The Wiedemann-Franz Law In D-Density-Wave Conductors

It was recently suggested that the typical characteristic of the psudogap of high-Tccuprates can be explained by the d-density-wave (DDW) order model. The DDW state ischaracterized by a condensate of electron-hole pairs. In such a state, parity and time-reversalsymmetry as well as the translation invariance by one lattice constant and rotation byπ／2 arebroken. Although the debate about the mechanism for the psudogap is far from settled, theoreticalinvestigations for the features of the two-dimensional (2D) DDW state are interesting andimportant, and are likely to be helpful in understanding the superconducting mechanism andnormal-state features of high-Tc cuprates. Recently, the effect of impurity scattering in the DDWstate has been received much attention. Several authors studied the quasiparticle transport indisordered DDW conductors. Some results are in agreement, while some problems are still indebate, such as the validation of the Wiedemann-Franz law.In this paper, within the self-consistent T-matrix approximation, the methods of Green`sfunction and diagrammatic techniques in quantum statistics are used to study the effects ofnonmagnetic impurity scattering in 2D DDW state. The electrical and thermal conductivities arecalculated, and the Wiedemann-Franz law is shown to be valid at low temperatures and for a smallconcentration of impurities. Our results are as follows:(1) The Feymann rules are obtained for the effects of nonmagnetic impurity scattering in theDDW state. It is found that these rules are quite different from those of the normal state due to theexistence of DDW order. It is believed that these rules can be used to study the effects ofnonmagnetic impurity scattering on equilibrium and transport properties in DDW state, such asconductivity, magnetoresistance, Hall effect et al.(2) We calculated the electrical and thermal conductivities. The Wiedemann-Franz law isshown to be valid at low temperatures and for a small concentration of impurities.The aim of this work is to predict theoretically the validation of the Wiedemann-Franz law atlow temperatures and for a small concentration of impurities by calculating the electrical andthermal conductivities. Our predictions and the results might be helpful for the investigation ofthe mechanism for psudogap in high-Tc cuprates.