The modification of glass nanopipettes with polyethyleneimines (PEIs) has been successfully achieved by a relatively simple method, and the smallest tip opening is around 3 nm. Thus, in a much wider range of glass pipettes with radii from several nanometers to a few micrometers, the ion current rectification (ICR) phenomenon has been observed. The influences of different KCl concentrations, pH values, and tip radii on the ICR are investigated in detail. The sizes of PEIs have been determined by dynamic light scattering, and the effect of the sizes of PEIs for the modification, especially for a few nanometer-pipettes in radii, is also discussed. These findings systemically confirm and complement the theoretical model and provide a platform for possible selectively molecular detection and mimic biological ion channels.

IntroductionThe research on graphene and post-graphene two-dimensional (2D) materials has been one of the most exciting research fields in the last decade [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Graphene is a Dirac material that has exhibited a lot of interesting/superior physical properties, including extremely high mobility, room temperature quantum Hall effect, and long spin lifetimes [1][2][3][4]13,17]. 2D boron nitride is an insulating material, which could be used a tunneling barrier and protecting layer for other 2D materials [7,8,10]. Semiconducting 2D transition metal dichalcogenides and black phosphorus could be very useful for nano electronics devices [6,7,9,14,16], such as field effect transistor with large on/off ratio. Superconducting 2D materials also provide interesting physical properties, such as Ising superconductivity [11,12,18]. Furthermore, the structures consisting of various 2D materials, van der Waals structures, have shown unusual properties and new phenomena [8,10]. Due to their ultra-thin nature, an electric field could give rise to the large modulation of the Fermi level, thus, providing a unique way to greatly modulate their physical properties. This electric field gating effect makes 2D materials very promising candidates for future nanoelectronics applications [9,19]. Recently, 2D ferromagnetic/antiferromagntic materials has also attracted a lot of interest [20][21][22][23][24][25][26]. Very intriguingly, Gong et al have demonstrated the 2D ferromagnetism in Cr2Ge2Te6 (CGT) down to 2 layers using optical Kerr 3 rotation [26]. However, for the 2D CGT, the electrical transport properties and the electric field effect have been lacking.In this study, we report the preparation and characterization of ferromagnetic thin flakes of Cr2Ge2Te6 (CGT) with thickness down to a few nanometers. Furthermore, large modulation of the channel resistance based on the 2D CGT flakes is demonstrated via the electric field effect.These results make CGT a very important ferromagnetic 2D materials candidate to the van der Waals structures consisting of various 2D materials [8,10,27]. Experimental methodsThe CGT single crystal is a layered material belonging to the R3 group. High-quality CGT single crystals are synthesized using the flux method from high-purity elemental Cr (99.99%), Ge (99.999%) and Te (> 99.999%) materials ordered from Alfa Aesar Company. A mixture of these materials with an atomic ratio of Cr: Ge: Te equal to 10: 13.5: 76.5, is sealed in evacuated quartz ampoules and heated at 1000 °C for 1 hour, followed by slow cooling to 450 °C for a period of 90 hours. The residual Ge and Te fluxes are removed by a centrifugation step at the end. The detailed chemical and structural properties of synthesized Cr2Ge2Te6 single crystal can be found in our previous report [28].The 2D CGT flakes are prepared using the well-established mechanical exfoliation method [29]. The SiO2/Si wafers are first cut to be ~ 10 × 10 mm 2 , and followed by an ultrasonical cleaning in acetone, IPA an...

International audienceIn lattice cryptography, worst-case to average-case reductions rely on two problems: Ajtai’s SIS and Regev’s LWE, which both refer to a very small class of random lattices related to the group G=Znq. We generalize worst-case to average-case reductions to all integer lattices of sufficiently large determinant, by allowing G to be any (sufficiently large) finite abelian group. Our main tool is a novel generalization of lattice reduction, which we call structural lattice reduction: given a finite abelian group G and a lattice L, it finds a short basis of some lattice L¯ such that L⊆L¯ and L¯/L≃G. Our group generalizations of SIS and LWE allow us to abstract lattice cryptography, yet preserve worst-case assumptions: as an illustration, we provide a somewhat conceptually simpler generalization of the Alperin-Sheriff-Peikert variant of the Gentry-Sahai-Waters homomorphic scheme. We introduce homomorphic mux gates, which allows us to homomorphically evaluate any boolean function with a noise overhead proportional to the square root of its number of variables, and bootstrap the full scheme using only a linear noise overhead

The electrochemical behaviors of graphene sheets attached to a self-assembled monolayer (SAM) on a gold electrode have been investigated. A gold electrode is sequentially modified by the SAM of n-octadecyl mercaptan (C 18 H 37 SH), followed by controllable adsorption of graphene sheets to obtain a graphene/SAM modified Au electrode. The graphene/SAM modified Au electrode is characterized electrochemically by using ruthenium hexaammine (Ru(NH 3 ) 6 3+) as a redox probe, and by atomic force microscopy (AFM) and scanning electron microscopy (SEM). The experimental results indicate that the heterogeneous electron transfer (ET) blocked by the SAM can be restored by graphene sheets and that the graphene/SAM modified Au electrode has a smaller interfacial capacitance, as compared with that of a bare Au electrode. The apparent ET rate constant of Ru(NH 3 ) 6 3+, k app , on the graphene/SAM modified Au electrode has been also evaluated quantitatively by cyclic voltammetry (CV) and scanning electrochemical microscopy (SECM), and is equal to 4.2 × 10 -2 and 6.8 × 10 -2 cm s -1 , respectively. In addition, the electrochemical responses of free bases of DNA (guanine (G), adenine (A), thymine (T), and cytosine (C)) on the graphene/SAM modified Au electrode show that the graphene/SAM modified Au electrode possesses electrochemical properties similar to those of a graphene modified electrode rather than an Au electrode.

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