Magnetic field dependent electronic Raman response of cuprate superconductors

•We study the effect of high magnetic field on the electronic Raman response of heavy hole doped cuprates.•We show the energy of the pair breaking peak softens as the magnetic field increases.•We show the density of Cooper pairs is decreasing as the magnetic field is increased.•The decrease of the density of Cooper pairs in the magnetic field is nonlinear. The theory of electronic Raman scattering in cuprate superconductors based on the t–J model is evolved to describe the magnetic field dependent electronic Raman response. The magnetic field dependence of Raman response in the overdoped regime is studied at different doping cases. The results show that the peak and intensity in the B1g and B2g symmetry give depletion as the magnetic field increased. We indicate the decrease of the superconducting order parameter Δ under the magnetic field. The overall density of Cooper pairs is also investigated and yields suppression with the increase of the magnetic fields.