Exploring non-trivial band structure and spin polarizations in $d$-wave altermagnets tailored by anisotropic optical fields

The subject of the present paper is a detailed theoretical investigation of the energy spectrum and bandgaps, as well as topological and collective properties and linear response, in $d$-wave altermagnets in the presence of an off-resonance optical dressing field. We consider the altermagnets with both $d_{x^2-y^2}$ and $d_{xy}$ pairing symmetries and focus on anisotropic dressing fields applied to an anisotropic and non-linear electron Hamiltonian. We have uncovered several crucial properties of the resulting electron-dressed states; specifically, we found that a finite bandgap is opened by linearly polarized irradiation, a phenomenon not observed in Dirac materials. Some of the crucial properties of the electron dressed states in the presence of the linearly polarized light can be uncovered only in the second-order perturbation expansion, which is often omitted. We found that introducing an anisotropic driving field leads to several subtle yet important changes in the Edelstein susceptibilities of altermagents, enabling the fine-tuning of their spin polarizations. We calculate the Berry curvature for various types of altermagnets and obtain closed-form analytical expressions for circularly polarized irradiation. We demonstrate that the optical driving field can generate finite Berry curvature in the absence of altermagnetic order. All these results are expected to become a crucial contribution to the rapidly developing fields of spintronics and device physics.