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In two-dimensional Fermi liquids, odd-parity Fermi surface deformations haveanomalously slow relaxation rates that are suppressed as $T^4$ with temperature$T$, distinct from the standard Fermi-liquid $T^2$ scaling. We demonstrate herethat these long-lived modes, which are often hidden in linear response, have asignificant impact on nonlinear transport by establishing a directproportionality of nonlinear thermoelectric currents to the anomalously largerelaxation time. These currents exist in topological time-reversal invariantFermi liquids, and their magnitude is characterized by new topological heatcapacitance terms that we refer to as the {\em Berry curvature capacity} andthe {\em velocity-curvature capacity}. We quantify the effect in bismuthtelluride, which is an efficient thermoelectric and a topological insulatorwith a hexagonal Fermi surface. Our findings demonstrate the potential toexplore topological and many-body effects in Fermi liquids through thenonlinear thermoelectric response, urging further experimental studies.

Nonlinear Thermoelectric Probes of Anomalous Dynamics in Topological Fermi Liquids