Interplay of spin, valley and layer pseudospins in folded MoS$_{2}$ bilayers

Two dimensional material such as graphene and transition metal dichalcogenide is much like a piece of sheet paper. Different from sheet paper, each of two dimensional materials has its own crystal lattice. Folding of two dimensional materials can make artificial bilayer or even multilayer structures, whose structural symmetry depend on how the folding line is oriented relative to the crystal lattice. The folded artificial structures with different stacking orders are also expected to tune the interlayer coupling, thus leading to unusual behaviors and new phenomena. In this talk, I will present our recent study of folded MoS$_{2}$ bilayers, which were obtained by folding exfoliated MoS$_{2}$ monolayers. As characterized by second harmonic generation and photoluminescence, folded bilayers can exhibit broken inversion symmetry and reduced interlayer coupling, evoking strong valley and/or spin polarizations that were not achieved in natural MoS$_{2}$ bilayer of Bernal stacking. Our work provides an effective and versatile means to understand the interaction between spin, valley and layer pseudospin degrees of freedom in MoS2 bilayer and engineer transition metal dichalcogenide materials with desirable electronic and optical properties.