A generalized semiclassical quantization condition for cyclotron
orbits was recently proposed by Gao and Niu , that goes beyond the
Onsager relation . In addition to the integrated density of states, it
formally involves magnetic response functions of all orders in the
magnetic field. In particular, up to second order, it requires the
knowledge of the spontaneous magnetization and the magnetic
susceptibility, as was early anticipated by Roth . We study three
applications of this relation focusing on two-dimensional electrons.
First, we obtain magnetic response functions from Landau levels. Second
we obtain Landau levels from response functions. Third we study magnetic
oscillations in metals and propose a proper way to analyze Landau plots
(i.e. the oscillation index nn
as a function of the inverse magnetic field
1/B1/B)
in order to extract quantities such as a zero-field phase-shift. Whereas
the frequency of 1/B1/B-oscillations
depends on the zero-field energy spectrum, the zero-field phase-shift depends on the geometry of the
cell-periodic Bloch states via two contributions: the Berry phase and
the average orbital magnetic moment on the Fermi surface. We also
quantify deviations from linearity in Landau plots (i.e. aperiodic
magnetic oscillations), as recently measured in surface states of
three-dimensional topological insulators and emphasized by Wright and
McKenzie .
Landau levels, response functions and magnetic oscillations from a generalized Onsager relation
