Two-dimensional materials offer new opportunities for both fundamental science and technological applications, by exploiting the electron's spin 1 . While graphene is very promising for spin communication due to its extraordinary electron mobility, the lack of a band gap restricts its prospects for semiconducting spin devices such as spin diodes and bipolar spin transistors 2 . The recent emergence of 2D semiconductors could help overcome this basic challenge. In this letter we report the first important step towards making 2D semiconductor spin devices. We have fabricated a spin valve based on ultra-thin (~ 5 nm) semiconducting black phosphorus (bP), and established fundamental spin properties of this spin channel material which supports all electrical spin injection, transport, precession and detection up to room temperature (RT). Inserting a few layers of boron nitride between the ferromagnetic electrodes and bP alleviates the notorious conductivity mismatch problem and allows efficient electrical spin injection into an n-type bP. In the non-local spin valve geometry we measure Hanle spin precession and observe spin relaxation times as high as 4 ns, with spin relaxation lengths exceeding 6 µm. Our experimental results are in a very good agreement with first-principles calculations and demonstrate that Elliott-Yafet spin relaxation mechanism is dominant. We also demonstrate that spin transport in ultra-thin bP depends strongly on the charge carrier concentration, and can be manipulated by the electric field effect. 2 Electron spin is an important degree of freedom which can complement or even replace charge in information storage and logic devices 3 . For spin-based electronics, it is essential to have materials with long spin relaxation times at RT 1 . With respect to the material selection, semiconductors in particular offer new opportunities that are unfeasible in metal-based spintronics devices. These include doping by the electric field effect and gate controlled amplification/switching actions 4 . The boom of semiconductor spintronics started with the demonstration of the electrical spin injection into GaAs by R. Fiederling et al., also later by H.Ohno et al. 5,6 . I. Appelbaum and his colleagues further fostered this by adding silicon into the spintronics materials family 7 . More recently 2D materials such as graphene have captured the interest of engineers and scientists on the grounds of their high electronic mobility and the simultaneous ability to tune their charge carrier concentrations by the electric field effect 8 .Graphene has already been investigated very extensively in the spintronics community since the first unequivocal demonstration of RT spin injection by N. Tombros et al., 1,9 . While the first devices showed spin lifetimes of only 0.1 ns 9 , the new generation of graphene devices that have surfaces within the last year show remarkable spin lifetimes of ~ 10 ns, making graphene suitable for spin communication channels 10 .Conversely, the zero-band gap nature of graphene does not al...

The van-der-Waals stacking technique enables the fabrication of heterostructures, where two conducting layers are atomically close. In this case, the finite layer thickness matters for the interlayer electrostatic coupling. Here we investigate the electrostatic coupling of two graphene layers, twisted by θ = 22 • such that the layers are decoupled by the huge momentum mismatch between the K and K' points of the two layers. We observe a splitting of the zero-density lines of the two layers with increasing interlayer energy difference. This splitting is given by the ratio of single-layer quantum capacitance over interlayer capacitance Cm and is therefore suited to extract Cm. We explain the large observed value of Cm by considering the finite dielectric thickness dg of each graphene layer and determine dg ≈ 2.6Å. In a second experiment we map out the entire density range with a Fabry-Pérot resonator. We can precisely measure the Fermi-wavelength λ in each layer, showing that the layers are decoupled. We find that λ exceeds 600 nm at the lowest densities and can differ by an order of magnitude between the upper and lower layer. These findings are reproduced using tight-binding calculations. arXiv:1907.00582v1 [cond-mat.mes-hall] 1 Jul 2019 2 a b c d C hBN hBN 2xGraphene Graphite topgate C 2. 2μ m 2 . 3 μ m 3.5nm K b K' b θ K t K' t Sample A Sample B FIG. 1. a) Top-view and side-view of two aligned layers of graphene that are decoupled in the middle (blue part) by a thin intermediate layer of hBN. A graphite back gate and a local top gate allow to control the density and thereby the carrier wavelength in the upper-and lower layer individually. b) Using atomic force microscopy we measured the encapsulated hBN layer to be 3.5nm thick (sample A). c) Alternatively, the decoupling wavefunctions can be achieved by twisting two graphene layers (sample B). d) For large twist angles, the valleys in the upper/lower layer (Kt, K b ) are separated by a large momentum, leading to an effective electronic decoupling of the layers.The van-der-Waals stacking technique allows scientists to bring two conductive crystalline layers into atomically close proximity [1]. This has been exploited in a variety of experiments, including the formation of layer polarized, counter-propagating Landau levels [2] and experiments that build on strong capacitive coupling such as Coulomb-drag measurements [3] or interlayer exciton condensation [4,5].There are two main approaches of how to bring two conductive layers in close proximity, while suppressing an overlap of the layer wavefunctions: One approach introduces a thin layer of hexagonal Boron-Nitride (hBN) (see e.g. [3,4,6]) as depicted in Fig. 1a,b, and the other twists the layers by a large angle (θ > 5 • ) [2, 7-9]; see Fig. 1c,d. In the former case, decoupling is achieved by spatial separation. In the latter case, the layers are ultimately close, but they remain decoupled due to a large momentum mismatch (K t − K b ) between the upper and lower layer ( Fig. 1d). Experimental signatures of decoup...

The fundamental spin-orbit coupling and spin mixing in graphene and rippled honeycomb lattice materials silicene, germanene, stanene, blue phosphorene, arsenene, antimonene, and bismuthene is investigated from first principles. The intrinsic spin-orbit coupling in graphene is revisited using multi-band k · p theory, showing the presence of non-zero spin mixing in graphene despite the mirror symmetry. However, the spin mixing itself does not lead to the the Elliott-Yafet spin relaxation mechanism, unless the mirror symmetry is broken by external factors. For other aforementioned elemental materials we present the spin-orbit splittings at relevant symmetry points, as well as the spin admixture b 2 as a function of energy close to the band extrema or Fermi levels. We find that spin-orbit coupling scales as the square of the atomic number Z, as expected for valence electrons in atoms. For isolated bands, it is found that b 2 ∼ Z 4 . The spin-mixing parameter also exhibits giant anisotropy which, to a large extent, can be controlled by tuning the Fermi level. Our results for b 2 can be directly transferred to spin relaxation time due to the Elliott-Yafet mechanism, and therefore provide an estimate of the upper limit for spin lifetimes in materials with space inversion center.