Spin-Valley Physics of TMDs Under Strain Explored

By Bhavna KavetiAug 15 2022Reviewed by Susha Cheriyedath, M.Sc.

Transition metal dichalcogenides are useful in investigating the manifestations of spin-valley physics under the external stimulus. A study published in the New Journal of Physics explored the effect of strain on orbital angular momenta, Berry curvatures, and effective g-factors via the ab initio method.

​​​​​​​Study: First-principles insights into the spin-valley physics of strained transition metal dichalcogenides monolayers. Image Credit: Andrey Keno/Shutterstock.com

The results revealed an unexpected decrease in spin expectation value of the conduction band under compressive strain at K-valleys, increasing the dark exciton’s dipole strength by more than one order of magnitude. Furthermore, the direct exciton’s g-factors under strain revealed that with an increase in tensile strain, the absolute value of g-factors increased.

One percent variation in strain modified the bright exciton’s g-factors by approximately 0.3 and 0.2 for tungsten (W) and molybdenum (Mo), and for dark exciton’s g-factors, it was approximately 0.5 and 0.3 for W and Mo, respectively. Conducting magneto-optical experiments helped visualize these predictions in the strained sample at low temperatures. The calculations suggested that the strain effect was a possible cause of g-factor fluctuations.

Furthermore, comparing different transition metal dichalcogenides revealed the direct correlation between spin-orbit coupling (SOC) and spin-valley. Under applied strain, the sensitivity of spin-valley features increased with SOC. Thus, monolayered tungsten selenide (WSe₂) was a suitable material to investigate the role of strain on spin-valley physics due to its high SOC.

Transition Metal Dichalcogenides

Transition metal dichalcogenides are van der Waals materials that enable investigations on fundamental and applied physics in electronics, optoelectronics, spintronics, opto-spintronics, and valleytronics. Monolayered transition metal dichalcogenides with hexagonal crystal structure and optical band gap are direct semiconductors with electrons and holes localized at first Brillouin zone’s K-points and signatures of excitons in the optical spectra.

The lack of crystal lattice’s inversion symmetry and the presence of heavy metal elements mark strong SOC physics at K-valleys via spin polarization in the out-of-plane direction. Thus, the spin-valley locking of holes and electrons allows selective excitation of exciton quasi-particles wither from K or -K valley.

To this end, magneto-optical spectroscopy helps explore the spin-valley physics of holes, electrons, and excitons in monolayered transition metal dichalcogenides. A valley Zeeman splitting is observed due to K and −K valleys degeneracy lifting under an external magnetic field.

Although the excitonic spectra measure the exciton g-factor, simultaneously accounting for the contributions of hole and electron. Additional emission peaks are required to estimate the individual contributions of valence and conduction bands in transition metal dichalcogenides.

In addition to spin-valley physics, transition metal dichalcogenides are suitable materials for straintronics. Applying controllable strain on them can adjust the exciton’s optical emission energy by several hundreds of millielectronvolts. Additionally, strain suppresses the nonradiative exciton recombination, preserving the photoluminescence’s quantum yield close to unity.

Spin-Valley Physics of Strained Transition Metal Dichalcogenides

The present study investigated the transition metal dichalcogenides with hexagonal crystal structures for their spin-valley physics under applied strain. Previously multiple phonon-mediated emission peaks were utilized to unravel the valence and band g-factors whose measurements were in concurrence with first-principles calculations. Here, the first-principles calculations helped evaluate the contribution of Bloch to the g-factors of the band.

In the current work, first-principles calculations helped evaluate spin and orbital angular momenta, effective g-factors, and Berry curvatures of molybdenum (MoS₂), molybdenum selenide (MoSe₂), molybdenum telluride (MoTe₂), tungsten sulfide (WS₂) and tungsten selenide (WSe₂).

K-valley under compressive strain showed an unexpected spin-mixing regime for the conduction band with spin-down electrons. The direct excitons originating from K-valley’s low energy bands (dark excitons) revealed two trends in the Zeeman effect.

An increasing trend in the g-factor’s absolute value was observed for positive strain value. On the other hand, a decreasing trend in the factor’s absolute value was observed for the negative strain value. Among various trends exhibited by transition metal dichalcogenides, the larger SOC effect made WSe₂ a suitable material to study the effect of strain on spin-valley physics.

While previous literature lacked the combination of magneto-optics and strained transition metal dichalcogenides. In this work, magneto-optics were used to probe the g-factor features in strained transition metal dichalcogenides, wherein connecting the dipole matrix elements with g-factor trends revealed that the dipole strength of the dark excitons was modified based on spin-mixing.

Conclusion

To conclude, transition metal dichalcogenides were explored to study their spin-valley physics under biaxial strain. Several transition metal dichalcogenides with hexagonal crystal structures were used to analyze orbital angular momenta, spin-mixing, g-factors, and Berry curvatures. The results revealed compressive strain-dependent spin-mixing features at the K-valleys.

Furthermore, the symmetry analysis of energy bands and SOC Hamiltonian revealed the mechanism behind the reduction of spin value (S_z) at K-valley was based on spin-flip coupling between the spin-down conduction band and the spin-up conduction band.

The present study established the impact of strain on the spin-valley properties of monolayered transition metal dichalcogenides. In addition to insights into these systems wherein the many effects competed with strain, the study helps investigate proximity effects and interlayer excitons in transition metal dichalcogenides and their heterostructures.

Reference

Junior, P.E.F., Zollner, K., Woźniak, T.,   Kurpas, M.,   Gmitra^, M., Fabian, J. (2022). First-Principles Insights into The Spin-Valley Physics of Strained Transition Metal Dichalcogenides Monolayers. New Journal of Physics. https://iopscience.iop.org/article/10.1088/1367-2630/ac7e21

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