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How does magnetoresistance reveal information about the Fermi surface?

I'm analyzing data on a suspected topological semimetal. I know that techniques like de Haas–van Alphen or Shubnikov–de Haas oscillations are key, but I want to move beyond just identifying frequencies. I need a clearer picture of how the electron orbits in a magnetic field, constrained by the Fermi surface geometry, directly manifest in the resistance we measure.

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By Reema Answered 10 months ago

In my lab work, we treat magnetoresistance as a powerful lens. Here’s the intuitive picture: When you apply a strong magnetic field, electrons execute closed "cyclotron" orbits in momentum space, tracing out contours of the Fermi surface. The orbit's area is quantized. As you sweep the field, electrons sequentially jump between these quantized orbits, causing oscillations in the density of states at the Fermi level. This directly modulates conductivity. By measuring the oscillation period versus field direction, you're essentially taking a tomographic scan each period inversely gives an extremal cross-sectional area of the Fermi surface, building up its 3D shape.

 

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