Electronic transport in single or a few layers of graphene is the subject of intense interest at present. The specific band structure of graphene, with its unique valley structure and Dirac neutrality point separating hole states from electron states, has led to the observation of new electronic transport phenomena such as anomalously quantized Hall effects, absence of weak localization and the existence of a minimum conductivity. In addition to dissipative transport, supercurrent transport has also been observed. Graphene might also be a promising material for spintronics and related applications, such as the realization of spin qubits, owing to the low intrinsic spin orbit interaction, as well as the low hyperfine interaction of the electron spins with the carbon nuclei. Here we report the observation of spin transport, as well as Larmor spin precession, over micrometre-scale distances in single graphene layers. The 'non-local' spin valve geometry was used in these experiments, employing four-terminal contact geometries with ferromagnetic cobalt electrodes making contact with the graphene sheet through a thin oxide layer. We observe clear bipolar (changing from positive to negative sign) spin signals that reflect the magnetization direction of all four electrodes, indicating that spin coherence extends underneath all of the contacts. No significant changes in the spin signals occur between 4.2 K, 77 K and room temperature. We extract a spin relaxation length between 1.5 and 2 mum at room temperature, only weakly dependent on charge density. The spin polarization of the ferromagnetic contacts is calculated from the measurements to be around ten per cent.

We present a fast method to fabricate high quality heterostructure devices by picking up crystals of arbitrary sizes. Bilayer graphene is encapsulated with hexagonal boron nitride to demonstrate this approach, showing good electronic quality with mobilities ranging from 17 000 cm 2 V −1 s −1 at room temperature to 49 000 cm 2 V −1 s −1 at 4.2 K, and entering the quantum Hall regime below 0.5 T. This method provides a strong and useful tool for the fabrication of future high quality layered crystal devices.A critical step for high mobility graphene device fabrication and the rising field of van der Waals heterostructures[1] is marked by the development of polymer based dry transfer methods for two-dimensional (2D) crystals. [2][3][4][5] With these methods, high quality graphene devices on hexagonal boron nitride (h-BN) and more complicated stacks have become generally accessible, but the early methods face a major setback. The method of stacking the crystals one by one typically leaves each transferred crystal contaminated by polymer. To obtain a high quality device, thorough cleaning is required before proceeding with device fabrication or measurement. This cleaning step typically involves several hours of annealing [3][4][5] or it may go as far as nanobrooming the entire graphene flake using contact mode atomic force microscopy (AFM). [6,7] Altogether this makes the fabrication of a multilayer heterostructure not only very time consuming, but also risky as each step may again introduce contaminants to the stack. This issue has recently been overcome by L. Wang et al. [8], introducing a method that allows for polymer free assembly of layered materials based on van der Waals force. Instead of depositing a 2D crystal, e.g. h-BN, directly on top of another crystal, e.g. graphene, one can use the h-BN to pick up the graphene from the substrate. This can be done because the van der Waals force between the atomically flat h-BN and graphene is stronger than between the graphene or the h-BN and the rough SiO 2 substrate. The power of this method lies in the fact that now the interface between the two crystals has not been contaminated by polymer, and one can directly pick up the next crystal. This way the materials inside the stack not only remain much cleaner, but a stack can also be fabricated considerably faster. One problem when using this method is the reduced capability to pick up graphene flakes larger than the used top h-BN crystal. Therefore one has to etch through the stack before making one-dimensional (1D) contacts to the graphene. While resulting in very high quality devices with electron mean free paths up to 21 µm and good electrical * pj.zomer@gmail.com contact, [8] this limitation can be problematic for certain device types for which 1D contacts are not desirable, e.g. spintronic devices that include tunnel barriers at the contact interface. [9] In this letter we present a method which allows for fabrication of high quality graphene devices encapsulated in h-BN by successively picking up crystals. The a...

We present electronic transport measurements of single-and bilayer graphene on commercially available hexagonal boron nitride. We extract mobilities as high as 125 000 cm 2 V −1 s −1 at room temperature and 275 000 cm 2 V −1 s −1 at 4.2 K. The excellent quality is supported by the early development of the ν = 1 quantum Hall plateau at a magnetic field of 5 T and temperature of 4.2 K. We also present a new and accurate transfer technique of graphene to hexagonal boron nitride crystals. This technique is simple, fast and yields atomically flat graphene on boron nitride which is almost completely free of bubbles or wrinkles. The potential of commercially available boron nitride combined with our transfer technique makes high mobility graphene devices more accessible.

Electronic spin transport in graphene field-effect transistors Popinciuc, M.; Jozsa, C.; Zomer, P. J.; Tombros, N.; Veligura, A.; Jonkman, H. T.; van Wees, B. J. Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Spin transport experiments in graphene, a single layer of carbon atoms ordered in a honeycomb lattice, indicate spin-relaxation times that are significantly shorter than the theoretical predictions. We investigate experimentally whether these short spin-relaxation times are due to extrinsic factors, such as spin relaxation caused by low impedance contacts, enhanced spin-flip processes at the device edges, or the presence of an aluminum oxide layer on top of graphene in some samples. Lateral spin valve devices using a field-effect transistor geometry allowed for the investigation of the spin relaxation as a function of the charge density, going continuously from metallic hole to electron conduction ͑charge densities of n ϳ 10 12 cm −2 ͒ via the Dirac charge neutrality point ͑n ϳ 0͒. The results are quantitatively described by a one-dimensional spin-diffusion model where the spin relaxation via the contacts is taken into account. Spin valve experiments for various injector-detector separations and spin precession experiments reveal that the longitudinal ͑T 1 ͒ and the transversal ͑T 2 ͒ relaxation times are similar. The anisotropy of the spin-relaxation times ʈ and Ќ , when the spins are injected parallel or perpendicular to the graphene plane, indicates that the effective spin-orbit fields do not lie exclusively in the two-dimensional graphene plane. Furthermore, the proportionality between the spinrelaxation time and the momentum-relaxation time indicates that the spin-relaxation mechanism is of the Elliott-Yafet type. For carrier mobilities of 2 ϫ 10 3 -5ϫ 10 3 cm 2 / V s and for graphene flakes of 0.1-2 m in width, we found spin-relaxation times on the order of 50-200 ps, times which appear not to be determined by the extrinsic factors mentioned above.

We experimentally study the electronic spin transport in hBN encapsulated single layer graphene nonlocal spin valves. The use of top and bottom gates allows us to control the carrier density and the electric field independently. The spin relaxation times in our devices range up to 2 ns with spin relaxation lengths exceeding 12 µm even at room temperature. We obtain that the ratio of the spin relaxation time for spins pointing out-of-plane to spins in-plane is τ ⊥ /τ || ≈ 0.75 for zero applied perpendicular electric field. By tuning the electric field this anisotropy changes to ≈0.65 at 0.7 V/nm, in agreement with an electric field tunable in-plane Rashba spin-orbit coupling.PACS numbers: 72.80. Vp, 85.75.Hh Keywords: Graphene, spin transport, Rashba spin-orbit interaction, anisotropic spin relaxation, Hanle precession, electric fieldThe generation, manipulation and detection of spin information has been the target of several studies due to the implications for novel spintronic devices [1, 2]. In the recent years graphene has attracted a lot of attention in spintronics due to its theoretically large intrinsic spin relaxation time and length of the order of τ s ≈ 100 ns and λ s ≈ 100 µm respectively [4, 9]. Although experimental results still fall short of these expectations [3][4][5] 7], graphene has already achieved the longest measured nonlocal spin relaxation length [5, 9] and furthest transport of spin information at room temperature [10]. However, the mechanisms for spin relaxation in graphene are still under heavy debate with various theoretical models proposed [4, 8, 9,[11][12][13].To take advantage of the long spin relaxation times in graphene, e.g. for spin logic devices, one requires easy control of the spin information, for example by an applied electric field. Single layer graphene is an ideal system for this purpose, not only because of its high mobilities and low intrinsic spin-orbit fields (SOF), but also due to the simple relation between the carriers' wavevector, the applied perpendicular electric field and the induced Rashba SOF [4, 7, 9,[15][16][17][18][19]. In bilayer graphene a more complicated behavior is expected when spin-orbit coupling is considered [21].Here we report nonlocal spin transport measurements on single layer graphene in which we address both topics specified above. Our devices consist of a single layer graphene flake on hexagonal Boron Nitride (hBN) of which a central region is encapsulated with another hBN flake and hence protected from the environment. The presence of a top and bottom gate give rise to two independent electric fields that are experienced by the graphene: [22], where tg(bg) ≈ 3.9 is the dielectric constant, d tg(bg) is the dielectric thickness and V 0 tg(bg) the position of the charge neutrality point for the top (bottom) gate. Their difference controls the carrier density in the graphene (n = (E bg − E tg ) 0 /e) and their average gives the effective electric field experienced by the graphene (Ē = (E tg + E bg )/2), which breaks the inversion symmetry in t...

We performed spin transport measurements on boron nitride based single layer graphene devices with mobilities up to 40 000 cm 2 V −1 s −1 . We could observe spin transport over lengths up to 20 µm at room temperature, the largest distance measured so far for graphene. Due to enhanced charge carrier diffusion, spin relaxation lengths are measured up to 4.5 µm. The relaxation times are similar to values for lower quality SiO2 based devices, around 200 ps. We find that the relaxation rate is determined in almost equal measures by the Elliott-Yafet and D'Yakonov-Perel mechanisms.The potential of graphene [1] as an emerging material for spintronics has been established, revealing spin relaxation lengths λ of 2 µm at room temperature [2]. Spins relax over a length λ = √ D s τ s , where D s is the spin diffusion constant and τ s the spin relaxation time. One straightforward way to achieve spin transport over larger distances is to enhance D s by fabricating high mobility devices. On the other hand, τ s is theoretically predicted to range up to hundreds of nanoseconds [3]. However, observations made in the recent years by experimentalists [2, 4-13] do not match up to the high expectations set by theory. Measurements typically indicate τ s to be in the hundred picoseconds range and the discrepancy between theory and experiment and the exact relaxation mechanism remain yet unclear. Some works suggest that spin relaxation is dominated by the Elliott-Yafet (EY) mechanism [4,11,14], where τ s is proportional to the momentum relaxation time τ p and spins lose their information during scattering events. Other efforts indicate that the D'Yakonov-Perel (DP) mechanism is stronger [3,15,16], where τ s is inversely proportional to τ p and spins dephase in between scattering events.In identifying the limiting factors on spin transport in graphene, the substrate deserves special attention. For charge transport it has already been shown that the standard silicon oxide substrate reduces the mobility of charge carriers considerably [17]. The SiO 2 substrate is expected to also affect the spin relaxation in graphene through its roughness, trapped charges and surface phonons [16]. One approach to reduce the substrate roughness and screen impurities is to use epitaxial graphene on silicon carbide [12,18]. However, the presence of localized states is believed to affect spin transport in this system [13]. Alternatively, eliminating the influence of the substrate by suspending the graphene flake yields a 3 orders of magnitude increase in mobility [19,20]. Suspended spintronic graphene devices have been studied and a lower bound for τ s of ∼200 ps was found [10]. Determination of the actual value was however not possible since the presence of local supports for the suspended device was found to dominate the extraction of τ s .Atomically flat hexagonal boron nitride (h-BN) was found to be a much better substrate than SiO 2 for high quality graphene electronics [21][22][23], yielding a 2 orders of magnitude increase in mobility. In this manuscri...

at integer multiples of 2e 2 /h at zero magnetic field in a high mobility suspended graphene ballistic nanoconstriction. This quantization evolves into the typical quantum Hall effect for graphene at magnetic fields above 60 mT. Voltage bias spectroscopy reveals an energy spacing of 8 meV between the first two subbands. A pronounced feature at 0.6 × 2e 2 /h present at a magnetic field as low as ∼0.2 T resembles the '0.7 anomaly' observed in quantum point contacts in a GaAs-AlGaAs two-dimensional electron gas, possibly caused by electron-electron interactions 11 . Conductance quantization in zero magnetic field in graphene ribbons is expected to strongly depend on the type of edge termination 6,7,[12][13][14] . In the case of ideal non-disordered armchair edges the valley degeneracy is lifted, leading to a quantization sequence 0 (for a semiconducting ribbon), 1,2,3,... × G 0 , when the Fermi energy is raised or lowered from the charge neutrality point. Here G 0 = 2e 2 /h, with e the electron charge, h the Planck constant and the factor two is due to the spin degeneracy. For zigzag edges on the other hand, theory predicts a quantization in odd multiples 1,3,5,... × G 0 , reflecting the presence of both spin, as well as valley degeneracy. However, realistic devices have a finite (edge) disorder which will dominate the electronic transport in long and narrow ribbons, making the experimental observation of conductance quantization very challenging. Signatures of the formation of one-dimensional subbands because of quantum confinement have been reported for nanoribbons fabricated on a silicon oxide (SiO 2 ) substrate 15,16 . However, those devices are not in the ballistic regime because they have the characteristics of a diffusive, disordered system and lack uniform doping owing to strong interaction with the substrate. In such a narrow and long ribbon an edge disorder of typically only a few per cent of missing carbon atoms will prevent the observation of quantum ballistic transport and conductance quantization [17][18][19] . A way to circumvent this problem is to prepare a constriction with a length comparable or shorter than the width, for which conductance quantization is theoretically possible for an edge disorder of 10% or even higher [18][19][20] . To investigate quantum ballistic 1 Molecular Electronics, Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, NL-9747AG Groningen, The Netherlands, 2 Physics of Nanodevices, Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh, NL-9747AG Groningen, The Netherlands. *e-mail: n.tombros@rug.nl. No current annealing was applied to region C. b, A schematic cross-section of the device. The graphene layer is suspended about 1 µm above the 500 nm thick SiO 2 and the electrodes are kept in place by pillars of LOR polymer. The n+ doped silicon substrate is used as a back gate electrode to control the charge-carrier density.transport and conductance quantization in graphene it is therefore crucial to prepare a narrow, short...

Spin relaxation in graphene is investigated in electrical graphene spin valve devices in the nonlocal geometry. Ferromagnetic electrodes with in-plane magnetizations inject spins parallel to the graphene layer. They are subject to Hanle spin precession under a magnetic field B applied perpendicular to the graphene layer. Fields above 1.5 T force the magnetization direction of the ferromagnetic contacts to align to the field, allowing injection of spins perpendicular to the graphene plane. A comparison of the spin signals at B=0 and B=2 T shows a 20% decrease in spin relaxation time for spins perpendicular to the graphene layer compared to spins parallel to the layer. We analyze the results in terms of the different strengths of the spin-orbit effective fields in the in-plane and out-of-plane directions and discuss the role of the Elliott-Yafet and Dyakonov-Perel mechanisms for spin relaxation.