Gyrotropic Magnetic Effect in Black Phosphorus Irradiated with Bicircular Light

Abstract

The gyrotropic magnetic effect (GME), which emerges as the low-frequency limit of natural gyrotopy, is a fundamental property of Bloch electrons on the Fermi surface in materials lacking inversion symmetry. While Weyl semimetals were among the first systems predicted to host the GME, this effect has not yet been experimentally observed in these materials. Here, we theoretically propose a robust scheme to generate a significant GME in anisotropic nodal-line semimetals using Floquet engineering with bicircular light (BCL). We show that BCL irradiation can selectively break spatial and time-reversal symmetries, inducing a topological phase transition from a nodal-line semimetal to a Weyl semimetal with a minimal number of Weyl nodes. Crucially, the Weyl nodes with opposite chirality are separated in energy, a key requirement for a non-zero GME. Using first-principles calculations combined with Floquet theory, we identify compressed black phosphorus as an ideal material platform. The intrinsic anisotropy of black phosphorus amplifies the GME, resulting in a measurable gyrotropic current that is several orders of magnitude larger than that in previously proposed systems. Our work not only provides a concrete path toward the experimental realization of GME but also opens new avenues for exploring the interplay of light, symmetry, and topology in quantum materials.

Figures (2)

• Figure 1: The conceptual illustration and model results of light-dressed an anisotropic nodal line semimetal. (a) The conceptual illustration and proposed setup for a gyrotropic current driven by trefoil BCL. (b) A nodal ring with varying energy is located at the $k_y-k_z$ plane before application of light to the system. (c) Two-frequency Lissajous curves for $\alpha=0$ and $\pi/2$. (d) The transition from a NLSM to WSM under illumination with BCL. (e) The band structures around two Weyl nodes for different BCL polarization state $\alpha$. (f) The BCL-controlled energy separation (black line) between Weyl nodes and the magnitude of the gyrotropic current (red line). The values of parameters are $C=0.03$ eV, $D=0.05$ eV Å$^{2}$, $v=0.4$ eV Å$^{-1}$, $\epsilon_1=- \epsilon_2=0.45$ eV Å$^{-4}$, $eA_0/\hbar = 0.1$ Å$^{-1}$, $\hbar\omega=1$ eV, $\alpha=\pi/2$, and $\varphi=\pi/4$. We fix magnetic field in the $z$ direction with amplitude of 3 T.
• Figure 2: The electronic structure evolution and gyrotropic current induced by trefoil BCL in compressed BP. (a) The atomic structure of BP and a schematic for irradiation of BCL field. (b) Without light irradiation, the nodal ring in the compressed BP exhibits a variation in energy relative to the Fermi level. (c) Evolution of electronic band structures of compressed BP under the irradiation of BCL, and the band gap is enlarged with an increase of light intensity. (d) The degree of $\mathcal{M}_x\mathcal{T}$ breaking under the BCL irradiation. (e) The enlarged view of band structure around two Weyl nodes is shown to emphasize the energy separation. The insets show the evolution of the Wannier charge centers around the $W^{+}$ and $W^{-}$, respectively. (f) Trajectory of the Weyl nodes (marked by the filled dots) in momentum space as $\alpha$ evolves from 0 to $2\pi$ by rotating the light waveform. (g) The calculated surface state projected on the semi-infinite (100) surface of compressed BP under the irradiation of BCL. (h) The energy of Weyl nodes as a function of BCL with polarization state $\alpha$. (i) The gyrotropic current at different light intensities. For (e), (g), (h) and (i), we set the light intensity $eA_0/\hbar = 0.025$ Å$^{-1}$, incident angle $\varphi=\pi/4$, and magnetic field in the $z$ direction with amplitude of 1 T.