First-principles insights into the spin-valley physics of strained transition metal dichalcogenides monolayers

Abstract

Transition metal dichalcogenides (TMDCs) are ideal candidates to explore the manifestation of spin-valley physics under external stimuli. In this study, we investigate the influence of strain on the spin and orbital angular momenta, effective g-factors, and Berry curvatures of several monolayer TMDCs (Mo and W based) using a full ab initio approach. At the K-valleys, we find a surprising decrease of the conduction band spin expectation value for compressive strain, consequently increasing the dipole strength of the dark exciton by more than one order of magnitude (for ∼ 1 % – 2 % strain variation). We also predict the behavior of direct excitons g-factors under strain: tensile (compressive) strain increases (decreases) the absolute value of g-factors. Strain variations of ∼1% modify the bright (A and B) excitons g-factors by ∼0.3 (0.2) for W (Mo) based compounds and the dark exciton g-factors by ∼0.5 (0.3) for W (Mo) compounds. Our predictions could be directly visualized in magneto-optical experiments in strained samples at low temperature. Additionally, our calculations strongly suggest that strain effects are one of the possible causes of g-factor fluctuations observed experimentally. By comparing the different TMDC compounds, we reveal the role of spin–orbit coupling (SOC): the stronger the SOC, the more sensitive are the spin-valley features under applied strain. Consequently, monolayer WSe2 is a formidable candidate to explore the role of strain on the spin-valley physics. We complete our analysis by considering the side valleys, Γ and Q points, and by investigating the influence of strain in the Berry curvature. In the broader context of valley- and strain-tronics, our study provides fundamental microscopic insights into the role of strain in the spin-valley physics of TMDCs, which are relevant to interpret experimental data in monolayer TMDCs as well as TMDC-based van der Waals heterostructures.

Signatures of Electric Field and Layer Separation Effects on the Spin-Valley Physics of MoSe2/WSe2 Heterobilayers: From Energy Bands to Dipolar Excitons

“…In this section, we explore the spin and orbital degrees of freedom for the relevant band edges (indicated in Figure 1 g) at zero electric field and at the equilibrium interlayer distance. We follow recent first-principles developments, to compute the orbital angular momenta in monolayer TMDCs [ 64 , 65 , 66 , 67 ], which has also been successfully applied to investigate a variety of more complex TMDC-based systems and van der Waals heterostructures [ 27 , 53 , 57 , 80 , 85 , 92 , 93 , 94 , 95 , 96 , 97 , 98 , 99 ]. We do not aim to provide a detailed description of the methodology here, but briefly summarize the main points.…”

“…[ 53 , 57 , 64 , 67 , 80 ] but here we extend our analysis to incorporate more bands, and later investigate the dependence of electric field and interlayer distance. We emphasize here that the electronic and spin properties calculated with the DFT also provide a reliable benchmark for further studies, as WIEN2k [ 81 ] is one of the most accurate DFT codes available [ 100 ], and is particularly suitable for studying the spin-physics of 2D materials and van der Waals heterostructures [ 23 , 24 , 27 , 95 , 101 , 102 , 103 , 104 , 105 ].…”

“…For the monolayer cases, we use the same in-plane lattice parameters and thicknesses as used in the heterostructure, so that we can directly compare the monolayer values of and to the heterostructure. The amount of strain of ∼0.1% for the in-plane lattice parameter has a very small influence on the spin-valley physics of individual monolayer TMDCs [ 77 , 95 ], with contributions in the order of from the unstrained values; therefore, any changes of are clear signatures of interlayer hybridization. For the heterostructure bands at the K point, , , and , we observe the typical sign changes from R to H stackings, because of the opposite K/K ( twist) and K/−K ( twist) alignment [ 20 , 64 ].…”

“…Furthermore, the effects of band mixing in the R stacking are less pronounced, because at zero field and at the equilibrium distance the values of have the same sign and similar magnitude, whereas in the H stacking, has the opposite sign, and any admixture of the energy bands can significantly alter . For the highly delocalized bands at and Q points, we find values of and that are in between the values of the individual MoSe and WSe monolayers, but still with , thus making spin the dominant degree of freedom, as in the monolayer case [ 95 ]. The g-factor values, , can be found by adding and (we also present graphically in the Section 3.2 and Section 3.3 , as a function of the electric field and interlayer distance).…”

Spin-polarization anisotropy controlled by bending in tungsten diselenide nanoribbons and tunable excitonic states

“…Frisenda et al 30 showed experimentally the redshift of both optical band gaps and exciton energies of several TMD monolayers with an increase in the biaxial strain, and the measured energy change of excitons in peak A for the WSe 2 monolayer is 63 meV for a 1% change of the strain. Faria et al 31 showed the effects of both biaxial strains and an external magnetic field on the spin–valley related properties of TMD monolayers.…”