Probing topological signatures in an optically driven α−T3 lattice

The $\alpha \text{−}{T}_3$ lattice, an interpolation model between the honeycomb lattice of $\mathrm{graphene}(\alpha =0$) and the dice $\mathrm{lattice}(\alpha =1$), undergoes a topological phase transition across $\alpha =1/\sqrt{2}$ when exposed to a circularly polarized off-resonant light. In this work, several features of the topological transition have been captured via various Berry phase mediated magnetic and thermoelectric effects. For instance, both the Berry curvature and the orbital magnetic moment associated with the flat band change their respective signs across $\alpha =1/\sqrt{2}$. The orbital magnetization varies linearly with the chemical potential in the forbidden gaps of the quasienergy spectrum. The slope of the orbital magnetization in the gap changes by one unit of $e/h$ as soon as $\alpha$ crosses the value $1/\sqrt{2}$ which is a direct manifestation of the corresponding change in Chern number by one unit. While the anomalous Nernst coefficient vanishes in the gaps, the anomalous Hall conductivity, however, gets quantized in a different manner on either side of $\alpha =1/\sqrt{2}$. The broken particle-hole symmetry for $0<\alpha <1$ offers valley-contrasting features in the thermoelectric coefficients as well as in the orbital magnetization which further open up the possibility to use the underlying driven system in the valley caloritronic applications.