# What causes the Shubnikov-de Haas Oscillations?

If I have a 2DEG with a voltage in the $x$-direction and a $B$-Field in the $z$-direction (so I also get a hall-voltage in the $y$-direction (classicaly)). But if I do this stuff at low temperatures I can observe some quantum effects like Shubnikov-de Haas Oscillations and the Quantum Hall Effect.

I understand how the Quantum Hall Effect emerges but I can't seem to understand why the Shubnikov-de Haas Oscialltions happen.

As far as I know, if the Fermi-Energy (or chemical potential) starts to cross the density of states (as a function of energy) (which represents one Landau Level) it causes all the electrons to conduct a current. At that region the resistence rises. If the Landau Level is passed (the Fermi-Energy is between two Landau Levels) the resistence seems to drop again, but I don't know why.

What causes the Shubnikov-de Haas Oscillations? Why do Shubnikov-de Haas Oscillations occur?

• The magnetic field causes them. Maybe what you're really looking for here is a better explanation of why they occur. – John Duffield Jul 28 '15 at 9:33
• You are correct. I added that question. – Thomas Elliot Jul 28 '15 at 11:24

Roughly speaking, the conductivity is inversely proportional to the scattering rate $1/\tau$ (in the Drude model, the longitudinal conductivity is $\sigma_0=\frac{n e^2 \tau}{m}$). From Fermi's golden rule, $1/\tau$ is proportional to the number of density of states a quasiparticle can scatter into, which is proportional to the density of states near the chemical potential. In the presence of a magnetic field, the energy levels are quantized into equally spaced Landau levels. Therefore the density of states at the chemical potential(or Fermi energy) $N(\mu)$ oscillates in $1/B$ periodically, where $B$ is the magnetic field, as the chemical potential passes each Landau level by varying the magnetic field. Therefore $1/\tau$ oscillates as well and the oscillation of $\sigma$ follows. That gives the SdH oscillation.