Thermoelectric transport in topological flat bands

The measurement of the quantum anomalous Hall effect was the first experimental realization of a Chern insulator, an example of a material where the behavior of the system depends not only on local parameters but also on nonlocal invariants and the vorticity of the electron states. These systems are fundamentally separate from topologically trivial insulators and are host to many exciting quantum effects. In my talk, I will introduce the idea of a topological invariant and will generalize it by introducing the quantum geometry, a geometric structure endowed on the Brillouin zone that contains information on the quantum states of the electrons. I will then present the transverse and longitudinal thermal transport coefficients I derived in terms of the quantum geometry, which serves as the thermal analogue to the quantum Hall effect. Finally, I will explicitly calculate these coefficients for topological flat bands at integer fillings and show that they have a finite but unconventional Lorentz ratio.