do this depends on the tools at your disposal. If it's truly pencil, paper, and a ruler only, then you'll only be able to get a very rough answer. (Think: how many points are needed to uniquely define a parabola.) If you ...

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The band structure is the relation between energy and momentum. It will take the actual crystal orbitals to specify the actual wave function. From these you can control the Wannier orbitals. However, band structure calculations are based on translational symmetry and in this formalism it is not possible to include local correlations that are important in ...

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There is no direct correlation between the band structure of a covalent material and the directional character of the corresponding Wannier functions. The reason is quite general. There is no direct relation between the spectrum of the eigenvalues and the spatial properties of the eigenfunctions. The only thing which is possible to establish easily is how ...

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No, it applies whenever there are free charges. So, it applies to semiconductors too (especially doped ones) or even insulators if you can heat them up enough without melting them... EDIT: by way of example, here is a classic paper that applies Thomas-Fermi screening to semiconductor heterostructures: https://doi.org/10.1103/PhysRevB.41.7929 The formulas in ...

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As you noted, states in the valence band have momentum, but the point is that the valence band is completely filled. If we see electrons with $k>0$ as moving to the right, and $k<0$ moving to the left, then since the band is filled the electrons moving in one direction compensate the electrons moving in the oposite, and the net conduction associated to ...

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I will just talk about conduction and valence bands in general here, since it really seems that is what your question aims at (though I may be mistaken!). Let's just talk in one dimensional terms. In a metal, the conduction band is only partially full. With no electric field applied, there are just as many electrons moving in the positive x direction as ...

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Non metals are insulators and so cannot completely screen charge. In terms of your formula, the density of free free-charges $n$ is zero for non metals, and so $\lambda_{TF}=\infty$.

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I believe that you are correct; there would be Bloch oscillations and the dc conductivity would arguably be zero (or undefined). However, I don't think that the AC conductivity would be zero. That said, it's impossible to actually test this situation...

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The resolution to this paradox is realizing that the electrons are originating from two different initial states, one photo-emitted from surface A, $\vert \psi_A\rangle$, and the other surface B, $\vert \psi_B\rangle$. Because the initial states for your two scenarios are different, they naturally have different binding energies (i.e. different starting ...

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