  For a long period of time, we have been seeking how Berry curvature influnces
the transport properties in materials breaking time-reversal symmetry. In
time-reversal symmetric material, there will be no thermoelectric current
induced by Berry curvature in linear regime. However, the nonlinear Hall
current can be shown in non-magnetic and non-centrosymmetric materials, where
Berry curvature dipole plays an important role. Most studies are developed from
semi-classical Boltzmann equation. Here we show the quantum kinetic theory for
nonlinear Nernst effect and introduce a new type of Berry curvature dipole:
thermoelectric Berry curvature dipole. This new Berry curvature dipole will
also induce the thermoelectric transport in nonlinear regime even in
time-reversal invariant crystals. We will also apply our theory to topological
crystalline insulator with tilted Dirac cone.

Mesoscale and Nanoscale Physics;Quantum Physics