Restricted Wiedemann-Franz Law and Vanishing Thermoelectric Power in One-Dimensional Conductors

In one-dimensional conductors with linear $E\mathrm{\text{−}}k$ dispersion (Dirac systems), intra-branch thermalization is favored by elastic electron-electron interaction in contrast with electron systems with a nonlinear (parabolic) dispersion. We show that under external electric fields or thermal gradients, the carrier populations of different branches, treated as Fermi gases, have different temperatures as a consequence of self-consistent carrier-heat transport. Specifically, in the presence of elastic phonon scattering, the Wiedemann-Franz law is restricted to each branch with its specific temperature. In addition, thermoelectric power vanishes due to electron-hole symmetry, which is validated by experiment.

Figure 1

Scattering diagrams for elastic electron-electron interaction: (a) Feynmann diagram; (b) intra-intra-branch scattering; (c) inter-inter-branch scattering ; (d) intra-inter-branch scattering.

Figure 2

Temperature ($T_{+}$) and heat flow ($U_{+}$) profiles for carriers with positive Fermi velocity as a function of the current for: ${\lambda }_0=20L$ (a), (b), ${\lambda }_0=L$ (c), (d), and ${\lambda }_0=0.25L$ (e), (f).