Advanced Solid State Physics

10.4 Diffusive and Ballistic Transport We now try to get a uniform picture of the transport e.g. if the frequency is so high tha ...

To describe this equation in a simpler way we could define a complex conductivityσor a complex dielectricityε. Both is possible ...

The frequency dependent conductivity is σ(ω) = j(ω) E(ω) = nev(ω) E(ω) = neμ 1 −iωτ 1 +ω^2 τ^2 (116) If we think of low frequenc ...

(a) (b) Figure 71: a) Dielectric constantεvs.ω. The dielectric constant is positive for frequencies above the plasma frequency; ...

withlthe length,wthe width andtthe thickness of the transmission line. For high frequencies the skin depth gets smaller than the ...

Dispersion relation general With Amperes law, Faraday’s law and the electric displacement asD = εEas well asB = μHthe following ...

11 Quasiparticles In many-body quantum mechanics it is convenient to simplify problems because the initial equations may be too ...

In a system ofNatoms the number of variables which describe the motion is 3 N(x, y and z compo- nents). So there are also 3 Npho ...

Figure 73: a) electron in ionic crystal (KCL). Forces are symbolized by arrows. b) Electron in a kind of equilibrium. The ions c ...

(a) (b) Figure 74: a) Phonon dispersion and photon dispersion; b) Dispersion relationship of polaritons. The photon dispersion c ...

can solve this system of equations by calculating ∣∣ ∣∣ ∣ μ 0 ε 0 ω^2 −k^2 μ 0 ω^2 Ne^2 / m ω^2 −ω^2 T ∣∣ ∣∣ ∣= 0, (133) which g ...

Figure 76: Dielectric constant as a function ofωωT. . Calculating the expectation value of this operator in the ground state of ...

Figure 77: (a) Ground state of a linear ferromagnetic chain at zero temperature, (b) excited state where one spin is flipped, (c ...

Sx,Sy<< Sz. It is now reasonable to neglect product terms ofSxSx,SySyandSxSyrenamingSz toS. This results in the linearized ...

Figure 78: Magnon dispersion relation (1 dimensional, for nearest neighbor interaction). The slope for long wavelengths is propo ...

Figure 79: Charge density in a metal are also seen in plasma. Plasma is a gas of positive and negative charges. If you move the ...

For most metals this plasma frequency is up in the ultraviolet which means that in the visible spectrum they look shiny but in a ...

this is used in stained glass^11. In order to make red glass, gold particles are added during the production process. The surfac ...

11.5 Occupation If there aren’t any electron-electron interactions (free electron model) the probability of occupation is given ...

If the resistance at room temperature is under 150 μΩcm, the resistance will decrease if the system cools down. But if the resis ...