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.