The Schrödinger equation dictates that the propagation of nearly free electrons through a weak periodic potential results in the opening of bandgaps near points of the reciprocal lattice known as Brillouin zone boundaries 1 . However, in the case of massless Dirac fermions, it has been predicted that the chirality of the charge carriers prevents the opening of a bandgap and instead new Dirac points appear in the electronic structure of the material 2,3 . Graphene on hexagonal boron nitride exhibits a rotation-dependent moiré pattern 4,5 . Here, we show experimentally and theoretically that this moiré pattern acts as a weak periodic potential and thereby leads to the emergence of a new set of Dirac points at an energy determined by its wavelength. The new massless Dirac fermions generated at these superlattice Dirac points are characterized by a significantly reduced Fermi velocity. Furthermore, the local density of states near these Dirac cones exhibits hexagonal modulation due to the influence of the periodic potential.Owing to its hexagonal lattice structure with a diatomic unit cell, graphene has low-energy electronic properties that are governed by the massless Dirac equation 6 . This has a number of consequences, among them Klein tunnelling [7][8][9][10] , which prevents electrostatic confinement of charge carriers and inhibits the fabrication of standard semiconductor devices. This has motivated a number of recent theoretical investigations of graphene in periodic potentials 2,3,[11][12][13][14][15] , which explored ways of controlling the propagation of charge carriers by means of various superlattice potentials. On the analytical side, one-dimensional potentials render particle propagation anisotropic 2,3,11,14 and generate new Dirac points, where the electron and hole bands meet, at energies ±hv F |G|/2 given by the reciprocal superlattice vectors G (refs 2,3), where v F is the Fermi velocity. Numerical approaches have extended several of these results to the case of two-dimensional potentials 2,3,14,15 . Unlike for Schrödinger fermions, the periodic potentials generally induce new Dirac points but do not open bandgaps in graphene, owing to the chiral nature of the Dirac fermions.Recent scanning tunnelling microscope (STM) topography experiments have reported well-developed moiré patterns in graphene on crystalline substrates, which suggests that the latter generate effective periodic potentials 4,5,16,17 . Of particular interest is hexagonal boron nitride (hBN), because it is an insulator which only couples weakly to graphene. Furthermore, graphene on hBN exhibits the highest mobility ever reported for graphene on any substrate 18 , and has strongly suppressed charge inhomogeneities 4,5 . Hexagonal boron nitride is a layered material whose planes have the same atomic structure as graphene, with a 1.8% longer lattice constant. The influence of the weak graphene-substrate interlayer coupling on the electronic transport and spectroscopic properties of graphene is not well understood. In particular, there ...

We study the response of graphene to high-intensity 10^11-10^12 Wcm^-2, 50-femtosecond laser pulse excitation. We establish that graphene has a fairly high (~3\times10^12Wcm^-2) single-shot damage threshold. Above this threshold, a single laser pulse cleanly ablates graphene, leaving microscopically defined edges. Below this threshold, we observe laser-induced defect formation that leads to degradation of the lattice over multiple exposures. We identify the lattice modification processes through in-situ Raman microscopy. The effective lifetime of CVD graphene under femtosecond near-IR irradiation and its dependence on laser intensity is determined. These results also define the limits of non-linear applications of graphene in femtosecond high-intensity regime.Comment: 4 pages, 3 figure

The role of many-body interactions is experimentally and theoretically investigated near the saddle point absorption peak of graphene. The time and energy-resolved differential optical transmission measurements reveal the dominant role played by electron-acoustic phonon coupling in band structure renormalization. Using a Born approximation for electron-phonon coupling and experimental estimates of the dynamic lattice temperature, we compute the differential transmission line shape. Comparing the numerical and experimental line shapes, we deduce the effective acoustic deformation potential to be D ac eff ≃ 5 eV. This value is in accord with recent theoretical predictions but differs from those extracted using electrical transport measurements. [5][6][7][8][9] can significantly alter the electronic band structure and optical properties of graphene. When a light pulse interacts with graphene, the observation of many-body effects caused by transient photoexcited carriers is limited to short, subpicosecond time scales due to high electron scattering rates and short lifetimes. Over longer time scales (1-100 ps), the photoexcitation energy is converted into heat, and band structure renormalization effects due to electron-phonon interactions and possibly thermally excited charge carriers at the elevated temperatures [10] can be measured.The long time scale electron-phonon (e-ph) interactions in graphene have numerous ramifications. The intrinsic carrier mobility in high quality graphene devices is limited by e-ph scattering [11][12][13][14][15]. Efficient optoelectronic device design also relies on the conversion of the energy of photoexcited carriers to electrical current before it dissipates through e-ph interactions [16][17][18]. Ultrafast heat generation and dissipation dynamics in devices, which is an important topic in nanoscale heat management, is also crucially dependent on the interaction of electronic excitations with phonons [19].The exact nature and strength of e-ph coupling in graphene is unclear at present. Specifically, the electronacoustic phonon interaction strength, characterized by the deformation potential D ac eff , has been controversial. The experimental estimates obtained from electrical transport measurements [13][14][15] range from 16-50 eV, while theoretical predictions indicate acoustic deformation potential in the range of ∼2.8 − 7 eV [4,11,20,21]. Since many observables are proportional to jD Here we report ultrafast pump-probe measurements of photon energy dependent differential transmission in graphene. Instead of focusing on the heavily studied K point of the graphene band structure [23][24][25][26][27][28], our study uniquely concentrates on the region near the M point. The absorption maxima associated with the van Hove singularity at the M point ( Fig. 1) enables sensitive probing of e-ph interactions through the measurement of pump-induced changes in the absorption spectrum. In contrast, the region near the K point has a relatively featureless, flat absorption profile which does not ...

The effect of shade from one PV module on another is incorporated into a model for the power generated by PV systems. The model is calibrated with data from the Tucson Electric Power solar test yard. Shade de-rating factors from the model are compared with data every minute of the day and every day of the year. The model is then used to predict final yields (kWh/kWoc) for different PV system deployments with various (non-tracking) module orientations and ground-cover ratios. Several heuristics are put forth to help understand how the observed non-linear response to shade can impact the yield from PV systems. In one example, we find that a PV system deployed in the Tucson Electric Power solar test yard could produce 22% more kWh for the month of December (and 3.8% more annually) if the modules were separated by twice as much distance. In another example, we predict that a system in Tucson with south-facing modules at 12-degrees from horizontal can generate 1.5 times as many kWhlyr per square-meter of land compared to a system with modules at 32-degrees (the latitude angle).These examples emphasize the non-linear impact of partial shade on PV system performance.

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