Transport properties in the d-density-wave state in an external magnetic field: The Wiedemann-Franz law

We derive the electrical and thermal conductivities of the $d$-density-wave state in an external magnetic field $B$ in the low-temperature regime and in the presence of impurities. We show that in the zero-temperature limit, $T \to 0$, the Wiedemann-Franz (WF) law remains intact irrespectively of the value of the applied field and chemical potential $\mu$ as soon as there is a scattering from impurities. For finite $T \lesssim |\mu|$ the WF law violation is possible and it is enhanced by the external field. Depending on the relative values of $B$ and $T$ the electrical conduction may dominate the heat conduction and vice versa. For $\mu \gg T$ the WF is restored even in the presence of the external field.