Third-order Hall effect in the surface states of a topological insulator

Time reversal and inversion symmetric materials fail to yield linear nonlinear responses since they possess net zero Berry curvature. However, higher-order Hall response can be generated in these systems upon constraining the crystalline symmetries. Motivated by recently discovered third-order (TOH) mediated connection polarizability, namely, variation of with respect an applied electric field, here, we investigate existence such a effect surface states hexagonal warped topological insulators (e.g., ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$) under application only field. Using semiclassical Boltzmann formalism, tilt warping on polarizability tensor and, consequently, TOH effect, provided Dirac cone remains gapless. We find that magnitude increases significantly increasing strength warping, therefore, provide tunability this effect. In addition, also explore chemical doping system. Interestingly, show, based symmetry analysis, leading-order system, which directly verified experiments.