Continuum mechanics break down in bending stiffness calculations of mono- and few-layered two-dimensional (2D) van der Waals crystal sheets, because their layered atomistic structures are uniquely characterized by strong in-plane bonding coupled with weak interlayer interactions. Here, we elucidate how the bending rigidities of pristine mono- and few-layered molybdenum disulfide (MoS 2 ), graphene, and hexagonal boron nitride (hBN) are governed by their structural geometry and intra- and inter-layer bonding interactions. Atomic force microscopy experiments on the self-folded conformations of these 2D materials on flat substrates show that the bending rigidity of MoS 2 significantly exceeds those of graphene or hBN of comparable layers, despite its much lower tensile modulus. Even on a per-thickness basis, MoS 2 is found to possess similar bending stiffness to hBN and is much stiffer than graphene. Density functional theory calculations suggest that this high bending rigidity of MoS 2 is due to its large interlayer thickness and strong interlayer shear, which prevail over its weak in-plane bonding.
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Electric fields and substrates dramatically accelerate spin relaxation in graphene
Electrons in graphene are theoretically expected to retain spin states much longer than most materials, making graphene a promising platform for spintronics and quantum information technologies. Here, we use first-principles density-matrix (FPDM) dynamics simulations to show that interaction with electric fields and substrates strongly enhances spin relaxation through scattering with phonons. Consequently, the relaxation time at room temperature reduces from microseconds in free-standing graphene to nanoseconds in graphene on the hexagonal boron nitride (hBN) substrate, which is the order of magnitude typically measured in experiments. Further, inversion symmetry breaking by hBN introduces a stronger asymmetry in electron and hole spin lifetimes than predicted by the conventional D'yakonov-Perel' (DP) model for spin relaxation. Deviations from the conventional DP model are stronger for in-plane spin relaxation, resulting in out-of-plane to in-plane lifetime ratios much greater than 1/2 with a maximum close to the Dirac point. These FPDM results, independent of symmetry-specific assumptions or material-dependent parameters, also validate recent modifications of the DP model to explain such deviations. Overall, our results indicate that spin-phonon relaxation in the presence of substrates may be more important in graphene than typically assumed, requiring consideration for graphene-based spin technologies at room temperature.
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- Award ID(s):
- 1956015
- PAR ID:
- 10347316
- Date Published:
- Journal Name:
- Physical review
- Volume:
- 105
- ISSN:
- 2469-9985
- Page Range / eLocation ID:
- 115122
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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