Off-resonant light-induced topological phase transition and thermoelectric transport in semi-Dirac materials

We show that a semi-Dirac (SD) system with an inversion symmetry breaking mass exhibits a topological phase transition when irradiated with off-resonant light. Using Floquet theory, we derive the band structure, Chern numbers, phase diagram, and we show that as the light intensity is swept at fixed mass, the SD system undergoes normal-Chern-normal insulator transition. Along the phase boundaries we observe single semi-Dirac-cone (SSDC) semimetal states in which one SD cone is gapless and the other gapped. The nontrivial Berry curvature distribution $\Omega(\mathbf{k}) \neq -\Omega ( - \mathbf{k} )$ generates an orbital magnetization $M$ and anomalous Nernst ($\alpha_{xy}$) and thermal Hall ($\kappa_{xy}$) conductivities. We show that $M$ remains constant as the Fermi level $E_F$ scans the insulating gap, but it changes linearly with it in the Chern insulator (CI) phase, as expected. In the normal insulator phase, we find that $\alpha_{xy}$ exhibits a dip-peak profile which is reversed in the CI phase. We also find that switching the light's circular polarization from left to right induces a sign change in $M$, $\alpha_{xy}$, and $\kappa_{xy}$, regardless of the topological phase, thereby allowing us to reverse the direction of flow of the transverse charge and heat currents. Further, we evaluate the components of the charge ($\sigma_{aa}$), thermoelectric ($\alpha_{aa}$), and thermal ($\kappa_{aa}$) conductivity tensors ($a=x, y$) and examine the effect of light on them. With a linear dispersion along the $y$-direction, we find that $\alpha_{yy}$ and $\kappa_{yy}$ are significantly larger than $\alpha_{xx}$ and $\kappa_{xx}$, respectively, due to the much larger squared Dirac velocity $v_y^2$ compared to $v_x^2$.