Effect of non-phonon modes on the isotope effect and Hall resistivity in cuprates

Non-phonon boson modes are widely observed in cuprates. Their existence may cause many interesting phenomena. In this work, we investigate their effects on the T_c isotope coefficient and Hall resistivity. (1) The coexistence of phonon and non-phonon modes leads to anomalous isotope effect. In special, if one of the boson modes (either phonon or non-phonon) is pair-breaking, large isotope coefficient α>0.5 can be obtained and a scaling of α~ln²(T_c) as T_c →0 is predicted. This study indicates that α>0.5 may be caused by pair-breaking phonon. (2) If the non-phonon boson mode is stablized by the magnetic field, the Hall coefficient shows a strong field dependence, in special near a van Hove filling. This may challenge the current understanding of the ``Hall number'': p to 1+p or p to infinity?