Anomalous photo-thermal effects in multi-layered semi-Dirac black phosphorus

Abstract

The multi-layered potassium-doped black phosphorus (BP) is a gapped semi-Dirac two-dimensional normal insulator (NI), and can be transformed into a time-reversal symmetry broken Chern insulator (CI) through photo-excitation with a high-frequency photon beam. This transition from an NI to CI, modeled within the Floquet theory of periodic perturbations, introduces non-trivial topological features to BP dispersion manifesting in a finite Berry curvature (Ω). We utilize Ω, the dispersion-governed internal momentum-dependent magnetic field, in conjunction with a longitudinal temperature gradient to examine a pair of anomalous thermoelectric effects which pertain to the transverse heat flow in BP in the CI phase in the absence of an external magnetic field. The anomalous variants of the Ettinghausen (EE) and Righi–Leduc effects (RLE) are quantitatively analyzed via their respective coefficients in this work. The strength of anomalous EE and RLE coefficients is found to be a direct outcome of the sum of Berry curvatures over the occupied bands and is shown to drop as the Fermi level (μ) is positioned high in the conduction states or deep in the valence region. In contrast, for a μ placed in the bandgap, much larger values of the coefficients are predicted. The position of μ and the strength of Ω serve as effective regulators for the EE and RLE coefficients. Finally, we point out how beyond the role of Ω and μ, several laboratory accessible methods can be utilized to modulate the EE and RLE coefficients, including an application of strain, variations in dopant concentration, and the energy fluence of incident radiation.