The linear dispersion relation in graphene gives rise to a surprising prediction: the resistivity due to isotropic scatterers, such as white-noise disorder or phonons, is independent of carrier density, n. Here we show that electron-acoustic phonon scattering is indeed independent of n, and contributes only 30 Omega to graphene's room-temperature resistivity. At a technologically relevant carrier density of 1 x1012 cm-2, we infer a mean free path for electron-acoustic phonon scattering of >2 microm and an intrinsic mobility limit of 2 x 105 cm2 V-1 s-1. If realized, this mobility would exceed that of InSb, the inorganic semiconductor with the highest known mobility ( approximately 7.7 x 104 cm2 V-1 s-1; ref. 9) and that of semiconducting carbon nanotubes ( approximately 1 x 105 cm2 V-1 s-1; ref. 10). A strongly temperature-dependent resistivity contribution is observed above approximately 200 K (ref. 8); its magnitude, temperature dependence and carrier-density dependence are consistent with extrinsic scattering by surface phonons at the SiO2 substrate and limit the room-temperature mobility to approximately 4 x 104 cm2 V-1 s-1, indicating the importance of substrate choice for graphene devices.

These authors contributed equally to this work. Since the experimental realization of graphene 1 , extensive theoretical work has focused on short-range disorder 2-5 , "ripples" 6, 7 , or charged impurities 2, 3, 8-13 to explain the conductivity as a function of carrier density σ(n)[1,14-18], and its minimum value σ min near twice the conductance quantum 4e 2 /h[14, 15, 19, 20]. Here we vary the density of charged impurities n imp on clean graphene 21 by deposition of potassium in ultra high vacuum. At non-zero carrier density, charged impurity scattering produces the ubiquitously observed 1, 14-18 linear σ(n) with the theoretically-predicted magnitude. The predicted asymmetry 11 for attractive vs. repulsive scattering of Dirac fermions is observed. σ min occurs not at the carrier density which neutralizes n imp , but rather the carrier density at which the average impurity potential is zero 10 . σ min decreases initially with n imp , reaching a minimum near 4e 2 /h at non-zero n imp , indicating that σ min in present experimental samples does not probe Dirac-point physics 14, 15, 19, 20 but rather carrier density inhomogeneity due to the impurity potential 3, 9, 10 .

Layered transition metal dichalcogenides (TMDs) draw much attention as the key semiconducting material for two-dimensional electrical, optoelectronic, and spintronic devices. For most of these applications, both n- and p-type materials are needed to form junctions and support bipolar carrier conduction. However, typically only one type of doping is stable for a particular TMD. For example, molybdenum disulfide (MoS2) is natively an n-type presumably due to omnipresent electron-donating sulfur vacancies, and stable/controllable p-type doping has not been achieved. The lack of p-type doping hampers the development of charge-splitting p-n junctions of MoS2, as well as limits carrier conduction to spin-degenerate conduction bands instead of the more interesting, spin-polarized valence bands. Traditionally, extrinsic p-type doping in TMDs has been approached with surface adsorption or intercalation of electron-accepting molecules. However, practically stable doping requires substitution of host atoms with dopants where the doping is secured by covalent bonding. In this work, we demonstrate stable p-type conduction in MoS2 by substitutional niobium (Nb) doping, leading to a degenerate hole density of ∼ 3 × 10(19) cm(-3). Structural and X-ray techniques reveal that the Nb atoms are indeed substitutionally incorporated into MoS2 by replacing the Mo cations in the host lattice. van der Waals p-n homojunctions based on vertically stacked MoS2 layers are fabricated, which enable gate-tunable current rectification. A wide range of microelectronic, optoelectronic, and spintronic devices can be envisioned from the demonstrated substitutional bipolar doping of MoS2. From the miscibility of dopants with the host, it is also expected that the synthesis technique demonstrated here can be generally extended to other TMDs for doping against their native unipolar propensity.

Irradiation of graphene on SiO2 by 500 eV Ne and He ions creates defects that cause intervalley scattering as is evident from a significant Raman D band intensity. The defect scattering gives a conductivity proportional to charge carrier density, with mobility decreasing as the inverse of the ion dose. The mobility decrease is 4 times larger than for a similar concentration of singly charged impurities. The minimum conductivity decreases proportional to the mobility to values lower than 4e(2)/pih, the minimum theoretical value for graphene free of intervalley scattering. Defected graphene shows a diverging resistivity at low temperature, indicating insulating behavior. The results are best explained by ion-induced formation of lattice defects that result in midgap states.

We reduce the dimensionless interaction strength α in graphene by adding a water overlayer in ultra-high vacuum, thereby increasing dielectric screening. The mobility limited by long-range impurity scattering is increased over 30 percent, due to the background dielectric constant enhancement leading to reduced interaction of electrons with charged impurities. However, the carrier-densityindependent conductivity due to short range impurities is decreased by almost 40 percent, due to reduced screening of the impurity potential by conduction electrons. The minimum conductivity is nearly unchanged, due to canceling contributions from the electron/hole puddle density and longrange impurity mobility. Experimental data are compared with theoretical predictions with excellent agreement. PACS numbers:Most theoretical and experimental work on graphene has focused on its gapless, linear electronic energy dispersion E = v F k. One important consequence of this linear spectrum is that the dimensionless coupling constant α (or equivalently r s , defined here as the ratio between the graphene Coulomb potential energy and kinetic energy) is a carrier-density independent constant [1, 2], and as a result, the Coulomb potential of charged impurities in graphene is renormalized by screening, but strictly maintains its long-range character. Thus there is a clear dichotomy between long-range and short-range scattering in graphene, with the former giving rise to a conductivity linear [2,3] in carrier density (constant mobility), and the latter having a constant conductivity independent of carrier density. Charged impurity scattering necessarily dominates at low carrier density, and the minimum conductivity at charge neutrality is determined by the charged impurity scattering and the self-consistent electron and hole puddles of the screened impurity potential [3,4,5,6].Apart from the linear spectrum, an additional striking aspect of graphene, setting it apart from all other twodimensional electron systems, is that the electrons are confined to a plane of atomic thickness. This fact has a number of ramifications which are only beginning to be explored [7]. One such consequence is that graphene's properties may be tuned enormously by changing the surrounding environment. Here we provide a clear demonstration of this by reducing the dimensionless coupling constant α in graphene by more than 30 percent through the addition of a dielectric layer (ice) on top of the graphene sheet. Upon addition of the ice layer, the mobility limited by long-range scattering by charged impurities increases by 31 percent, while the conductivity limited by short-range scatterers decreases by 38 percent. The minimum conductivity value remains nearly unchanged. The FIG. 1:Schematic illustrating dielectric screening in graphene. The dielectric environment controls in the interaction strength parameterized by the coupling constant α.opposing effects of reducing α on short-and long-range scattering are easily understood theoretically. The major effect on long-range...