User:Zudovlabtry/SDH

When a 2DES is subject to weak magnetic fields $$B$$ and low temperatures $$T$$, the linear response exhibits oscillations controlled by the ratio of the Fermi energy, $$E_f$$, to the cyclotron energy, $$\omega_{c}=eB/m$$. These oscillations are periodic in the inverse magnetic field, $$1/B$$, and are a result of $$E_f$$ sweeping through the Landau level (LL) energy spectrum. As a LL passes through $$E_f$$ it depopulates as the electrons become free to flow.

These oscillations are of importance due to their ability to yield information about three important physical parameters. The oscillation frequency, when plotted as a function of $$1/B$$, characterizes the Fermi surface and gives direct examination of the carrier density. Minima of these oscillations occur at integer values of the quantity $$\nu=n_{e}h/eB$$, where $$n_{e}$$ is the electron density and $$h$$ and $$e$$ are fundamental constants. Thus by using adjacent minima one can obtain the carrier density directly.

The other two physical parameters obtained from SdHOs are the effective mass, $$m^{*}$$, of the charge carriers and the quantum lifetime, $$\tau_{q}$$. Theoretically the amplitude of these oscillations is given by
 * $$\Delta\rho_{SHO}=4\rho_{o}\delta\cos(2\pi\nu)\frac{X(T)}{\sinh X(T)}$$

where $$\rho_{o}$$ is the resistance at zero magnetic field and $$X(T)=2\pi^{2}T/\omega_{c}$$. By performing a temperature dependent study of SdHOs one can extract $$m^*$$ from the thermal damping factor and performing a Dingle analysis yields the value of $$\tau_{q}$$.