Optimizing Dirac fermions quasi-confinement by potential smoothness engineering

Abstract

With the advent of high mobility encapsulated graphene devices, new electronic components ruled by Dirac fermions optics have been envisioned and realized. The main building blocks of electron-optics devices are gate-defined p-n junctions, which guide, transmit and refract graphene charge carriers, just like prisms and lenses in optics. The reflection and transmission are governed by the p-n junction smoothness, a parameter difficult to tune in conventional devices. Here we create p-n junctions in graphene, using the polarized tip of a scanning gate microscope, yielding Fabry-Pérot interference fringes in the device resistance. We control the p-n junctions smoothness using the tip-to-graphene distance, and show increased interference contrast using smoother potential barriers. Extensive tight-binding simulation reveal that smooth potential barriers induce a pronounced quasi-confinement of Dirac fermions below the tip, yielding enhanced interference contrast. On the opposite, sharp barriers are excellent Dirac fermions transmitters and lead to poorly contrasted interferences.Our work emphasizes the importance of junction smoothness for relativistic electron optics devices engineering.

Gradient-index electron optics in graphene pn junctions

“…By smoothing the profile of the electrostatic potential (α = 2), we obtain a circular junction with a gradually changing refractive index, which is certainly the most appealing and novel device for gradient-index electron optics. Such a device has been realized recently experimentally [4,70]. Current flow patterns are shown in Figure 10 together with semi-classical trajectories, which agree roughly with the quantum current.…”

“…These junctions show interesting physical properties like Mie scattering [29] and whispering gallery modes [69]. They have been realized recently in experiments [4,70].…”

Graphene whisperitronics: transducing whispering gallery modes into electronic transport

“…3g (corresponding to n-p-n junction) reflects the tip-induced potential, and can be fitted to evaluate it accurately (see Refs. 19,36 and section 6 of the supplementary materials).…”

“…It would indeed combine a less invasive approach with the extreme tunability of coupling offered by the tunnel barrier. Finally, the high quality factor required to improve the sensitivity of such devices can readily be engineered by tuning the potential smoothness, as reported in Ref 36. Opening the way towards such perspectives, this work bridges the recently discovered WGMs of graphene p-n islands with the field of Dirac fermion optics, heralding the advent of relativistic whisperitronics, a promising field for the engineering of disruptive quantum devices.…”

Spatial mapping of disordered 2D materials: the conductance Sudoku

“…Through multiple measurements of local and non-local resistances [42], one can in principle experimentally determine the multiterminal conductance matrix. The possibilities have been vastly improved by techniques that enable to directly probe the local conductances at the nanoscale such as scanning gate microscopy [43][44][45][46] and multi-probe scanning tunneling spectroscopy [47,48], to name but a few. These recent experimental developments provide extra motivation to explore what type of information can be obtained from a disordered device through selectively interrogating its transport properties, which is precisely the underlying idea behind this work.…”