Nonlinear optical selection rules of excitons in monolayer transition metal dichalcogenides

Abstract

We propose an analytical approach for calculating the linear and nonlinear optical (NLO) responses of monolayer transition metal dichalcogenides (TMDs) including excitonic effects. An effective Hamiltonian reproducing the trigonal warping (TW) of the energy dispersion, is used to derive analytical expressions for excitonic matrix elements. Based on this approach, we provide an informative diagram, which encompasses all excitonic selection rules. The diagram enables us to identify main transitions for the first-, second-and thirdorder optical responses. As a case study, we calculate the optical conductivity and second/third harmonic generation responses of monolayer MoS 2 and demonstrate that the analytical approach accurately reproduces the spectra obtained using the Bethe-Salpeter equation (BSE). Therefore, the analytical approach provides an efficient and reliable method for calculating the NLO spectra as accurate as the full BSE method. Moreover, it enables us to obtain valuable physical insight into the fundamental transitions responsible for individual resonances, which is not straightforward in the full BSE method.

Exciton absorption, band structure, and optical emission in biased bilayer graphene

“…These extrema are denoted mini-valleys, and the inter-mini-valley (IMV) vector between these k IMV . The mini-valleys play an important role for the brightness of the ground state exciton since its small, but non-zero, transition dipole moment is a consequence of the symmetry breaking induced by trigonal warping [8,9,19]. In fact, without trigonal warping (i.e., with full rotational symmetry around K and K ) the ground state exciton is completely dark [8,9].…”

Nonlinear spectroscopy of excitonic states in transition metal dichalcogenides

“…carrier spin, v F is the Fermi velocity, ∆ is the gap between the conduction and the valence bands, and λ c,v are the spin splittings of the conduction c and valence v bands. The Fermi velocity is given as hv F = ∆/2m [50], and the trigonal warping constant is determined as 56,58]. Finally, we assume the following model to describe the dependence of the bandgap on the dielectric environment [59]…”

Calculation of the nonlinear response functions of intra-exciton transitions in two-dimensional transition metal dichalcogenides

“…In Ref. [21] an analytical study of the nonlinear optical response of monolayer TMDs was presented. Due to their broken inversion symmetry TMDs are not centrosymmetric (at least when stacked in an odd number of layers), and as a consequence both even and odd orders of non linear optical processes are always permitted [22].…”

“…Due to their broken inversion symmetry TMDs are not centrosymmetric (at least when stacked in an odd number of layers), and as a consequence both even and odd orders of non linear optical processes are always permitted [22]. Moreover, these materials shown large nonlinear optical coefficients [21], increasing their potential for applications, such as optical modulators [23,24]. The possibility of characterizing different properties of the 2D material from their nonlinear optical response has also been considered [25,26].…”