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We study longitudinal electric and thermoelectric transport coefficients ofDirac fermions on a simple lattice model where tuning of a single parameterenables us to change the type of Dirac cones from type-I to type-II. We payparticular attention to the behavior of the critical situation, i.e., thetype-III Dirac cone. We find that the transport coefficients of the type-IIIDirac fermions behave as the limiting case of neither the type-I nor type-II.On the one hand, the qualitative behaviors of the type-III case are similar tothose of the type-I case. On the other hand, the transport coefficients do notchange monotonically upon increasing the tilting; namely, the largestthermoelectric response is obtained not for the type-III case but for theoptimally tilted type-I case. For the optimal case, the sizable transportcoefficients are obtained; for example, the dimensionless figure of merit is0.18.

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