A two-dimensional Dirac fermion microscope

Abstract

The electron microscope has been a powerful, highly versatile workhorse in the fields of material and surface science, micro and nanotechnology, biology and geology, for nearly 80 years. The advent of two-dimensional materials opens new possibilities for realizing an analogy to electron microscopy in the solid state. Here we provide a perspective view on how a two-dimensional (2D) Dirac fermion-based microscope can be realistically implemented and operated, using graphene as a vacuum chamber for ballistic electrons. We use semiclassical simulations to propose concrete architectures and design rules of 2D electron guns, deflectors, tunable lenses and various detectors. The simulations show how simple objects can be imaged with well-controlled and collimated in-plane beams consisting of relativistic charge carriers. Finally, we discuss the potential of such microscopes for investigating edges, terminations and defects, as well as interfaces, including external nanoscale structures such as adsorbed molecules, nanoparticles or quantum dots.

Graphene transistor based on tunable Dirac fermion optics

“…Experimental evidence of DFO characteristics has been demonstrated and quantitatively characterized with two independent metrics by isolating the net DFO contribution to device resistance and by measuring a full set of transmission coefficients. Our analysis establishes multiple methodologies for the quantitative analysis of the DFO effect, leading to further device designing optimization (29,30). The fully characterizable and tunable DFO collimator and reflector provide the foundations for future microscopic-scale electron-optical components, toward highly integrated and electrically controllable optical circuits with variable wavelength and functionality for device operation.…”

Dirac fermion optics and directed emission from single- and bilayer graphene cavities

“…Correspondingly, optics analogues comprise Klein tunneling in single-layer graphene p-n-p junctions [1][2][3][4][5][6][7], p-n junctions [8][9][10], or Fabry-Pérot type settings [7,11,12] as well as anti-Klein tunneling in bilayer graphene [1,[13][14][15][16][17] where in particular circular p-n junctions were considered [18]. Collimation [8,19], various electron lensing [20][21][22][23], and guiding [24][25][26][27][28][29][30] phenomena were investigated in this context. Complementary to the use of top gates in several of the aforementioned electron steering experiments, recently a scanning tunneling setting has been employed to create disklike cavities in graphene defined by circular p-n junctions and to probe whispering-gallery-type resonant states that are most stable against decay from the cavity via Klein tunneling [31]; in a first subsequent theory work nonreciprocity of these whispering gallery modes was predicted [32].…”

Development of gateless quantum Hall checkerboard p–n junction devices

“…The advantage of these complex configurations is that a whole set of quantized resistances becomes accessible and can provide overwhelming evidence of device functionality in addition to being a future application for quantum-based electrical standards. Specific applications of general checkerboard devices, much like those that will be demonstrated and proposed, also include the construction of a multi-interfaced, twodimensional Dirac fermion microscope [31], custom programmable quantized resistors [32], and mesoscopic valley filters [33]. It is therefore also important to verify these checkerboard devices as functional so that their fabrication methods can be justified for use in other applications.…”