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The two-dimensional (2D) MA2Z4 family has received extensive attention inmanipulating its electronic structure and achieving intriguing physicalproperties. However, engineering the electronic properties remains a challenge.Herein, based on first-principles calculations, we systematically investigatethe effect of biaxial strains on the electronic structures of 2D RashbaMoSiGeN4 (MSGN), and further explore how the interlayer interactions affect theRashba spin splitting in such strained layered MSGNs. After applying biaxialstrains, the band gap decreases monotonically with increasing tensile strainsbut increases when the compressive strains are applied. Anindirect-direct-indirect band gap transition is induced by applying a moderatecompressive strain (< 5%) in the MSGNs. Due to the symmetry breaking andmoderate spin-orbit coupling (SOC), the monolayer MSGN possess an isolatedRashba spin splitting (R) near the Fermi level, which could be effectivelyregulated to the Lifshitz transition (L) by biaxial strain. For instance, aL-R-L transformation of Fermi surface is presented in monolayer and a morecomplex and changeable L-R-L-R evolution is observed in bilayer and trilayerMSGNs as the biaxial strain vary from -8% to 12%, which actually depend on theappearance, variation, and vanish of the Mexican hat band in the absence of SOCunder different strains. The contribution of Mo-dz2 orbital hybridized withN-pz orbital in the highest valence band plays a dominant role on the bandevolution under biaxial strains, where the R-L evolution corresponds to thedecreased Mo-dz2 orbital contribution. Our study highlights the biaxial straincontrollable Rashba spin splitting, in particular the introduction and even theevolution of Lifshitz transition near Fermi surface, which makes the strainedMSGNs as promising candidates for future applications in spintronic devices.

Biaxial strain modulated electronic structures of layered two-dimensional MoSiGeN4 Rashba systems