Moir? band structures of twisted phosphorene bilayers

We report on the theoretical electronic spectra of twisted phosphorene bilayers exhibiting moir patterns, as computed by means of a continuous approximation to the moir superlattice Hamiltonian. Our model is constructed by interpolating between effective I'-point conduction-and valence-band Hamiltonians for the different stacking configurations approximately realized across the moir supercell, formulated on symmetry grounds. We predict the realization of three distinct regimes for P-point electrons and holes at different twist angle ranges: a Hubbard regime for small twist angles 0 < 2, where the electronic states form arrays of quantum-dot-like states, one per moir supercell; a Tomonaga-Luttinger regime at intermediate twist angles 2 degrees < theta less than or similar to 10 degrees, characterized by the appearance of arrays of quasi-1D states; and, finally, a ballistic regime at large twist angles 0 10, where the band-edge states are delocalized, with dispersion anisotropies modulated by the twist angle. Our method correctly reproduces recent results based on large-scale ab initio calculations at a much lower computational cost and with fewer restrictions on the twist angles considered.

Automated summary

We present the theoretical electronic spectra of twisted phosphorene bilayers with moiré patterns, calculated using a continuous approximation to the moiré superlattice Hamiltonian. Three distinct regimes for P-point electrons and holes at different twist angle ranges are predicted: a Hubbard regime for small twist angles (0 < 2), a Tomonaga-Luttinger regime at intermediate twist angles (2 degrees < theta < 10 degrees), and a ballistic regime at large twist angles (0 > 10). Our method provides accurate results similar to large-scale ab initio calculations, but with lower computational cost and fewer restrictions on twist angles.