Rabi oscillations in semiconductor multi-wave mixing response

We studied the semiconductor response with respect to high intensity resonant excitation on short time scale when the contribution of the Fermi statistics of the electrons and holes prevails. We studied both the single and double pulse excitations. For the latter case we considered the time evolution of the multi-wave mixing exciton polarization. The main difference between the excitation by a single pulse or by two non-collinear pulses is that the Rabi oscillations of the multi-wave mixing response are characterized by two harmonics. Analyzing the operator dynamics governed by the external excitation we found that there are three invariant spin classes, which do not mix with the evolution of the system. Two classes correspond to the bright exciton states and one contains all dark states. We found that the dynamics of the classes is described by six frequencies and the Rabi frequencies are only two of them (one for each bright class). We discuss the effect of the dispersion of the electrons and holes and the Coulomb interaction describing the semiconductor by the semiconductor Bloch equation (SBE). We show that if initially the system is in the ground state then the SBE preserves the invariant spin classes thus proving absence of the dark excitons in the framework of this description. We found that due to the mass difference between holes of different kind additional Rabi frequencies, two of those present in the operator dynamics, should appear in the evolution of the exciton polarization.Comment: 18 pages, 5 figure

Optical signatures of states bound to vacancy defects in monolayer MoS2_2

We show that pristine MoS$_2$ single layer (SL) exhibits two bandgaps $E_{g\parallel}=1.9$ eV and $E_{g\perp}=3.2$ eV for the optical in-plane and out-of-plane susceptibilities $\chi_\parallel$ and $\chi_\perp$, respectively. In particular, we show that odd states bound to vacancy defects (VDs) lead to resonances in $\chi_\perp$ inside $E_{g\perp}$ in MoS$_2$ SL with VDs. We use density functional theory, the tight-binding model, and the Dirac equation to study MoS$_2$ SL with three types of VDs: (i) Mo-vacancy, (ii) S$_2$-vacancy, and (iii) 3$\times$MoS$_2$ quantum antidot. The resulting optical spectra identify and characterize the VDs.Comment: 5 pages, 5 figure

Electronic and Optical Properties of Vacancy Defects in Transition Metal Dichalcogenides

A detailed first-principle study has been performed to evaluate the electronic and optical properties of single-layer (SL) transition metal dichalcogenides (TMDCs) (MX${}_2$; M= transition metal such as Mo, W and X= S, Se, Te), in the presence of vacancy defects (VDs). Defects usually play an important role in tailoring electronic, optical, and magnetic properties of semiconductors. We consider three types of VDs in SL TMDCs i) $X$-vacancy, $X_{2}$-vacancy, and iii) $M$-vacancy. We show that VDs lead to localized defect states (LDS) in the band structure, which in turn give rise to sharp transitions in in-plane and out-of-plane optical susceptibilities, $\chi_{\parallel}$ and $\chi_{\perp}$. The effects of spin orbit coupling (SOC) are also considered. We find that SOC splitting in LDS is directly related to the atomic number of the transition metal atoms. Apart from electronic and optical properties we also find magnetic signatures (local magnetic moment of $\sim\mu_{B}$) in MoSe$_{2}$ in the presence of Mo vacancy, which breaks the time reversal symmetry and therefore lifts the Kramers degeneracy. We show that a simple qualitative tight binding model (TBM), involving only the hopping between atoms surrounding the vacancy with an on-site SOC term, is sufficient to capture the essential features of LDS. In addition, the existence of the LDS can be understood from the solution of the 2D Dirac Hamiltonian by employing infinite mass boundary conditions. In order to provide a clear description of the optical absorption spectra, we use group theory to derive the optical selection rules between LDS for both $\chi_{\parallel}$ and $\chi_{\perp}$.Comment: 14 pages, 11 figure

Dirac electrons in the presence of matrix potential barrier: application to graphene and topological insulators

Scattering of a 2D Dirac electrons on a rectangular matrix potential barrier is considered using the formalism of spinor transfer matrices. It is shown, in particular, that in the absence of the mass term, the Klein tunneling is not necessarily suppressed but occurs at oblique incidence. The formalism is applied to studying waveguiding modes of the barrier, which are supported by the edge and bulk states. The condition of existence of the uni-directionality property is found. We show that the band of edge states is always finite with massless excitations, while the spectrum of the bulk states, depending on parameters of the barrier, may consist of the infinite or finite band with both, massive and massless, low-energy excitations. The effect of the Zeeman term is considered and the condition of appearance of two distinct energy dependent directions corresponding to the Klein tunneling is found.Comment: published versio