Correlated electrons tunnelling trough pseudo Fermi arcs in hyperbolic Fermi surfaces of topological materials

In the last decades, basic ideas of topology have completely transformed the prediction of quantum transport phenomena. Following this trend, we go deeper into the incorporation of modern mathematics into quantum material science. We rephrase a few major results from algebraic geometry in the language of quantum materials. Particularly, we show that hyperbolic geometry of the Fermi surface results in the Fermi liquid breakdown and correlated transport effects. As a mechanism for realizing these correlations, we introduce pseudo-Fermi arcs connecting separate pockets of hyperbolic Fermi surface. A break of time reversal symmetry via tunneling through a pseud-arc is referred as Fermi Surface Geometry Effect (FS-GE). The predictable power of FS-GE is tested on the spin and anomalous Hall effects, traditionally associated with intrinsic time-reversal symmetry breaking. An index, H_F, quantifying FS-GE in a particular direction, shows a universal correlation (R^2 = 0.97) with the experimentally measured intrinsic anomalous Hall conductivity in that direction, of 16 different compounds spanning a wide variety of crystal, chemical, and electronic structure families, where the topological methods give just R^2 = 0.52. This raises a question about the principal limits of topological physics, dominating now the predictions of non-trivial electron transport, and its transformation into a wider study of bandstructures' and Fermi surfaces' geometries, opening a horizon for prediction of phenomena beyond topological understanding.