Nonlinear Thermoelectric Probes of Anomalous Dynamics in Topological Fermi Liquids

In two-dimensional Fermi liquids, odd-parity Fermi surface deformations have anomalously slow relaxation rates that are suppressed as $T^4$ with temperature $T$, distinct from the standard Fermi-liquid $T^2$ scaling. We demonstrate here that these long-lived modes, which are often hidden in linear response, have a significant impact on nonlinear transport by establishing a direct proportionality of nonlinear thermoelectric currents to the anomalously large relaxation time. These currents exist in topological time-reversal invariant Fermi liquids, and their magnitude is characterized by new topological heat capacitance terms that we refer to as the {\em Berry curvature capacity} and the {\em velocity-curvature capacity}. We quantify the effect in bismuth telluride, which is an efficient thermoelectric and a topological insulator with a hexagonal Fermi surface. Our findings demonstrate the potential to explore topological and many-body effects in Fermi liquids through the nonlinear thermoelectric response, urging further experimental studies.