Nernst effect of the dice lattice in a strong magnetic field

The dice lattice bears a similar honeycomb lattice structure to graphene but with a non-dispersive flat band intersecting the Dirac bands at the band center. In this work, we investigate Nernst effect of the dice lattice in a strong magnetic field, focusing on the role of the flat band. By using the Chebyshev polynomial Green’s function method, we show that no Nernst effect ($S_{xy}=0$) is around the Dirac point in the clean limit contrary to the graphene case because of the existence of a zero Hall conductivity platform. However, an unconventional negative $S_{xy}$ of the double-peak structure emerges instead when the flat band is broadened by disorder and temperature. In addition, when a mass term of Dirac electrons is introduced in the system to open an energy gap, a negative single peak of $S_{xy}$ appears at the Dirac point and this is due to the derivative quantum Hall effect of non-Dirac electrons in the flat band appearing in the energy gap.