Strong Coulomb correlation and lattice effects on de Haas-van Alphen oscillation

Abstract

In the metallic regime of strongly correlated systems, we study the influence of (1) Coulomb correlations, (2) the periodic potential, and (3) the electron-phonon interaction on the de Hass-van Alphen (dHvA) effect. For simplicity, we use the one-band Hubbard Hamiltonian as a model for strongly correlated systems and calculate their contributions on the dHvA effect as a function of hole doping concentration, x. First, Coulomb correlation effects are estimated within the context of the renormalized band structure by following the almost localized Fermi liquid approach. Second, electrons moving on the periodic potential in a magnetic field is described by a series of magnetic subbands called Hofstadter spectrum. In contrast to Landau levels, this spectrum depends nonlinearly on fields, and the energy gap between two adjacent magnetic subbands depends on x. These differences lead to the x dependent saw-tooth wave form for the magnetization curve in two dimensions. Finally, the screened electron-phonon coupling constant is self-consistently estimated by including both the renormalized band structure and the dynamical screening contributions. The coupling constant depends on x because Coulomb correlations progressively suppress charge fluctuations as x is decreased. In the copper oxides, these three effects are expected to be present, and they lead to the enhancement of cyclotron mass as x is decreased and, thereby, change both the amplitude and frequency of the dHvA oscillation. We discuss the feasibility of observing these effects in the copper oxides.