We propose to engineer time-reversal-invariant topological insulators in two-dimensional (2D) crystals of transition metal dichalcogenides (TMDCs). We note that, at low doping, semiconducting TMDCs under shear strain will develop spin-polarized Landa
u levels residing in different valleys. We argue that gaps between Landau levels in the range of $10-100$ Kelvin are within experimental reach. In addition, we point out that a superlattice arising from a Moire pattern can lead to topologically non-trivial subbands. As a result, the edge transport becomes quantized, which can be probed in multi-terminal devices made using strained 2D crystals and/or heterostructures. The strong $d$ character of valence and conduction bands may also allow for the investigation of the effects of electron correlations on the topological phases.
We propose a theory of spin relaxation of electrons and holes in two-dimensional hexagonal crystals such as atomic layers of transition metal dichalcogenides (MoS2, WSe2, etc). We show that even in intrinsically defectless crystals, their flexural de
formations are able to generate spin relaxation of carriers. Based on symmetry analysis, we formulate a generic model for spin-lattice coupling between electrons and flexural deformations, and use it to determine temperature and material-dependent spin lifetimes in atomic crystals in ambient conditions.
We study the intra-valley spin-orbit mediated spin relaxation in monolayers of MoS2 within a two bands effective Hamiltonian. The intrinsic spin splitting of the valence band as well as a Rashba-like coupling due to the breaking of the out-of-plane i
nversion symmetry are considered. We show that, in the hole doped regime, the out-of-plane spin relaxation is not very efficient since the spin splitting of the valence band tends to stabilize the spin polarization in this direction. We obtain spin lifetimes larger than nanoseconds, in agreement with recent valley polarization experiments.
We analyze the couplings between spins and phonons in graphene. We present a complete analysis of the possible couplings between spins and flexural, out of plane, vibrations. From tight-binding models we obtain analytical and numerical estimates of t
heir strength. We show that dynamical effects, induced by quantum and thermal fluctuations, significantly enhance the spin-orbit gap.
