Valley drift and valley current modulation in strained monolayer MoS2

Abstract

Elastic-mechanical deformations are found to dramatically alter the electronic properties of monolayer (ML) $\mathrm{Mo}{\mathrm{S}}_{2}$; particularly, the low-energy Bloch bands are responsive to a directional strain. In this study, in-plane uniaxial deformation is found to drift the low-energy electron/hole valleys of strained $\mathrm{ML}\text{\ensuremath{-}}\mathrm{Mo}{\mathrm{S}}_{2}$ far away from $K/K'$ points in the Brillouin zone (BZ). The amount of drift differs notably from hole to electron bands, where the conduction band minimum (CBM) drifts nearly 2 times more than the valence band maximum (VBM) in response to a progressively increasing strain field (0--10%). The resulting strain-induced valley asymmetry/decoherence can lift the momentum degeneracy of valley carriers at the $K$ point, thereby affecting the low-energy valley excitations ($K$-valley polarization) in a strained $\mathrm{ML}\text{\ensuremath{-}}\mathrm{Mo}{\mathrm{S}}_{2}$ lattice. The quantum origin of this decoherent valley arises from the differences in the Bloch orbital wave functions of electron and hole states at the exciton band edges and their deformation under strain. A higher drift (g1.5 times) is noticed when strain is along the zigzag (ZZ) axis relative to the armchair (AC) axis, which is attributed to a faster decline in Young's modulus and Poisson's ratio (PR) along the ZZ direction. A similar valley drift only in the VBM of uniaxially strained $\mathrm{ML}\text{\ensuremath{-}}\mathrm{Mo}{\mathrm{S}}_{2}$ was reported in an earlier local density approximation (LDA) based density functional theory (DFT) study [Q. Zhang et al., Phys. Rev. B 88, 245447 (2013)], where a massive valley drift occurring at the CBM was fully overlooked. Moreover, the giant VBM drift reported therein is 6 times the drift observed in our DFT studies based on spin-orbit coupling (SOC) and Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA) functionals. The physical origin of valley drift has been ascertained in our thorough investigations. The robustness of our approach is substantiated as follows. With progressive increase in strain magnitude (0--10%), the band gap remains direct up to 2% uniaxial tensile strain, under SOC, which accurately reproduces the experimental strain-induced direct-to-indirect band gap transitions occurring at \ensuremath{\sim}2% strain. Based on LDA-DFT [Q. Zhang et al., Phys. Rev. B 88, 245447 (2013)], this crossover in band gap has been incorrectly reported to occur at a higher value of uniaxial strain of 4%. Moreover, the direct SOC band gap shows a linear redshift at a rate of 51--53 meV/(% of strain), under uniaxial tensile strain, which is in excellent quantitative agreement with experimentally observed rates in the redshift of direct excitonic transitions measured in several optical absorption and photoluminescence (PL) spectroscopy experiments. In addition, the Berry curvature \textohm{}($k$) of electron/hole bands gets significantly modulated in strained $\mathrm{ML}\text{\ensuremath{-}}\mathrm{Mo}{\mathrm{S}}_{2}$, where the intensity of the flux profile increases as a function of the magnitude of strain with an opposite drift around $K/K'$, when strained along the ZZ/AC direction. A strong strain-valley coupling leads to an enhancement in the strength of spin-orbit induced spin splitting of bands at VBM/CBM, which is sizably enhanced (\ensuremath{\sim}7 meV) simply by the strain-controlled orbital motions. Our findings are of prime importance in the valley physics of $\mathrm{Mo}{\mathrm{S}}_{2}$. Besides, the important theoretical insights emerging from this work will trigger further experimental investigations on $\mathrm{ML}\text{\ensuremath{-}}\mathrm{Mo}{\mathrm{S}}_{2}$ to realize its novel technological potential in nanoelectronics, spintronics, and valleytronics.