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

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 µ/ωc ≫ 1 (µ is the chemical potential and ωc 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.

Superconducting fluctuations at low temperature

“…We apply the Fourier transformation to this function and put the value obtainedÕ(r) in Eq. (19). Than, we evaluate the matrix elements for this operator and perform the integration over r. Finally, we perform the frequency summation left (over the fermion energy ε).…”

Superconducting fluctuations and the reduced dimensionality of the organic superconductorκ−(BEDT−TTF)2Cu(Clayton1, Ito2, Hayden3 et al. 2002Phys. Rev. B151120View full textAdd to dashboardCite

“…The DHVA effect consists of an oscillatory variation of the magnetizationM which varies periodically in inverse applied field. For a two-dimensional metal [20][21][22] , each Fermi surface sheet with area A, gives rise to a fundamental oscillatory magnetization, M = − e 2 V F bm e π X sinh X exp(−πm b /eBτ 0 )…”

Measuring the Chern number with quantum oscillations

“…4,28,29 Shubnikov-de Haas oscillations are the oscillations in longitudinal resistivity at external magnetic field strengths lower than the quantum Hall regime. Generically, the resistivity goes as 30 ρ xx ∝ cos 2π…”