Long wavelength local density of states oscillations near graphene step edges

Using scanning tunneling microscopy and spectroscopy, we have studied the local density of states (LDOS) of graphene over step edges in boron nitride. Long wavelength oscillations in the LDOS are observed with maxima parallel to the step edge. Their wavelength and amplitude are controlled by the energy of the quasiparticles allowing a direct probe of the graphene dispersion relation. We also observe a faster decay of the LDOS oscillations away from the step edge than in conventional metals. This is due to the chiral nature of the Dirac fermions in graphene.Comment: 5 pages, 4 figures, to appear in Phys. Rev. Let

Electronic excitation spectrum of metallic carbon nanotubes

We have studied the discrete electronic spectrum of closed metallic nanotube quantum dots. At low temperatures, the stability diagrams show a very regular four-fold pattern that allows for the determination of the electron addition and excitation energies. The measured nanotube spectra are in excellent agreement with theoretical predictions based on the nanotube band structure. Our results permit the complete identification of the electron quantum states in nanotube quantum dots.Comment: 4 pages, 3 figure

Real Time Electron Tunneling and Pulse Spectroscopy in Carbon Nanotube Quantum Dots

We investigate a Quantum Dot (QD) in a Carbon Nanotube (CNT) in the regime where the QD is nearly isolated from the leads. An aluminum single electron transistor (SET) serves as a charge detector for the QD. We precisely measure and tune the tunnel rates into the QD in the range between 1 kHz and 1 Hz, using both pulse spectroscopy and real - time charge detection and measure the excitation spectrum of the isolated QD.Comment: 12 pages, 5 figure

Dispersal-induced resilience to stochastic environmental fluctuations in populations with Allee effect

Many species are unsustainable at small population densities (Allee Effect). This implies that for population densities below a threshold, named Allee threshold, the population decreases instead of growing. In a closed local population, this makes that environmental fluctuations always leads to extinction. Here, we show how, in spatially extended habitats, dispersal can lead to a sustainable population in a region, provided the amplitude of environmental fluctuations is below an extinction threshold. We have identified two types of sustainable populations: high-density and low-density populations (through a mean-field approximation, valid in the limit of large dispersal length). Our results show that close to global extinction patches where population density is high, low or extinct coexist (even for homogeneous habitats). The extinction threshold increases proportionally to the squared root of the dispersal rate, decreases with the Allee threshold, and it is maximum for characteristic dispersal distances much larger than the spatial scale of synchrony of environmental fluctuations. The low-density population solution can be particularly interesting for future applications, as to understand non-recovery events after harvesting. This theoretical framework allows novel approaches to address the impact of other factors, as habitat fragmentation, on the population resilience to environmental fluctuations.Comment: 24 pages, 3 figures, 1 tabl

Spatial and Ecological Scaling of Stability in Spatial Community Networks

There are many scales at which to quantify stability in spatial and ecological networks. Local-scale analyses focus on specific nodes of the spatial network, while regional-scale analyses consider the whole network. Similarly, species- and community-level analyses either account for single species or for the whole community. Furthermore, stability itself can be defined in multiple ways, including resistance (the inverse of the relative displacement caused by a perturbation), initial resilience (the rate of return after a perturbation), and invariability (the inverse of the relative amplitude of the population fluctuations). Here, we analyze the scale-dependence of these stability properties. More specifically, we ask how spatial scale (local vs regional) and ecological scale (species vs community) influence these stability properties. We find that regional initial resilience is the weighted arithmetic mean of the local initial resiliences. The regional resistance is the harmonic mean of local resistances, which makes regional resistance particularly vulnerable to nodes with low stability, unlike regional initial resilience. Analogous results hold for the relationship between community- and species-level initial resilience and resistance. Both resistance and initial resilience are ``scale-free'' properties: regional and community values are simply the biomass-weighted means of the local and species values, respectively. Thus, one can easily estimate both stability metrics of whole networks from partial sampling. In contrast, invariability generally is greater at the regional and community-level than at the local and species-level, respectively. Hence, estimating the invariability of spatial or ecological networks from measurements at the local or species level is more complicated, requiring an unbiased estimate of the network (i.e. region or community) size

Electronic Transport Spectroscopy of Carbon Nanotubes in a Magnetic Field

We report magnetic field spectroscopy measurements in carbon nanotube quantum dots exhibiting four-fold shell structure in the energy level spectrum. The magnetic field induces a large splitting between the two orbital states of each shell, demonstrating their opposite magnetic moment and determining transitions in the spin and orbital configuration of the quantum dot ground state. We use inelastic cotunneling spectroscopy to accurately resolve the spin and orbital contributions to the magnetic moment. A small coupling is found between orbitals with opposite magnetic moment leading to anticrossing behavior at zero field.Comment: 7 pages, 4 figure