Tuning a Circular p-n Junction in Graphene from Quantum Confinement to Optical Guiding

The motion of massless Dirac-electrons in graphene mimics the propagation of photons. This makes it possible to control the charge-carriers with components based on geometrical-optics and has led to proposals for an all-graphene electron-optics platform. An open question arising from the possibility of reducing the component-size to the nanometer-scale is how to access and understand the transition from optical-transport to quantum-confinement. Here we report on the realization of a circular p-n junction that can be continuously tuned from the nanometer-scale, where quantum effects are dominant, to the micrometer scale where optical-guiding takes over. We find that in the nanometer-scale junction electrons are trapped in states that resemble atomic-collapse at a supercritical charge. As the junction-size increases, the transition to optical-guiding is signaled by the emergence of whispering-gallery modes and Fabry-Perot interference. The creation of tunable junctions that straddle the crossover between quantum-confinement and optical-guiding, paves the way to novel design-architectures for controlling electronic transport.Comment: 16 pages, 4 figure

Realization of a Tunable Artificial Atom at a Supercritically Charged Vacancy in Graphene

The remarkable electronic properties of graphene have fueled the vision of a graphene-based platform for lighter, faster and smarter electronics and computing applications. One of the challenges is to devise ways to tailor its electronic properties and to control its charge carriers. Here we show that a single atom vacancy in graphene can stably host a local charge and that this charge can be gradually built up by applying voltage pulses with the tip of a scanning tunneling microscope (STM). The response of the conduction electrons in graphene to the local charge is monitored with scanning tunneling and Landau level spectroscopy, and compared to numerical simulations. As the charge is increased, its interaction with the conduction electrons undergoes a transition into a supercritical regime 6-11 where itinerant electrons are trapped in a sequence of quasi-bound states which resemble an artificial atom. The quasi-bound electron states are detected by a strong enhancement of the density of states (DOS) within a disc centered on the vacancy site which is surrounded by halo of hole states. We further show that the quasi-bound states at the vacancy site are gate tunable and that the trapping mechanism can be turned on and off, providing a new mechanism to control and guide electrons in grapheneComment: 18 pages and 5 figures plus 14 pages and 15 figures of supplementary information. Nature Physics advance online publication, Feb 22 (2016

Scattering theory and ground-state energy of Dirac fermions in graphene with two Coulomb impurities

We study the physics of Dirac fermions in a gapped graphene monolayer containing two Coulomb impurities. For the case of equal impurity charges, we discuss the ground-state energy using the linear combination of atomic orbitals (LCAO) approach. For opposite charges of the Coulomb centers, an electric dipole potential results at large distances. We provide a nonperturbative analysis of the corresponding low-energy scattering problem

Resonant tunnelling between the chiral Landau states of twisted graphene lattices

A class of multilayered functional materials has recently emerged in which the component atomic layers are held together by weak van der Waals forces that preserve the structural integrity and physical properties of each layer. An exemplar of such a structure is a transistor device in which relativistic Dirac Fermions can resonantly tunnel through a boron nitride barrier, a few atomic layers thick, sandwiched between two graphene electrodes. An applied magnetic field quantises graphene's gapless conduction and valence band states into discrete Landau levels, allowing us to resolve individual inter-Landau level transitions and thereby demonstrate that the energy, momentum and chiral properties of the electrons are conserved in the tunnelling process. We also demonstrate that the change in the semiclassical cyclotron trajectories, following an inter-layer tunnelling event, is analogous to the case of intra-layer Klein tunnelling

Temperature-Dependent Three-Dimensional Anisotropy of the Magnetoresistance in WTe

Extremely large magnetoresistance (XMR) was recently discovered in WTe2, triggering extensive research on this material regarding the XMR origin. Since WTe2 is a layered compound with metal layers sandwiched between adjacent insulating chalcogenide layers, this material has been considered to be electronically two-dimensional (2D). Here we report two new findings on WTe2: (1) WTe2 is electronically 3D with a mass anisotropy as low as 2, as revealed by the 3D scaling behavior of the resistance RðH; θÞ ¼ RðεθHÞ with εθ ¼ ðcos2θ þ γ−2sin2θÞ1=2, θ being the magnetic field angle with respect to the c axis of the crystal and γ being the mass anisotropy and (2) the mass anisotropy γ varies with temperature and follows the magnetoresistance behavior of the Fermi liquid state. Our results not only provide a general scaling approach for the anisotropic magnetoresistance but also are crucial for correctly understanding the electronic properties of WTe2, including the origin of the remarkable “turn-on” behavior in the resistance versus temperature curve, which has been widely observed in many materials and assumed to be a metalinsulator transition

Origin of the turn-on temperature behavior in WTe2.

A hallmark of materials with extremely large magnetoresistance (XMR) is the transformative turn-on temperature behavior: when the applied magnetic field H is above certain value, the resistivity versus temperature ρ(T ) curve shows a minimum at a field dependent temperature T ∗, which has been interpreted as a magnetic-field-driven metal-insulator transition or attributed to an electronic structure change. Here, we demonstrate that ρ(T ) curves with turn-on behavior in the newly discovered XMR material WTe2 can be scaled as MR ∼ (H/ρ0) m with m ≈ 2 and ρ0 being the resistivity at zero field. We obtained experimentally and also derived from the observed scaling the magnetic field dependence of the turn-on temperature T ∗ ∼ (H − Hc) ν with ν ≈ 1/2, which was earlier used as evidence for a predicted metal-insulator transition. The scaling also leads to a simple quantitative expression for the resistivity ρ∗ ≈ 2ρ0 at the onset of the XMR behavior, which fits the data remarkably well. These results exclude the possible existence of a magnetic-field-driven metal-insulator transition or significant contribution of an electronic structure change to the low-temperature XMR in WTe2. This work resolves the origin of the turn-on behavior observed in several XMR materials and also provides a general route for a quantitative understanding of the temperature dependence of MR in both XMR and non-XMR materials