Light-induced anomalous Hall, Nernst, and thermal Hall effects in black phosphorus thin films

Light irradiation is a common and flexible method to induce Berry curvature in low-dimensional materials by breaking time-reversal symmetry. The recent Floquet band engineering in black phosphorus (BP) was successfully realized in experiment [S. Zhou et al., Nature (London) 614, 75 (2023)], hereby, we study the anomalous Hall, Nernst, and thermal Hall effects in BP thin films irradiated by an off-resonant circularly polarized light. Using the $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ Hamiltonian and Floquet theory, we derive the effective Hamiltonian and Berry curvature through two-photon processes up to the second order. We find that the light slightly increases the band gap, and the Berry curvature increases with increasing light intensity. Notably, the anomalous Hall conductivity exhibits a negative plateau width equal to the band gap, which is four orders of magnitude larger than that of monolayer BP. On the contrary, the anomalous Nernst conductivity is always zero within the band gap, showing a dip-peak profile. The anomalous thermal Hall conductivity trend mirrors that of the anomalous Hall conductivity, in line with the Wiedemann-Franz law. Our results provide a feasible method to obtain a finite Berry curvature and shed light on possible topological phase in BP thin films.