Direct Evidence of Klein and Anti-Klein Tunneling of Graphitic Electrons in a Corbino Geometry.

Transport measurement of electron optics in monolayer graphene p-n junction devices has been traditionally studied with negative refraction and chiral transmission experiments in Hall bar magnetic focusing setups. We show direct signatures of Klein (monolayer) and anti-Klein (bilayer) tunneling with a circular "edgeless" Corbino geometry made out of gated graphene p-n junctions. Noticeable in particular is the appearance of angular sweet spots (Brewster angles) in the magnetoconductance data of bilayer graphene, which minimizes head-on transmission, contrary to conventional Fresnel optics or monolayer graphene which show instead a sharpened collimation of transmission paths. The local maxima on the bilayer magnetoconductance plots migrate to higher fields with increasing doping density. These experimental results are in good agreement with detailed numerical simulations and analytical predictions.

Graphene transistor based on tunable Dirac fermion optics.

We present a quantum switch based on analogous Dirac fermion optics (DFO), in which the angle dependence of Klein tunneling is explicitly utilized to build tunable collimators and reflectors for the quantum wave function of Dirac fermions. We employ a dual-source design with a single flat reflector, which minimizes diffusive edge scattering and suppresses the background incoherent transmission. Our gate-tunable collimator-reflector device design enables the quantitative measurement of the net DFO contribution in the switching device operation. We obtain a full set of transmission coefficients between multiple leads of the device, separating the classical contribution from the coherent transport contribution. The DFO behavior demonstrated in this work requires no explicit energy gap. We demonstrate its robustness against thermal fluctuations up to 230 K and large bias current density up to 102 A/m, over a wide range of carrier densities. The characterizable and tunable optical components (collimator-reflector) coupled with the conjugated source electrodes developed in this work provide essential building blocks toward more advanced DFO circuits such as quantum interferometers. The capability of building optical circuit analogies at a microscopic scale with highly tunable electron wavelength paves a path toward highly integrated and electrically tunable electron-optical components and circuits.

Atomic-Scale Characterization of Graphene p-n Junctions for Electron-Optical Applications.

Graphene p-n junctions offer a potentially powerful approach toward controlling electron trajectories via collimation and focusing in ballistic solid-state devices. The ability of p-n junctions to control electron trajectories depends crucially on the doping profile and roughness of the junction. Here, we use four-probe scanning tunneling microscopy and spectroscopy (STM/STS) to characterize two state-of-the-art graphene p-n junction geometries at the atomic scale, one with CMOS polySi gates and another with naturally cleaved graphite gates. Using spectroscopic imaging, we characterize the local doping profile across and along the p-n junctions. We find that realistic junctions exhibit non-ideality both in their geometry as well as in the doping profile across the junction. We show that the geometry of the junction can be improved by using the cleaved edge of van der Waals metals such as graphite to define the junction. We quantify the geometric roughness and doping profiles of junctions experimentally and use these parameters in non-equilibrium Green's function-based simulations of focusing and collimation in these realistic junctions. We find that for realizing Veselago focusing, it is crucial to minimize lateral interface roughness which only natural graphite gates achieve and to reduce junction width, in which both devices under investigation underperform. We also find that carrier collimation is currently limited by the non-linearity of the doping profile across the junction. Our work provides benchmarks of the current graphene p-n junction quality and provides guidance for future improvements.

Graphene Klein tunnel transistors for high speed analog RF applications.

We propose Graphene Klein tunnel transistors (GKTFET) as a way to enforce current saturation while maintaining large mobility for high speed radio frequency (RF) applications. The GKTFET consists of a sequence of angled graphene p-n junctions (GPNJs). Klein tunneling creates a collimation of electrons across each GPNJ, so that the lack of substantial overlap between transmission lobes across successive junctions creates a gate-tunable transport gap without significantly compromising the on-current. Electron scattering at the device edge tends to bleed parasitic states into the gap, but the resulting pseudogap is still sufficient to create a saturated output (I D -V D ) characteristic and a high output resistance. The modulated density of states generates a higher transconductance (g m ) and unity current gain cut-off frequency (f T ) than GFETs. More significantly the high output resistance makes the unity power gain cut-off frequency (f max ) of GKTFETs considerably larger than GFETs, making analog GKTFET potentially useful for RF electronics. Our estimation shows the f T /f max of a GKTFET with 1 µm channel reaches 33 GHz/17 GHz, and scale up to 350 GHz/53 GHz for 100 nm channel (assuming a single, scalable trapezoidal gate). The f max of a GKTFET is 10 times higher than a GFET with the same channel length.

Electron optics with p-n junctions in ballistic graphene.

Electrons transmitted across a ballistic semiconductor junction are expected to undergo refraction, analogous to light rays across an optical boundary. In graphene, the linear dispersion and zero-gap band structure admit highly transparent p-n junctions by simple electrostatic gating. Here, we employ transverse magnetic focusing to probe the propagation of carriers across an electrostatically defined graphene junction. We find agreement with the predicted Snell's law for electrons, including the observation of both positive and negative refraction. Resonant transmission across the p-n junction provides a direct measurement of the angle-dependent transmission coefficient. Comparing experimental data with simulations reveals the crucial role played by the effective junction width, providing guidance for future device design. Our results pave the way for realizing electron optics based on graphene p-n junctions.