Random Magnetic Field and Quasiparticle Transport in the Mixed State of High-TcCuprates

By a singular gauge transformation, the quasiparticle transport in the mixed state of high- $T_c$ cuprates is mapped into a charge-neutral Dirac moving in short-range correlated random scalar and long-range correlated vector potential. A fully quantum mechanical approach to longitudinal and transverse thermal conductivities is presented. The semiclassical Volovik effect is presented in a quantum mechanical way. The quasiparticle scattering from the random magnetic field which was completely missed in all the previous semiclassical approaches is the dominant scattering mechanism at sufficient high magnetic field. The implications for experiments are discussed.