We demonstrate that optical transparency of any two-dimensional system with a symmetric electronic spectrum is governed by the fine structure constant and suggest a simple formula that relates a quasi-particle spectrum to an optical absorption of such a system. These results are applied to graphene deposited on a surface of

We show that graphene deposited on a substrate has a non-negligible density of atomic scale defects. This is evidenced by a previously unnoticed D peak in the Raman spectra with intensity of ∼1% with respect to the G peak. We evaluated the effect of such impurities on electron transport by mimicking them with hydrogen adsorbates and measuring the induced changes in both mobility and Raman intensity. If the intervalley scatterers responsible for the D peak are monovalent, their concentration is sufficient to account for the limited mobilities currently achievable in graphene on a substrate.

We have accurately measured the effective mass in a dilute two-dimensional electron system in silicon by analyzing temperature dependence of the Shubnikov-de Haas oscillations in the lowtemperature limit. A sharp increase of the effective mass with decreasing electron density has been observed. Using tilted magnetic fields, we have found that the enhanced effective mass is independent of the degree of spin polarization, which points to a spin-independent origin of the mass enhancement and is in contradiction with existing theories.PACS numbers: 71.30.+h,73.40.Qv,71.18.+y The ground state of an ideal, strongly interacting two-dimensional (2D) electron system is predicted to be Wigner crystal [1]. The strength of the interactions is usually characterized by the ratio between the Coulomb energy and the Fermi energy, r s = E c /E F . Assuming that the effective electron mass is equal to the band mass, the interaction parameter r s in the single-valley case reduces to the Wigner-Seitz radius, 1/(πn s ) 1/2 a B and therefore increases as the electron density, n s , decreases (here a B is the Bohr radius in semiconductor). In the strongly-interacting limit, no analytical theory has been developed to date. According to numeric simulations [2], Wigner crystallization is expected in a very dilute regime, when r s reaches approximately 35. The refined numeric simulations [3] have predicted that prior to the crystallization, in the range of the interaction parameter 25 r s 35, the ground state of the system is a strongly correlated ferromagnetic Fermi liquid. At yet higher electron densities, at r s ∼ 1, the (weaklyinteracting) electron liquid is expected to be paramagnetic, with the effective mass, m, and Landé g factor renormalized by interactions. Enhancement of g and m within the Fermi liquid theory is due to spin exchange effects, with renormalization of the g factor being dominant compared to that of the effective mass [4]. In contrast, the dominant increase of m near the onset of Wigner crystallization follows from an alternative description of the strongly-interacting electron system beyond the Fermi liquid approach, which also predicts the renormalization of m to be strongly sensitive to the polarization of spins [5,6].In dilute silicon metal-oxide-semiconductor-fieldeffect-transistors (MOSFETs), a strong metallic temperature dependence of the resistance was observed a decade ago [7]. Although this anomaly was almost immediately attributed to strong electron-electron interactions, only after a strongly enhanced ratio of the spin and the cyclotron splittings was found at low n s [8] has it become clear that the system behaves well beyond the weakly interacting Fermi liquid. Later, it was reported that the magnetic field required to produce complete spin polarization, B c ∝ n s /gm, tends to vanish at a finite electron density ≈ 8 × 10 10 cm −2 [9, 10]. These findings point to a sharp increase of the spin susceptibility and possible ferromagnetic instability in dilute silicon MOSFETs. In very dilute GaAs/AlGaAs he...

We demonstrate the application of graphene as a support for imaging individual biological molecules in transmission electron microscope (TEM). A simple procedure to produce free-standing graphene membranes has been designed. Such membranes are extremely robust and can support practically any sub-micrometer object. Tobacco mosaic virus has been deposited on graphene samples and observed in a TEM. High contrast has been achieved even though no staining has been applied.

The discovery of the metal-insulator transition (MIT) in two-dimensional (2D) electron systems [1] challenged the veracity of one of the most influential conjectures [2] in the physics of disordered electrons, which states that "in two dimensions, there is no true metallic behaviour"; no matter how weak the disorder, electrons would be trapped and unable to conduct a current. However, that theory did not account for interactions between the electrons. Here we investigate the interplay between the electron-electron interactions and disorder near the MIT using simultaneous measurements of electrical resistivity and magnetoconductance. We show that both the resistance and interaction amplitude exhibit a fan-like spread as the MIT is crossed. From these data we construct a resistance-interaction flow diagram of the MIT that clearly reveals a quantum critical point, as predicted by the two-parameter scaling theory [3]. The metallic side of this diagram is accurately described by the renormalization group theory [4] without any fitting parameters. In particular, the metallic temperature dependence of the resistance sets in when the interaction amplitude reaches γ 2 ≈ 0.45 -a value in remarkable agreement with the one predicted by theory [4].The low amount of disorder in high mobility silicon metal-oxide-semiconductor field-effect transistors (Si MOSFETs) allows measurements to be made in the regime of very low electron densities where correlation effects due to electron-electron interactions become especially important. (Ratios r s ≡ E C /E F > 10 between Coulomb and Fermi energies are easily reached with Fermi energies of the order 0.7 meV.) This material system has the additional advantage that its electron spectrum has two almost degenerate valleys, which further enhances the correlation effects. Indeed, the lowtemperature drop of the resistance on the metallic side of the transition (Fig.