Landau levels, response functions and magnetic oscillations from a generalized Onsager relation

Abstract

A generalized semiclassical quantization condition for cyclotron orbits was recently proposed by Gao and Niu \cite{Gao}, that goes beyond the Onsager relation \cite{Onsager}. 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 \cite{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 $n$ as a function of the inverse magnetic field $1/B$) in order to extract quantities such as a zero-field phase-shift. Whereas the frequency of $1/B$-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 \cite{Wright}.

31 pages, 8 figures; v2: SciPost style; v3: several references added, small corrections, typos fixed; v4: abstract changed, generalized quantization condition called Roth-Gao-Niu; v5: minor modifications, 2 references added

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• Instantons in the Hofstadter butterfly: difference equation, resurgence and quantum mirror curves
• Revisiting the magnetic responses of bilayer graphene from the perspective of the quantum distance
• Saddle point anomaly of Landau levels in graphenelike structures
• Electronic Structure of Kramers Nodal-Line Semimetal YAuGe and Anomalous Hall Effect Induced by Magnetic Rare-Earth Substitution
• Odd-parity longitudinal magnetoconductivity in time-reversal symmetry broken materials
• Orbital magnetization reveals multiband topology
• Anomalous Landau levels and quantum oscillation in rotation-invariant insulators
• Landau level spectroscopy in current solid state physics
• Effect of pressure on the transport properties and thermoelectric performance of Dirac semimetal ZrTe5