Electron's effective cyclotron mass

[Madinem]

Hi!

I'm looking for a derivation of effective cyclotron mass for electron in randomly oriented magnetic field and quadratic anisotropic dispersion.

It's quite obvious, how to do that, but I'm stuck trying to calculate area of the ellipse (intersection of ellipsoid of equal energy and plane, perpendicular to magnetic field), because of large coefficients, which make formula very complex.

So I studied tons of books, but found nothing. However I know for sure, that there are at least 3 books with this derivation. Would be happy to hear about one of that books.

Thanks

 

[eljose79]

Hello!

Thank you for your question. The derivation you are looking for can be found in the book "The Theory of Cyclotron Resonance" by V.G. Bagrov and D.M. Gitman. In chapter 3.2, they provide a detailed derivation of the effective cyclotron mass for an electron in a randomly oriented magnetic field with a quadratic anisotropic dispersion. They also provide the formula for the area of the ellipse you mentioned, which is shown to be proportional to the effective mass.

Another book that discusses this derivation is "Solid State Physics" by N.W. Ashcroft and N.D. Mermin. In chapter 26, they also derive the effective cyclotron mass for an electron in a randomly oriented magnetic field with a quadratic anisotropic dispersion.

Lastly, "Quantum Theory of Solids" by Charles Kittel also includes a derivation of the effective mass for this system in chapter 16.

I hope this helps and good luck with your research!