  Irradiation of the strong light on the material leads to numerous non-linear
effects that are essential to understand the physics of excited states of the
system and for optoelectronics. Here, we study the non-linear thermoelectric
effect due to the electric and thermal fields applied on a non-centrosymmetric
system. The phenomenon arises on the Fermi surface with the transitions of
electrons from valence to conduction bands. We derive the formlism to
investigate these effects and find that the non-linearity in these effects
namely non-linear Seebeck and non-linear Peltier effects depends on the ratio
of the non-linear to the linear conductivities. The theory is tested for a
hexagonally warped and gapped topological insulator. Results show enhancement
in the longitudinal and Hall effects on increasing the warping strength while
show opposite behavior with the surface gap.
