Random magnetic field, random mass and quasi-particle transports in high $T_c$ cuprates
Abstract
By a singular gauge transformation, the quasi-particle transport in the mixed state of high $T_c$ cuprates is mapped into charge-neutral composite Dirac fermion moving in {\em long-range} correlated random scalar and vector potential and random mass. It is shown that $\kappa_{xx}/T = F_{1}(a \frac{T}{T_{c}} \sqrt{\frac{H_{c2}}{H}})$ acquires vertex correction. At high enough magnetic field $H \gg H_{c2} (\frac{T}{T_{c}})^{2}$, $\kappa_{xx}/T$ approaches a {\em different} universal value than its zero field counterpart. However the thermal Hall conductivity is much smaller $<\kappa_{xy}(H, T)/T>= \frac{T_{c}}{\epsilon_{F}}\sqrt{\frac{H}{H_{c2}}} F_{2}(b \frac{T}{T_{c}} \sqrt{\frac{H_{c2}}{H}})$. At $H \gg H_{c2} (\frac{T}{T_{c}})^{2}$, it {\em increases} as $\sqrt{H}$. Due to the previously neglected random magnetic fields, the properly defined thermal Hall {\em conductance} fluctuation in a mesoscopic sample satisfies {\em similar} scaling as $\kappa_{xx}/T$: $\sqrt{< (\tilde{\kappa}_{xy}/T)^{2} >} = F_{3}(c \frac{T}{T_{c}} \sqrt{\frac{H_{c2}}{H}})$. Therefore it is much larger than its average $<\kappa_{xy}/T>$ and should also approach a constant at high enough magnetic field. The implications for experiments are discussed.
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