Beside brief overview of its properties, i will concentrate on landau levels one of the phenomena that show extraordinary dependences due to graphenes unusual energy dispersion. Negative refraction gives rise to the klein paradox. These pn junctions in corporate a potential step for graphene diraclike fermions allowing us to investigate klein tunneling in graphene. Graphene klein tunnel transistors for high speed analog rf. The gktfet consists of a sequence of angled graphene pn junctions gpnjs. Contents the klein paradox role of chirality klein tunneling in singlelayer graphene klein tunneling and conductivity klein tunneling in bilayer graphene. However, no link between the klein paradox and the negative refraction has been found in graphene. Chiral tunnelling and the klein paradox in graphene nature. Suppressing klein tunneling in graphene using a one.
How does one confine charge carriers inside a device. The phenomenon is discussed in many contexts in particle, nuclear and astro physics but direct tests of the klein paradox using elementary particles have so far proved impossible. Many experiments in electron transport in graphene rely on the klein paradox for massless particles. Massless dirac fermions in graphene allow a close realization of kleins gedanken experiment, whereas massive chiral fermions in bilayer. However, electrostatically controlling the flow of electrons in graphene can be challenging as a result of klein tunneling, where electrons normally incident to a onedimensional potential barrier of height v are perfectly transmitted even as v. Graphene is a rapidly rising star on the horizon of materials science and condensedmatter physics. Chiral tunnelling and the klein paradox in graphene condensed. Quantum confinement of electrons can also be used to control their motion. The term klein paradox 1,2,3,4,5,6,7 refers to a counterintuitive relativistic process in which an incoming electron starts penetrating through a potential barrier if its height, v 0, exceeds the. The freedom of motion associated with the klein paradox creates a problem. But it is already making an impact in the arcane world of highenergy physics. Graphenes unique physical and chemical properties make it an attractive platform for use in micro and nanoelectronic devices. Many experiments in electron transport in graphene rely on the klein paradox for.
Klein paradox refers to the counterintuitive phenomenon that when a dirac particle is incident to a step potential with its height larger than twice the particles rest. The essential features of klein tunneling of massless fermions in graphene may be treated in one dimension without the need for dirac spinors. Institute for molecules and materials, radboud university nijmegen, 6525 ed nijmegen, the netherlands manchester centre for mesoscience and nanotechnology, university of manchester, manchester m 9pl, uk email. The socalled klein paradox unimpeded penetration of relativistic particles through high and wide potential barriers is one of the. Aug 20, 2006 the term klein paradox 1,2,3,4,5,6,7 refers to a counterintuitive relativistic process in which an incoming electron starts penetrating through a potential barrier if its height, v 0, exceeds the. The klein paradox for massless dirac fermions predicts that carriers in graphene hitting a potential step at normal incidence transmit with probability one regardless of the height and width of the step 2. Two dimensions needs a spinor treatment and is investi. Applications to graphene systems are also discussed. Graphene a new form of carbon with scientific impact and. In 1929, physicist oskar klein obtained a surprising result by applying the dirac equation to the. It is shown that normal incidence transmission probabilities for two kinds of graphene structure exhibit. The phenomenon is discussed in many contexts in particle, nuclear, and astrophysics, but direct tests of the klein paradox. Evidence against klein paradox in graphene iopscience. Aug 20, 2006 chiral tunnelling and the klein paradox in graphene.
In this paper, an analytical form of the realspace noninteracting green function of graphene material is developed. Chiral tunneling and the klein paradox in graphene core. Both these results can be identified as fine examples of the klein paradox. It is shown that a potential well or barrier in the dirac equation can become supercritical and emit positrons. Introduction to the physical properties of graphene. Klein paradox tunnelling and tsc fusion of d in pd nanoclusters frank dodd tony smith jr september 2015 vixra see for more details vixra 1501. In interpreting these numbers, one must, however, consider that several publica. A simple approach is to cut the graphene layer into the right shape, as for the quantum dot in the figure. 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. Jan 20, 2012 the essential features of klein tunneling of massless fermions in graphene may be treated in one dimension without the need for dirac spinors. The deltafunction part contains a nonvanishing positron amplitude. Chiral dynamics, klein tunneling in pn junctions klein backscattering and fabryperot resonances lorentz boost and magnetoresistance quantum hall effect reminder the halfinteger qhe in graphene energy gaps and splitting of landau levels qhe in pn and pnp junctions spin transport at graphene edge fine structure constant.
The explanation of this effect in terms of electronpositron production is reassessed. Graphene not only leads to the focusing of electrons 17 similar to the perfect optical lens, but also exhibits the klein paradox 18,19. Finally, we also discuss the existence of pn junctionlike structures between metal contacts and graphene, a topic that has an impact on. The early papers by klein, sauter and hund which investigate scattering off a high step potential in the context of the dirac equation are discussed to derive the paradox first obtained by klein. Bowen s p 2008 1d dirac equation, klein paradox and graphene. It becomes feasible therefore to test the klein paradox at a steplike potential discontinuity. The renewed interest in graphene1 and the close analogy of its band structure to the spectrum of the zero mass dirac equation suggests that a reexamination of several aspects of the one dimensional dirac equation should be carried out. The phenomenon is discussed in many contexts in particle, nuclear and astrophysics but direct tests of the klein paradox using elementary particles have so far proved impossible.
We find that for particular directions the transmission probability, t, is equal to 1, in particular t1 for forward scattering. Recently there obviously was observed experimental support of the klein paradox. Emphasis is placed on the relation ship between the klein paradox. Materials sciencegraphene holds enormous promise for transistors and other electronic devices see main text. In interpreting these numbers, one must, however, consider that several publi. Ii we turn to the underlying physics of the klein paradox and show that particle production and klein tunnelling arise naturally in the dirac equation.
Hence, many of the unusual properties of qed such as the klein paradox 25 can show up in graphene but at much smaller speeds or, identically, energy scales. Pdf history and physics of the klein paradox semantic. Klein paradox tunnelling and tsc fusion of d in pd. This strictly twodimensional material exhibits exceptionally high crystal and electronic quality, and, despite its short history, has already revealed a cornucopia of new physics and potential applications, which are briefly discussed here. Klein paradox and resonant tunneling in a graphene superlattice. At nonnormal incidence, this tunneling problem for 2d massless fermions can be represented as a 1d problem for massive dirac. The klein paradox short history scattering from potential step bosons and fermions resolution with pair production in and outstates conclusion finn ravndal, dept of physics, uio gausdal, 41 2011.
Pdf klein paradox and resonant tunneling in a graphene. These results were expanded to higher dimensions, and to other types of potentials, such as a linear step, a square barrier, a smooth potential, etc. Wafer scale graphene transfer kim et al nature 2010 mechanical peeling off in water supportgraphene nior cusio 2 ni or cu sio 2 rapid etching with fecl 3 aq graphene on polymer support graphene on arbitrary substrate transfer patterning patterned graphene on ni patterned graphene on arbtirary substrate postpatterning prepatterning. Beside brief overview of its properties, i will concentrate on landau levels one of the phenomena that show extraordinary dependences due to. Pdf chiral tunnelling and the klein paradox in graphene. Here we show that the effect can be tested in a conceptually simple condensedmatter experiment by using electrostatic barriers in single and bilayer graphene.
In this seminar i present graphene, a new material with promising application possibilities and important fundamental physics aspects. Apr 18, 2008 the freedom of motion associated with the klein paradox creates a problem. Graphene a new form of carbon with scientific impact and technological promise a graphic of the electron behaviour of graphene in a magnetic field as mapped with an electron microscope a visual representation of the unusual energymomentum relationship of the charge carriers in graphene, which gives rise to its unusual quantum behaviour. High quality cvd graphene of transferred by the clt technique 1 cl sem afm. We find that in the case of potential well, the bound states disappear from the spectrum for large enough potential depth. Mar 23, 2010 implications klein tunneling times high frequency graphene devices advances in engineering duration. Klein paradox tunnelling and tsc fusion of d in pd nano.
Chiral tunneling and the klein paradox in graphene. Mod01 lec11 the klein paradox, pair creation process and examples duration. Pdf chiral tunneling and the klein paradox in graphene. Number of manuscripts with graphene in the title posted on the preprint server. The electronic properties of graphene digital csic. No significant macroscopp,ic defects, wrinkles from the cu foil pmma xpsraman analysis analysis i i 006 raman mapping n ts r2r clt pmma or other functional groups on graphene in pmma or r2r i ty d g 0. Solutions of the one dimensional dirac equation with piecewise constant potentials are presented using standard methods. Pdf the socalled klein paradoxunimpeded penetration of relativistic particles through high and wide potential barriersis one of the most exotic and. Chiral tunnelling and the klein paradox in graphene m.
Wafer scale graphene transfer kim et al nature 2010 mechanical peeling off in water support graphene nior cusio 2 ni or cu sio 2 rapid etching with fecl 3 aq graphene on polymer support graphene on arbitrary substrate transfer patterning patterned graphene on ni patterned graphene on arbtirary substrate postpatterning prepatterning. Here we show that the effect can be tested in a conceptually simple condensedmatter experiment using electrostatic barriers in single and bilayer graphene. Diraclike quasiparticles ingraphene graphene is a single layer of carbon atoms densely packed in a. Chiral tunnelling and the klein paradox in graphene core. Graphene opens a way to investigate this counterintuitive behavior in a relatively simple benchtop experiment, whereas previously the klein paradox was only connected with some very exotic phenomena, such as collisions of ultraheavy nuclei or black hole evaporations for more references and explanations, see50, 56. Pdf history and physics of the klein paradox semantic scholar. This demonstration shows the reflection and transmission coefficients for a dirac particle with spinup incident on a square barrier of variable height the energy of the particle is fixed at 1 unit but its mass is allowed to vary from 0 to. Implications klein tunneling times high frequency graphene devices advances in engineering duration. Klein paradox if we solve the dirac equation in presence of a potential barrier. The renewed interest in graphene 1 and the close analogy of its band structure to the spectrum of the zero mass dirac equation suggests that a reexamination of several aspects of the one dimensional dirac equation should be carried out. Graphene holds enormous promise for transistors and other electronic devices. Elementary electronic properties of graphene 112 a. We conclude that, depending on the boundary condition, there is either a klein paradox that can be resolved by invoking a reservoir of occupied negative energy states that can be accessed, or no klein paradox if we assume that we have no such reservoir, since the boundary conditions on the side of the barrier depend on this choice.