Nonlinear Hall effect in two-dimensional class AI metals

Abstract

In a time-reversal invariant system, while the anomalous Hall effect identically vanishes in the linear response regime due to the constraint of time-reversal symmetry on the distribution of Berry curvature, a nonlinear Hall effect can emerge in the second-order response regime if the inversion symmetry is broken to allow a nonzero Berry curvature dipole (BCD) on the Fermi surface. In this work, we study the nonlinear Hall effect of the BCD origin in two-dimensional doped insulators and semimetals belonging to the symmetry class AI which has spinless time-reversal symmetry. Despite that the class AI does not host any strong topological insulator phase in two dimensions, we find that they can still be classified as topologically obstructed insulators and trivial insulators if putting certain constraint on the Hamiltonians. When the insulator gets closer to the phase boundary of the two distinct phases, we find that the BCDs will become more prominent if the doping level is located near the band edge. Moreover, when the insulator undergoes a phase transition between the two distinct phases, we find that the BCDs will dramatically change their signs. For the semimetals without inversion symmetry, we find that the BCDs will sharply reverse their signs when the doping level crosses the Dirac points. With the shift of the locations of Dirac points in energy, the critical doping level at which the BCDs sharply reverse their signs will accordingly change. Our study reveals that class AI materials can also have interesting geometrical and topological properties, and remarkable nonlinear Hall effect can also appear in this class of materials even though the spin-orbit coupling is negligible. Our findings broaden the scope of materials to study the nonlinear Hall effect and provide new perspectives for the application of this effect.

Time-reversal symmetric topological metal

“…The organic materials composed of light elements have weak spin-orbit coupling [79]. Therefore, the organic materials may be suitable candidates for the class AI topological phase [80].…”

Shift-current response as a probe of quantum geometry and electron-electron interactions in twisted bilayer graphene

“…Many interesting signatures of QG are revealed in transport properties and optical responses of these systems [12][13][14][15][16][17][18][19][20][21][22], and especially in the zero-magnetic field quantized anomalous linear hall effect in setups with time-reversal symmetry (TRS) [5,11,23]. The effects of QG go well beyond linear response, and can manifest themselves in nonlinear optical responses (NLOR) as shown recently [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. Furthermore, the NLOR does not require broken TRS, but rather a non-zero Berry curvature profile.…”

“…Furthermore, the NLOR does not require broken TRS, but rather a non-zero Berry curvature profile. These nonlinear effects can manifest in various ways, such as nonlinear response to DC fields (induced by Berry curvature dipole [24,28,29,[35][36][37][38][39]), second-harmonic generation (SHG), and bulk-photovoltaic effects like shift-current (SC) [30,31,33,40], and circular photogalvanic effects (CPGE) [26,41,42]. Recently, there has been a lot of emphasis on the non-linear response to AC fields [25,42,43] which not only serve as a probe of non-trivial topology but also heralds promises of more efficient and robust photovoltaic devices [34].…”