Linear Magnetoresistance in a Vortex Gas

Recent experiments on the high-T_C cuprate LSCO have revealed a substantial regime of doping, temperature, and magnetic field in which the magnetoresistance is linear in the applied field. This magnetoresistance adds on top of the T-linear resistivity, suggesting an interpretation, via Matthiessen's rule, as a field-dependent contribution to the quasiparticle scattering rate. We consider the possibility that the normal state in these experiments can be described as a vortex gas, in which local pairing correlations are modulated by vortices of finite but long lifetime, and inter-vortex interactions are negligible. In such a state, the vortex contribution to the electronic scattering rate (and therefore the resistivity) is proportional to the density of vortices, i.e. the magnetic field. We calculate the transport scattering rate in Born approximation for a simple model of a vortex gas with parameters relevant to LSCO, and find linear magnetoresistance with a coefficient in semi-quantitative agreement with experiments.