Lattice effects on de Haas-van Alphen oscillations in strongly correlated systems

We investigate the influence of a periodic potential and electron-phonon interactions on the de Haas-van Alphen (dHvA) effect in the presence of very strong Coulomb correlations. The inclusion of these correlations is essential for creating the insulating state at half-filling. We use the almost localized Fermi-liquid approach to include the Coulomb correlation induced metal-insulator transition at half-filling and to calculate the correlation effects within the context of renormalized band structures. The effects of a periodic potential on the electronic motion in a magnetic field are calculated by using a series of magnetic subbands called the Hofstadter spectrum. In contrast to Landau levels, these magnetic subbands have nonlinear field dependence and have nonuniform energy gaps between two adjacent subbands. The results of these differences appear as the field and the hole doping concentration x, dependence on the effective mass, chemical potential, and magnetization in two dimensions. The inclusion of strong Coulomb correlations leads to a substantial reduction in the electron-phonon coupling constant near the metal-insulator transition. Electron-phonon interactions are screened in the presence of strong Coulomb correlations because charge fluctuations are progressively suppressed by the correlation effects as half-filling is approached. Hence, the coupling constant decreases as x decreases. The screened coupling constant is estimated self-consistently by including the contributions from both the renormalized band and the dynamical screening effects. We show that both a periodic potential and electron-phonon interactions lead to mass enhancement as a function of x, thereby, changing both the amplitude and frequency of the dHvA oscillations. We discuss the feasibility of observing these effects in copper oxides.