Electrical and Thermal Transport by Nodal Quasiparticles in the DDW State

We compute the electrical and thermal conductivities and Hall conductivities of the $d$-density wave (DDW) state in the low-temperature impurity-scattering-dominated regime for low-dopings, at which they are dominated by nodal quasiparticles. We show that the longitudinal conductivity in this limit in the DDW state is not Drude-like. However, the thermal conductivty is Drude-like; this is a reflection of the discrepancy between electrical and thermal transport at finite frequency in the DDW state. An extreme example of this occurs in the $\mu=0$, $\tau\to\infty$ limit, where there is a strong violation of the Wiedemann-Franz law: ${\kappa_{xx}}/{\sigma_{xx}} \propto {T^2}$ at $\omega=0$ and ${\kappa_{xx}}/{\sigma_{xx}}=0$ at finite frequency. The DDW electrical and thermal Hall conductivities are linear in the magnetic field, $B$, for weak fields. The formation of Landau levels at the nodes leads to the quantization of these Hall conductivities at high fields. In all of these ways, the quasiparticles of the DDW state differ from those of the $d_{{x^2}-{y^2}}$ superconducting (DSC) state.