Thermoelectric transport properties of dice lattice

The dice lattice is a two-dimensional material with a unique geometry that consists of three sublattices^[1]. The flat band in the dice lattice intersects the Dirac band at the center of the band which leads to non-dispersive flat band^[2] and unique physical properties^[3]. To further promote the application of flat band system, we investigate the thermoelectric transport properties of dice lattice. Our results show that the super-metallic phases and adjoined narrow localization regimes can be generated near the band center E≈0 only through the broadening of the flat band without vacancy defects. When the vacancy defect is added, the electrons in the low energy state are completely localized. A pair of additional thermopower peaks appear near the center of the band. At relatively high temperatures, the thermopower peaks that appear show an unconventional dependence on temperature and disorder that is opposite to the Mott relationship, and their origin is attributed to the extremely narrow bandwidth of the wide flat band. In strong magnetic fields, when the flat band is widened by disorder and temperature, a double negative peak structure appears in Nernst coefficient (S_xy). In addition, when the mass term of a Dirac electron is added into the system to open the energy gap, a negative unimodal nernst peak appears near the Dirac point. This work elucidates the microcosmic mechanisms in the dice lattice and facilitates thermoelectric applications for future flat band systems.