We show that the strong coupling of pseudospin orientation and charge carrier motion in bilayer graphene has a drastic effect on transport properties of ballistic p-n-p junctions. Electronic states with zero momentum parallel to the barrier are confined under it for one pseudospin orientation, whereas states with the opposite pseudospin tunnel through the junction totally uninfluenced by the presence of confined states. We demonstrate that the junction acts as a cloak for confined states, making them nearly invisible to electrons in the outer regions over a range of incidence angles. This behavior is manifested in the two-terminal conductance as transmission resonances with non-Lorentzian, singular peak shapes. The response of these phenomena to a weak magnetic field or electric-field-induced interlayer gap can serve as an experimental fingerprint of electronic cloaking.

Electrons in graphene, behaving as massless relativistic Dirac particles, provide a new perspective on the relation between condensed matter and high-energy physics. We discuss atomic collapse, a novel state of superheavy atoms stripped of their discrete energy levels, which are transformed into resonant states. Charge impurities in graphene provide a convenient condensed matter system in which this effect can be explored. Relativistic dynamics also manifests itself in another system, graphene p-n junctions. We show how the transport problem in the presence of magnetic field can be solved with the help of a Lorentz transformation, and use it to investigate magnetotransport in p-n junctions. Finally, we review recent proposal to use Fabry-Pérot resonances in p-n-p structures as a vehicle to investigate Klein scattering, another hallmark phenomenon of relativistic dynamics.

We describe a new regime of magnetotransport in two dimensional electron systems in the presence of a narrow potential barrier imposed by external gates. In such systems, the Landau level states, confined to the barrier region in strong magnetic fields, undergo a deconfinement transition as the field is lowered. We present transport measurments showing Shubnikov-de Haas (SdH) oscillations which, in the unipolar regime, abruptly disappear when the strength of the magnetic field is reduced below a certain critical value. This behavior is explained by a semiclassical analysis of the transformation of closed cyclotron orbits into open, deconfined trajectories. Comparison to SdH-type resonances in the local density of states is presented.Electron cyclotron motion constrained by crystal boundaries displays many interesting phenomena, such as skipping orbits and electron focusing, which have yielded a wealth of information on scattering mechanisms in solids [1,2]. Since the 1980s, many groups have investigated electron transport in semiconducting two-dimensional electron systems (2DES), where gateinduced spatially varying electric fields can be used to alter cyclotron motion. A variety of interesting phenomena were explored in these systems, including quenching of the quantum Hall effect [3,4], Weiss oscillations due to commensurability between cyclotron orbits and a periodic grating [5], pinball-like dynamics in 2D arrays of scatterers [6], and coherent electron focusing [7].The experimental realization of graphene [8], a new high-mobility electron system, affords new opportunities to explore effects that were previously inaccessible. In particular, attempts to induce sharp potential barriers in III-V semiconductor quantum well structures have been limited by the depth at which the 2DES is buriedtypically about 100nm below the surface [9]. In contrast, electronic states in graphene, a truly two-dimensional material, are fully exposed and thus allow for potential modulation on ∼ 10 nm length scales using small local gates and thin dielectric layers [10][11][12][13]. Significantly, such length scales can be comparable to the magnetic length ℓ B = c/eB, which characterizes electronic states in quantizing magnetic fields. In this Letter we focus on one such phenomenon, the transformation of the discrete Landau level spectrum to a continuum of extended states in the presence of a static electric field.The behavior which will be of interest for us is illustrated by a toy model involving the Landau levels of a massive charged particle in the presence of an inverted parabolic potential U (x) = −ax 2 . Competition between the repulsive potential and magnetic confinement gives rise to a modified harmonic oscillator spectrum ε n (p y ) = e m B 2 − B 2 c (n + 1/2) − 2ap 2 y e 2 (B 2 − B 2 c ) (1) for B > B c , where m is the particle mass, p y is the y component of momentum, and B c = √ 2ma/e is the critical magnetic field strength. For strong magnetic field, B > B c , the spectrum consists of discrete (but dispersive) energy ban...