Strain-tunable orbital, spin-orbit, and optical properties of monolayer transition-metal dichalcogenides

Abstract

When considering transition-metal dichalcogenides (TMDCs) in van der Waals (vdW) heterostructures for periodic ab-initio calculations, usually, lattice mismatch is present, and the TMDC needs to be strained. In this study we provide a systematic assessment of biaxial strain effects on the orbital, spin-orbit, and optical properties of the monolayer TMDCs using ab-initio calculations. We complement our analysis with a minimal tight-binding Hamiltonian that captures the low-energy bands of the TMDCs around K and K' valleys. We find characteristic trends of the orbital and spinorbit parameters as a function of the biaxial strain. Specifically, the orbital gap decreases linearly, while the valence (conduction) band spin splitting increases (decreases) nonlinearly in magnitude when the lattice constant increases. Furthermore, employing the Bethe-Salpeter equation and the extracted parameters, we show the evolution of several exciton peaks, with biaxial strain, on different dielectric surroundings, which are particularly useful for interpreting experiments studying strain-tunable optical spectra of TMDCs.

Evidence of the direct-to-indirect band gap transition in strained two-dimensional WS2 , MoS2 , and WSe2Blundo1, Felici2, Yildirim3 et al. 2020Phys. Rev. Research1306800View full textAdd to dashboardCite

“…The displayed fits yield A = 45 +1 −2 meV/ε%, E I (0) = 2.13 +0.07 −0.04 eV and I = 92 +17 −9 meV/ε% [E A (0) is fixed to 2.00 eV, the strain-free ML exciton energy]. These data compare rather favorably with the experimental [35,45], and theoretical [17,18,[20][21][22][24][25][26][27]46] ones as reported in Table I. However, we notice a large discrepancy between the E I (0)-E A (0) value derived in this work (130 meV) and those reported in other works.…”

“…We ascribe this band to the K CB -VB indirect band gap exciton. In fact, as predicted by numerous theoretical works [5,17,18,[20][21][22][23][24], the presence of strain in TMD MLs [17,18,[20][21][22][23][24][25]27] and bilayers [31,32] should result in a significant reordering of the energies of the critical points of the band structure. In particular, for tensile biaxial strains ε > 1% in WS 2 MLs [17,18,[20][21][22]24,25,27], the valence band maximum should change from the K to the point of the reciprocal space.…”

“…In fact, as predicted by numerous theoretical works [5,17,18,[20][21][22][23][24], the presence of strain in TMD MLs [17,18,[20][21][22][23][24][25]27] and bilayers [31,32] should result in a significant reordering of the energies of the critical points of the band structure. In particular, for tensile biaxial strains ε > 1% in WS 2 MLs [17,18,[20][21][22]24,25,27], the valence band maximum should change from the K to the point of the reciprocal space. Even though this change (i) is expected to occur for values of ε that are well within reach of current strain modulation techniques [31,[33][34][35], and (ii) should result in rather dramatic variations of the optical properties of the material, the currently available experimental evidence of this direct-to-indirect transition is either not particularly apparent [36][37][38][39] or absent [13,34,35,31].…”

“…The negative value of ε z all over the surface is caused by the membrane thinning following the in-plane tensile strain. The strain field across the dome is expected to induce remarkable changes in the electronic properties of the curved TMD membrane [5,[17][18][19][20][21][22][23][24][25][26][27], giving rise to the peculiar phenomenology displayed in Fig. 1(c).…”

“…ε transition is the equivalent uniaxial strain at which the band gap turns indirect. [27], 127−184 [20], 148 [46] ε transition (%)…”