Anisotropic hybrid excitation modes in monolayer and double-layer phosphorene on polar substrates

We investigate the anisotropic hybrid plasmon-SO phonon dispersion relations in monolayer and double-layer phosphorene systems located on the polar substrates, such as SiO2, h-BN and Al2O3. We calculate these hybrid modes with using the dynamical dielectric function in the RPA by considering the electron-electron interaction and long-range electric field generated by the substrate SO phonons via Frohlich interaction. In the long-wavelength limit, we obtain some analytical expressions for the hybrid plasmon-SO phonon dispersion relations which represent the behavior of these modes akin to the modes obtaining from the loss function. Our results indicate a strong anisotropy in plasmon-SO phonon modes, whereas they are stronger along the light-mass direction in our heterostructures. Furthermore, we find that the type of substrate has a significant effect on the dispersion relations of the coupled modes. Also, by tuning the misalignment and separation between layers in double-layer phosphorene on polar substrates, we can engineer the hybrid modes.Comment: 10 pages, 7 figure

High temperature electron-hole superfluidity with strong anisotropic gaps in double phosphorene monolayers

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 $\sim 90$ K with onset carrier densities as high as $4 \times 10^{12}$ 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.Comment: 7 pages, 4 figure

Coulomb drag in anisotropic systems: a theoretical study on a double-layer phosphorene

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, \r{ho}yy/\r{ho}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.Comment: 10 pages, 9 figure

Plasmon modes in monolayer and double-layer black phosphorus under applied uniaxial strain

We study the effects of an applied in-plane uniaxial strain on the plasmon dispersions of monolayer, bilayer, and double-layer black phosphorus structures in the long-wavelength limit within the linear elasticity theory. In the low-energy limit, these effects can be modeled through the change in the curvature of the anisotropic energy band along the armchair and zigzag directions. We derive analytical relations of the plasmon modes under uniaxial strain and show that the direction of the applied strain is important. Moreover, we observe that along the armchair direction, the changes of the plasmon dispersion with strain are different and larger than those along the zigzag direction. Using the analytical relations of two-layer phosphorene systems, we found that the strain-dependent orientation factor of layers could be considered as a means to control the variations of the plasmon energy. Furthermore, our study shows that the plasmonic collective modes are more affected when the strain is applied equally to the layers compared to the case in which the strain is applied asymmetrically to the layers. We also calculate the effect of strain on the drag resistivity in a double-layer black phosphorus structure and obtain that the changes in the plasmonic excitations, due to an applied strain, are mainly responsible for the predicted results. This study can be readily extended to other anisotropic two-dimensional materials

Electron–hole superfluidity in strained Si/Ge type II heterojunctions

Excitons are promising candidates for generating superfluidity and Bose–Einstein condensation (BEC) in solid-state devices, but an enabling material platform with in-built band structure advantages and scaling compatibility with industrial semiconductor technology is lacking. Here we predict that spatially indirect excitons in a lattice-matched strained Si/Ge bilayer embedded into a germanium-rich SiGe crystal would lead to observable mass-imbalanced electron–hole superfluidity and BEC. Holes would be confined in a compressively strained Ge quantum well and electrons in a lattice-matched tensile strained Si quantum well. We envision a device architecture that does not require an insulating barrier at the Si/Ge interface, since this interface offers a type II band alignment. Thus the electrons and holes can be kept very close but strictly separate, strengthening the electron–hole pairing attraction while preventing fast electron–hole recombination. The band alignment also allows a one-step procedure for making independent contacts to the electron and hole layers, overcoming a significant obstacle to device fabrication. We predict superfluidity at experimentally accessible temperatures of a few Kelvin and carrier densities up to ~6 × 1010 cm−2, while the large imbalance of the electron and hole effective masses can lead to exotic superfluid phases