A new critical curve for the Lane-Emden system

We study stable positive radially symmetric solutions for the Lane-Emden system $-\Delta u=v^p$ in $\R^N$, $-\Delta v=u^q$ in $\R^N$, where $p,q\geq 1$. We obtain a new critical curve that optimally describes the existence of such solutions.Comment: 13 pages, 1 figur

Tuning a Schottky barrier in a photoexcited topological insulator with transient Dirac cone electron-hole asymmetry

The advent of Dirac materials has made it possible to realize two dimensional gases of relativistic fermions with unprecedented transport properties in condensed matter. Their photoconductive control with ultrafast light pulses is opening new perspectives for the transmission of current and information. Here we show that the interplay of surface and bulk transient carrier dynamics in a photoexcited topological insulator can control an essential parameter for photoconductivity - the balance between excess electrons and holes in the Dirac cone. This can result in a strongly out of equilibrium gas of hot relativistic fermions, characterized by a surprisingly long lifetime of more than 50 ps, and a simultaneous transient shift of chemical potential by as much as 100 meV. The unique properties of this transient Dirac cone make it possible to tune with ultrafast light pulses a relativistic nanoscale Schottky barrier, in a way that is impossible with conventional optoelectronic materials.Comment: Nature Communications, in press (12 pages, 6 figures

Ultrafast surface carrier dynamics in the topological insulator Bi2Te3

We discuss the ultrafast evolution of the surface electronic structure of the topological insulator Bi$_2$Te$_3$ following a femtosecond laser excitation. Using time and angle resolved photoelectron spectroscopy, we provide a direct real-time visualisation of the transient carrier population of both the surface states and the bulk conduction band. We find that the thermalization of the surface states is initially determined by interband scattering from the bulk conduction band, lasting for about 0.5 ps; subsequently, few ps are necessary for the Dirac cone non-equilibrium electrons to recover a Fermi-Dirac distribution, while their relaxation extends over more than 10 ps. The surface sensitivity of our measurements makes it possible to estimate the range of the bulk-surface interband scattering channel, indicating that the process is effective over a distance of 5 nm or less. This establishes a correlation between the nanoscale thickness of the bulk charge reservoir and the evolution of the ultrafast carrier dynamics in the surface Dirac cone

Time resolved ultrafast ARPES for the study of topological insulators: The case of Bi

We discuss the application of time-resolved ultrafast angle resolved photoelectron spectroscopy to the study of photoexcited topological insulators. Measurements performed on the prototype material Bi2Te3 clearly show that all the main processes involved in the ultrafast surface carrier dynamics of topological insulators can be clearly observed and quantitatively analyzed. The comparison with other experimental results shows that the relative position of surface and bulk conduction bands with respect to the system Fermi level play an essential role in the recombination processes following ultrafast optical excitation

Circular Dichroism and Superdiffusive Transport at the Surface of BiTeI

International audienceWe investigate the electronic states of BiTeI after the optical pumping with circularly polarized photons. Our data show that photoexcited electrons reach an internal thermalization within 300 fs from the arrival of the pump pulse. Instead, the dichroic contrast generated by the circularly polarized light relaxes on a timescale shorter than 80 fs. This result implies that orbital and spin polarization created by the circular pump pulse rapidly decays via manybody interaction. The remnant dichroic contrast at longer delay times is due to the helicity dependence of superdiffussive transport. We ascribe it to the lack of inversion symmetry in an electronic system far from equilibrium conditions