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

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 .

Symmetry relations in viscoplastic drag laws

The following note shows that the symmetry of various resistance formulae, often based on Lorentz reciprocity for linearly viscous fluids, applies to a wide class of nonlinear viscoplastic fluids. This follows from Edelen's nonlinear generalization of the Onsager relation for the special case of strongly dissipative rheology, where constitutive equations are derivable from his dissipation potential. For flow domains with strong dissipation in the interior and on a portion of the boundary, this implies strong dissipation on the remaining portion of the boundary, with strongly dissipative traction–velocity response given by a dissipation potential. This leads to a nonlinear generalization of Stokes resistance formulae for a wide class of viscoplastic fluid problems. We consider the application to nonlinear Darcy flow and to the effective slip for viscoplastic flow over textured surfaces.

Analysis and Characterization of Thermoelectric Microrefrigerators

Advances in film growth techniques have sparked a renewed interest in thermoelectric (TE) devices. A previous study suggested that a drastic improvement in the figure of merit can be achieved for superlattices and quantum wells by exploiting phonon scattering/reflection at interfaces [1] or carrier pocket engineering [2]. Thin-film devices are also of great significance because of their capability to handle considerably higher heat flux than conventional bulk modules [3]. Microrefrigerators consist of a single or multiple thin-film thermoelement(s). The use of thin films introduces the full complexity of solid-solid interfaces into any complete discussion of these refrigerators. Many investigators noted that the electrical contact resistance has adverse effects on TE cooling. Less attention has been paid to thermal interface resistance and the boundary Seebeck effects. While previous studies [4] have indicated that the interface effects are related to each other via boundary forms of the Wiedemann-Franz-Lorenz law and the Kelvin-Onsager relation, the impact of their mutual interactions on thermoelectric cooling has remained relatively unexplored.