Moiré band structures of twisted phosphorene bilayers

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