Non-Boltzmann thermoelectric transport in minimally twisted bilayer graphene

The electronic bands formed in moir\'e systems with twisted bilayer graphene (tBLG) have emerged as a tunable platform for studying many novel concepts of condensed matter physics due to new interaction and topological effects. In particular, the multitude of closely packed flat bands and a sequence of van Hove singularities (vHSs) in minimally tBLG can not only lead to nontrivial topological transport but also the breakdown of conventional Boltzmann transport formalism due to the competition between the scales of energy variation within the system and that of the external parameters such as temperature or electric field. Here, we demonstrate the violation of the semiclassical Mott relation in small-angle tBLG $(\ensuremath{\theta}\ensuremath{\sim}0.{45}^{\ensuremath{\circ}})$ even at room temperature, which we associate to a narrow diverging density of states. We also show the emergence of nonlinear effects in thermovoltage by exploiting vertical thermoelectric transport in an atomically thin tBLG device. Our results not only point towards the fundamental limitations of the applicability of the semiclassical Boltzmann approach in small-angle tBLG but also outline an experimental approach that can lead to the discovery of different broken-symmetry states.