Strain engineering of WS 2 , WSe 2 , and WTe 2

We perform first-principles calculations to investigate the structural, electronic, and vibrational properties of WS2 ,W Se 2, and WTe2 monolayers, taking into account the strong spin orbit coupling. A transition from a direct to an indirect band gap is achieved for compressive strain of 1% for WS2, 1.5% for WSe2, and 2% for WTe2, while the nature of the band gap remains direct in the case of tensile strain. The size of the band gap passes through a maximum under compressivestrainanddecreasesmonotonicallyundertensilestrain. A strong spin splitting is found for the valence band in all three compounds, which is further enhanced by tensile strain. The mobility of the electrons grows along the series WS2