Chemical potential oscillations and de Haas–van Alphen effect

An analytical theory of the de Haas–van Alphen effect, under the condition $\mu /ħ{\omega }_c\gg 1$ (where $\mu$ is the chemical potential and ${\omega }_c$ the cyclotron frequency) is investigated in two-dimensional and quasi-two-dimensional metals, taking into account the effects of spin splitting, impurity scattering, finite temperature, and a field-independent reservoir of electrons. The equation for the chemical potential as a function of magnetic field, temperature, and a non-field-quantized reservoir of states is derived. It follows that the semiclassical expression in low-dimensional systems is generally no longer a Fourier-like series. The difficulties in an unequivocal effective-mass determination from the temperature dependence of the oscillation amplitude in low-dimensional metals are pointed out. The influence of the chemical potential oscillations on the shape of the magnetization oscillations is shown analytically: the sawtoothed, inverted sawtoothed, and symmetrical wave forms are found in high-purity two-dimensional metals at very low temperatures from a semiclassical expression.