Phononic thermal conductivity in silicene: the role of vacancy defects and boundary scattering

We calculate the thermal conductivity of free-standing silicene using the phonon Boltzmann transport equation within the relaxation time approximation. In this calculation, we investigate the effects of sample size and different scattering mechanisms such as phonon-phonon, phonon-boundary, phonon-isotope and phonon-vacancy defect. Moreover, the role of different phonon modes is examined. We show that, in contrast to graphene, the dominant contribution to the thermal conductivity of silicene originates from the in-plane acoustic branches, which is about 70\% at room temperature and this contribution becomes larger by considering vacancy defects. Our results indicate that while the thermal conductivity of silicene is significantly suppressed by the vacancy defects, the effect of isotopes on the phononic transport is small. Our calculations demonstrate that by removing only one of every 400 silicon atoms, a substantial reduction of about 58\% in thermal conductivity is achieved. Furthermore, we find that the phonon-boundary scattering is important in defectless and small-size silicene samples, specially at low temperatures.Comment: 9 pages, 11 figure

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

Many-body effects due to the electron-electron interaction in silicene under an applied exchange field:The case of valley-spin coupling

We investigate the many-body effects induced by the electron–electron interaction in a valley–spin-polarized silicene under a perpendicularly applied exchange field. We calculate the real and imaginary parts of the self-energy within the leading order dynamical screening approximation where the screened interaction is obtained from the random phase approximation. Our study on the valley- and spin-dependent real and imaginary parts of the self-energy indicates that the different coupled valley–spin subbands may exhibit distinct characteristics. Moreover, we obtain the corresponding spectral functions and find that the plasmaron and quasiparticle peaks have different spectral weights and broadenings in all states. Interestingly, it seems that there are clear dependencies for the position and broadening of the peaks on valley–spin indexes. In addition, we study the effect of the electron–electron interaction on the renormalized velocity in the on-shell approximation and show that the renormalized velocity in gapped states becomes greater, and in gapless states, it becomes smaller as the wave vector grows

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

Competing effects of strain and vacancy defect on thermal conductivity of silicene: A computational study

We theoretically investigate the thermal conductivity of freestanding silicene under isotropic tensile strain in a wide range of temperature and in the presence of important scatterings. Based on the phonon Boltzmann transport equation within the relaxation time approximation and using the strain-dependent force constants obtained from the first-principle calculations, we calculate the variations of thermal conductivity of strained infinite and finite-size silicene with the single-vacancy defects and boundary scatterings and compare them with those in the case of unstrained silicene. Particularly, we are interested in exploring the competition between the two opposing effects; strain induces enhancement and vacancy defects cause reduction in thermal conductivity. We show that the presence of vacancy defects has a more remarkable and much stronger effect in strained silicene and is able to remove or shift the peak created by strain in the thermal conductivity of infinite silicene. Interestingly, we find that the thermal conductivity suppression due to the vacancy defects varies with strain. Furthermore, presented results indicate that by increasing the temperature, the thermal conductivity becomes less sensitive to the strain and the difference between infinite and finite size samples gradually disappears. Finally, our calculations show that the effect of specularity parameter of boundary scattering is more pronounced at intermediate strain values

A theoretical study of collective plasmonic excitations in double-layer silicene at finite temperature

We explore the temperature-dependent plasmonic modes of an n-doped double-layer silicene system which is composed of two spatially separated single layers of silicene with a distance large enough to prevent interlayer electron tunneling. By applying an externally applied electric field, we numerically obtain the poles of the loss function within the so-called random phase approximation to investigate the effects of temperature and geometry on the plasmon branches in three different regimes: topological insulator, valley-spin polarized metal, and band insulator. Also, we present the finite-temperature numerical results along with the zero-temperature analytical ones to support a discussion of the distinct effects of the external electric field and temperature on plasmon dispersion. Our results show that at zero temperature both the acoustic and optical modes decrease when the applied electric field is increased and experience a discontinuity at the valley-spin polarized metal phase as the system transitions from a topological insulator to a band insulator. At finite temperature, the optical plasmons are damped around this discontinuity, and the acoustic modes may exhibit a continuous transition. Moreover, while the optical branch of plasmons changes non-monotonically and noticeably with temperature, the acoustic branch dispersion displays a negligible growth with temperature for all phases of silicene. Furthermore, our finite-temperature results indicate that the dependency of two plasmonic branches on the interlayer separation is not affected by temperature at long wavelengths; the acoustic mode energy varies slightly with an increase in the interlayer distance, whereas the optical mode remains unchanged

Plasmon-phonon coupling in a valley-spin-polarized two-dimensional electron system: A theoretical study on monolayer silicene

We study the hybrid excitations due to the coupling between surface optical phonons of a polar insulator substrate and plasmons in the valley-spin-polarized metal phase of silicene under an exchange field. We perform the calculations within the generalized random-phase approximation where the plasmon-phonon coupling is taken into account by the long-range Fröhlich interaction. Our investigation on two hybridized plasmon branches in different spin and valley subbands shows distinct behavior compared to the uncoupled case. Interestingly, in one valley, it is found that while the high-energy hybrid branch is totally damped in the spin-up state, it can be well defined in the spin-down state. Moreover, we show that the electron-phonon coupling is stronger in both spin-down subbands, regardless of valley index, due to their higher electron densities. In addition, we study the effects of electron-phonon coupling on the quasiparticle scattering rate of four distinct spin-valley locked subbands. The results of our calculations predict a general enhancement in the scattering rate for all subbands and a jump in the case of spin-down states. This sharp increase associated with the damping of hybrid plasmon modes is almost absent in the uncoupled case. The results suggest an effective way for manipulating collective modes of valley-spin-polarized silicene which may become useful in future valleytronic and spintronic applications