Topological thermoelectrics: analytical framework, material aspects and machine learning.

Topological quantum materials offer new levers for thermoelectric (TE) design by reshaping band geometry, carrier scattering, and heat transport. This review provides a unified account of these opportunities from three complementary perspectives. First, we develop an analytical framework based on the Bernevig-Hughes-Zhang model, which makes explicit how Berry curvature, entropy, and chemical potential jointly control the anomalous Nernst response across trivial, critical, and topological regimes. Within a Landauer-Büttiker picture, we show how helical edge channels can act as nearly ideal step-like energy filters when transmission is engineered to be strongly energy dependent, clarifying that topological protection alone yields vanishing thermopower and that sizeable Seebeck and Nernst signals require controlled particle-hole asymmetry without sacrificing conductance. Second, we survey material platforms where these mechanisms are realized or anticipated: three-dimensional topological insulators and quantum spin Hall monolayers such as jacutingaite, Dirac and Weyl semimetals, goniopolar and magnetic topological semimetals, altermagnets, and systems hosting topological magnons and phonons. Particular emphasis is placed on the interplay of band inversion, spin-orbit coupling, magnetism, and lattice thermal conductivity, as well as on transverse Nernst and Ettingshausen geometries. Finally, we review emerging machine-learning strategies for topological TEs, covering data curation, descriptor engineering, tree-based and neural-network models, graph-based approaches, active-learning loops, and literature mining workflows that directly target power factor and figure of merit. Together, these analytical, materials, and data-driven perspectives outline design principles and computational pathways for exploiting topology as a controllable resource in next-generation TE materials and devices.