de Haas–van Alphen effect in two-dimensional and quasi-two-dimensional systems

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 multiband systems. By using this formula, the dHvA oscillation and its temperature dependence for the two-band system are shown. By introducing the interlayer hopping (tz), we examine the crossover from two dimensions, where the oscillation of the chemical potential plays an important role in the magnetization oscillation, to three dimensions, where the oscillation of the chemical potential can be neglected as is well know by the Lifshitz and Kosevich formula. The crossover is seen at 4tz~8tabH/φ₀, where a and b are lattice constants, φ₀ 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 β-α oscillation as well as the fundamental oscillations are suppressed by tz, while the β+α oscillation gradually increases as tz increases and it has a maximum at tz/t≈0.025. This interesting dependence on the dimensionality can be observed in the quasi-two-dimensional organic conductors with uniaxial pressure.