Abstract:
In this work we present the results of theoretical analysis of the de Haas-van Alphen oscillations in quasi-two-dimensional conductors. We have been studying the effect of the Fermi-liquid correlations of charge carriers on the above oscillations. It was shown that at reasonably low temperatures and weak electron scattering the Fermi-liquid interactions may cause noticeable changes in both amplitude and shape of the oscillations even at realistically small values of the Fermi-liquid parameters. Also, we show that the Fermi-liquid interactions in the system of the charge carriers may cause magnetic instability of a quasi-two-dimensional conductor near the peaks of quantum oscillations in the electron density of states at the Fermi surface, indicating the possibility for the diamagnetic phase transition within the relevant ranges of the applied magnetic fields.

Abstract:
Here, we present the results of theoretical analysis of the de Haas-van Alphen oscillations in quasi-two-dimensional normal metals. We had been studying effects of the Fermi surface (FS) shape on these oscillations. It was shown that the effects could be revealed and well pronounced when the FS curvature becomes zero at cross-sections with extremal cross-sectional areas. In this case both shape and amplitude of the oscillations could be significantly changed. Also, we analyze the effect of the FS local geometry on the angular dependencies of the oscillation amplitudes when the magnetic field is tilted away from the FS symmetry axis by the angle $\theta.$ We show that a peak appears at $\theta \approx 0$ whose height could be of the same order as the maximum at the Yamaji angle. This peak emerges when the FS includes zero curvature cross-sections of extremal areas. Such maximum was observed in experiments on the $\alpha-(BETS)_4TIHg(SeCN)_4.$ The obtained results could be applied to organic metals and other quasi-two-dimensional compounds.

Abstract:
We calculate the de Haas-van Alphen (dHvA) effect waveform using the canonical ensemble for different Fermi surface scenarios applicable to the underdoped cuprate superconductor YBa2Cu3O6.5, in which quantum oscillations have recently been observed. The harmonic content of the dHvA waveform of the principal F ~ 500 T frequency is consistent with the existence of a second thermodynamically dominant section of Fermi surface that acts primarily as a charge reservoir. Oscillations in the charge density to and from this reservoir are shown to potentially contribute to the observed large quantum oscillations in the Hall resistance.

Abstract:
An analytical form of the quantum magnetization oscillations (de Haas-van Alphen effect) is derived for two- and quasi two-dimensional metals in normal and superconducting mixed states. The theory is developed under condition that the chemical potential is much greater than the cyclotron frequency, which is proved to be valid for using grand canonical ensemble in the systems of low dimensionality. Effects of impurity, temperature, spin-splitting and vortex lattice - in the case of superconductors of type II -, are taken into account. Contrary to the three dimensional case, the oscillations in sufficiently pure systems of low dimensionality and at sufficiently low temperatures are characterized by a saw-tooth wave form, which smoothened with temperature and concentration of impurities growth. In the normal quasi two-dimensional systems, the expression for the magnetization oscillations includes an extra factor expressed through the transfer integral between the layers. The additional damping effect due to the vortex lattice is found. The criterion of proximity to the upper critical field for the observation of de Haas-van Alphen effect in the superconducting mixed state is established.

Abstract:
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.

Abstract:
Deploying a recently developed semiclassical theory of quasiparticles in the superconducting state we study the de Haas-van Alphen effect. We find that the oscillations have the same frequency as in the normal state but their amplitude is reduced. We find an analytic formulae for this damping which is due to tunnelling between semiclassical quasiparticle orbits comprising both particle-like and hole-like segments. The quantitative predictions of the theory are consistent with the available data.

Abstract:
We study the de Haas-van Alphen (dHvA) oscillation in two-dimensional and quasi-two-dimensional systems. We give a general formula of the dHvA oscillation in two-dimensional multi-band systems. By using this formula, the dHvA oscillation and its temperature-dependence for the two-band system are shown. By introducing the interlayer hopping $t_z$, we examine the crossover from the two-dimension, where the oscillation of the chemical potential plays an important role in the magnetization oscillation, to the three-dimension, where the oscillation of the chemical potential can be neglected as is well know as the Lifshitz and Kosevich formula. The crossover is seen at $4 t_z \sim 8 ta b H /\phi_0$, where a and b are lattice constants, $\phi_0$ is the flux quantum and 8t is the width of the total energy band. We also study the dHvA oscillation in quasi-two-dimensional magnetic breakdown systems. The quantum interference oscillations such as $\beta-\alpha$ oscillation as well as the fundamental oscillations are suppressed by the interlayer hopping $t_z$, while the $\beta+\alpha$ oscillation gradually increases as $t_z$ increases and it has a maximum at $t_z/t\approx 0.025$. This interesting dependence on the dimensionality can be observed in the quasi-two-dimensional organic conductors with uniaxial pressure.

Abstract:
We study the effects of the Zeeman term on the de Haas van Alphen (dHvA) oscillation in two-dimensional two-band systems. We found that the Fourier transform amplitudes of the oscillations are not described by the spin reduction factor in the Lifshitz-Kosevich formalism in two-dimensional systems. The anomalous dependence on the effective $g$-factor can be observed by tilting-angle dependence of the dHvA oscillation in quasi-two-dimensional organic conductors and Sr$_2$RuO$_4$.

Abstract:
The problem of Dirac fermions in graphite subject to a perpendicular magnetic field is studied. We show analytically that the weak inter-layer interaction between the graphene sheets leads to anomalies in the Shubnikov-de Haas and de Haas-van Alphen magneto-oscillations governed by the orbits around extremal cross-sections of the graphite Fermi surface. The calculation of the Landau plot performed within a four band continuum model reveals that magneto-oscillations are aperiodic, except of the case of vanishing inter-layer interaction at the H point of the graphite Brillouin zone. Also for all other orbits along the H-K-H edge the magneto-oscillations are only asymptotically periodic in the quasi-classical limit, with the phase corresponding to massive fermions.

Abstract:
De Haas-van Alphen oscillations were measured in lanthanum tritelluride (LaTe_3) to probe the partially gapped Fermi surface resulting from charge density wave (CDW) formation. Three distinct frequencies were observed, one of which can be correlated with a FS sheet that is unaltered by CDW formation. The other two frequencies arise from FS sheets that have been reconstructed in the CDW state.