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We calculate the optical conductivity of an anisotropic two-dimensional system with Rashba spin-flip excitation within the Kubo formalism. We show that the anisotropic Rashba effect caused by an external field changes significantly the magnitude of the spin splitting. Furthermore, we obtain an analytical expression for the longitudinal optical conductivity associated with inter-band transitions as a function of the frequency for an arbitrary polarization angle. We find that the diagonal components of the optical conductivity tensor are direction-dependent and the spectrum of optical absorption is strongly anisotropic with an absorption window. The height and width of this absorption window are very sensitive to the system anisotropy. While the height of absorption peak increases with increasing effective mass anisotropy ratio, the peak intensity is larger when the light polarization is along the armchair direction. Moreover, the absorption peak width becomes broader as the density of state mass or Rashba interaction is enhanced. These features can be used to determine parameters relevant for spintronics through the optical absorption spectrum.

We theoretically study the Coulomb drag resistivity in a double-layer electron system with highly anisotropic parabolic band structure using Boltzmann transport theory. As an example, we consider a double-layer phosphorene on which we apply our formalism. This approach, in principle, can be tuned for other double-layered systems with paraboloidal band structures. Our calculations show the rotation of one layer with respect to another layer can be considered a way of controlling the drag resistivity in such systems. As a result of rotation, the off-diagonal elements of drag resistivity tensor have non-zero values at any temperature. In addition, we show that the anisotropic drag resistivity is very sensitive to the direction of momentum transfer between two layers due to highly anisotropic inter-layer electron-electron interaction and also the plasmon modes. In particular, the drag anisotropy ratio, ρ yy /ρ xx , can reach up to ∼ 3 by changing the temperature. Furthermore, our calculations suggest that including the local field correction in dielectric function changes the results significantly. Finally, We examine the dependence of drag resistivity and its anisotropy ratio on various parameters like inter-layer separation, electron density, short-range interaction and insulating substrate/spacer.

Excitonic superfluidity in double phosphorene monolayers is investigated using the BCS mean-field equations. Highly anisotropic superfluidity is predicted where we found that the maximum superfluid gap is in the BEC regime along the armchair direction and in the BCS-BEC crossover regime along the zigzag direction. We estimate the highest Kosterlitz-Thouless transition temperature with maximum value up to ∼ 90 K with onset carrier densities as high as 4 × 10 12 cm −2 . This transition temperature is significantly larger than what is found in double electron-hole few-layers of graphene. Our results can guide experimental research towards the realization of anisotropic condensate states in electron-hole phosphorene monolayers.

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