Thermoelectric transport of type-I, II, and III massless Dirac fermions in a two-dimensional lattice model

We study longitudinal electric and thermoelectric transport coefficients of Dirac fermions on a simple lattice model where tuning of a single parameter enables us to change the type of Dirac cones from type I to type II. We pay particular attention to the behavior of the critical situation, i.e., the type-III Dirac cone. We find that the transport coefficients of the type-III Dirac fermions behave as the limiting case of neither type I nor type II. On the one hand, the qualitative behaviors of the type-III case are similar to those of the type-I case. On the other hand, the transport coefficients do not change monotonically upon increasing the tilting; namely, the largest thermoelectric response is obtained not for the type-III case but for the optimally tilted type-I case. For the optimal case, sizable transport coefficients are obtained; for example, the dimensionless figure of merit is 0.18.