de Haas-van Alphen oscillations with non-parabolic dispersions

de Haas-van Alphen oscillation spectrum of two-dimensional systems is studied for general power law energy dispersion, yielding a Fermi surface area of the form $S(E)\propto E^\alpha$ for a given energy $E$. The case $\alpha=1$ stands for the parabolic energy dispersion. It is demonstrated that the periodicity of the magnetic oscillations in inverse field can depend notably on the temperature. We evaluated analytically the Fourier spectrum of these oscillations to evidence the frequency shift and smearing of the main peak structure as the temperature increases.Comment: 14 pages, 2 figures, to appear in Eur. Phys. J.

Effect of electronic band dispersion curvature on de Haas-van Alphen oscillations

The effect of electronic band curvature, i.e. the deviation from parabolicity of electronic dispersion, on de Haas-van Alphen oscillations spectra is studied. Although the oscillations amplitude remain unaffected, it is demonstrated that non-quadratic terms of the Landau bands dispersion, which is particularly relevant in the case of Dirac fermions, induces a field- and temperature-dependent Onsager phase. As a result, a temperature-dependent shift of the de Haas-van Alphen oscillations frequency is predicted.Comment: 16 pages, 2 figure

Grassmann techniques applied to classical spin systems

We review problems involving the use of Grassmann techniques in the field of classical spin systems in two dimensions. These techniques are useful to perform exact correspondences between classical spin Hamiltonians and field-theory fermionic actions. This contributes to a better understanding of critical behavior of these models in term of non-quadratic effective actions which can been seen as an extension of the free fermion Ising model. Within this method, identification of bare masses allows for an accurate estimation of critical points or lines and which is supported by Monte-Carlo results and diagrammatic techniques

Random walks and magnetic oscillations in compensated metals

The field- and temperature-dependent de Haas-van Alphen oscillations spectrum is studied for an ideal two-dimensional compensated metal whose Fermi surface is made of a linear chain of successive orbits with electron and hole character, coupled by magnetic breakdown. We show that the first harmonics amplitude can be accurately evaluated on the basis of the Lifshits-Kosevich (LK) formula by considering a set of random walks on the orbit network, in agreement with the numerical resolution of semi-classical equations. Oppositely, the second harmonics amplitude does not follow the LK behavior and vanishes at a critical value of the field-to-temperature ratio which depends explicitly on the relative value between the hole and electron effective masses.Comment: 9 pages, 10 figures. Submitted to Physical Review