Universal Scaling Law of Quasiparticle Nernst Effect in Cuprates: A Unified Schematic Analysis for Transverse Transport

We discover a universal scaling law for the quasiparticle Nernst coefficient in underdoped cuprates, whose magnitude decreases exponentially with increasing temperature as confirmed in YBa${}_2$Cu${}_3$O${}_y$. We attribute it to the basic mathematical structure of the conductivity formula with a narrow effective bandwidth of nonzero Berry curvatures associated with the pseudogap. A unified scheme is then developed to analyze transverse transport in hole-doped cuprates and clarify the puzzling disparity in determining the pseudogap temperature from different measurements. Our proposal opens the avenue for exploring potential scaling laws in the intermediate temperature region and may have broad applications in strongly correlated or narrow band systems.