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.

Electrostatic properties of proteins are crucial for their functionality. Carboxyamides are small polar groups that, as peptide bonds, are principal structural components of proteins that govern their electrostatic properties. We investigated the medium dependence of the molar polarization and of the permanent dipole moments of amides with different state of alkylation. The experimentally measured and theoretically calculated dipole moments manifested a solvent dependence that increased with the increase in the media polarity. We ascribed the observed enhancement of the amide polarization to the reaction fields in the solvated cavities. Chloroform, for example, caused about a 25% increase in the amide dipole moments determined for vacuum, as the experimental and theoretical results demonstrated. Another chlorinated solvent, 1,1,2,2-tetrachloroethane, however, caused an "abnormal" increase in the experimentally measured amide dipoles, which the theoretical approaches we used could not readily quantify. We showed and discussed alternatives for addressing such discrepancies between theory and experiment.

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 dualsource 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 10 2 A/m, over a wide range of carrier densities. The characterizable and tunable optical components (collimatorreflector) 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. graphene | Dirac fermion | electron optics | quantum transport

Lack of a bandgap is one of the significant challenges for application of graphene as the active element of an electronic device. A bandgap can be induced in bilayer graphene by application of a potential difference between the two layers. The simplest geometry for creating such a potential difference is two overlayed graphene nanoribbons independently contacted. Calculations, based on density functional theory and the nonequilibrium Green's function formalism, show that transmission through such a structure is a strong function of applied bias. The simulated current voltage characteristics mimic the characteristics of resonant tunneling diode featuring negative differential resistance.

We show that the interplay between chiral tunneling and spin-momentum locking of helical surface states leads to spin amplification and filtering in a 3D topological insulator (TI). Our calculations show that the chiral tunneling across a TI pn junction allows normally incident electrons to transmit, while the rest are reflected with their spins flipped due to spin-momentum locking. The net result is that the spin current is enhanced while the dissipative charge current is simultaneously suppressed, leading to an extremely large, gate-tunable spin-to-charge current ratio (∼20) at the reflected end. At the transmitted end, the ratio stays close to 1 and the electrons are completely spin polarized.

Graphene p-n junctions offer a potentially powerful approach towards 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 Nonequilibrium 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.

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.

We articulate the challenges and opportunities of unconventional devices using the photon like flow of electrons in graphene, such as Graphene Klein Tunnel (GKT) transistors. The underlying physics is the employment of momentum rather than energy filtering to engineer a gate tunable transport gap in a 2D Dirac cone bandstructure. In the ballistic limit, we get a clean tunable gap that implies subthermal switching voltages below the Boltzmann limit, while maintaining a high saturating current in the output characteristic. In realistic structures, detailed numerical simulations and experiments show that momentum scattering, especially from the edges, bleeds leakage paths into the transport gap and turns it into a pseudogap. We quantify the importance of reducing edge roughness and overall geometry on the low-bias transfer characteristics of GKT transistors and benchmark against experimental data. We find that geometry plays a critical role in determining the performance of electron optics based devices that utilize angular resolution of electrons. *