The socalled klein paradoxunimpeded penetration of relativistic particles through high and wide potential barriersis one of the most exotic and counterintuitive consequences of quantum. 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. Massless dirac fermions in graphene allow a close realization of kleins gedanken experiment, whereas massive chiral fermions in bilayer. Chiral tunnelling and the klein paradox in graphene condensed. Electronic properties of graphene and 2d materials eva y. The klein paradox refers to the propagation of a relativistic quantum particle, described by the dirac equation, through a sufficiently high potential barrier without. The recent advent of condensedmatter systems with diraclike excitations, such as graphene and topological insulators, has opened up the possibility of observing klein tunnelling experimentally46. This plot shows the transmission coefficient for a barrier of height in graphene as a function of the angle of a plane wave incident on the barrier. Perfect andreev reflection due to the klein paradox in a topological. Pdf chiral tunnelling and the klein paradox in graphene. We find that in the case of potential well, the bound states disappear from the spectrum for large enough potential depth.

Graphene, a single plane of threefold coordinated carbon atoms, exhibits 1 many exotic electronic properties ranging from highly mobile ballistic transport 2,3 to the klein paradox. Chiral tunnelling and the klein paradox in graphene. Chiral tunnelling and the klein paradox in graphene author s. A suspended sheet of pure graphene a plane layer of c atoms bonded together in a honeycomb lattice is the most twodimensional system imaginable. Graphene samples are not perfect, but are divided into pools of electrons or holes. Fall 2008 department of physics and astronomy, the university of tennessee at knoxville, 37996. However, klein s result showed that if the potential is of the order of the electron mass. Pdf the socalled klein paradox unimpeded penetration of relativistic particles through high and wide potential barriersis one of the most. Graphene not only leads to the focusing of electrons 17 similar to the perfect optical lens, but also exhibits the klein paradox 18,19. Beside brief overview of its properties, i will con.

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. With the linear confining potential, we show that the dirac equation presents no bound state. An assembled graphene pet touch panel showing outstanding flexibility. A transparent ultralar gearea graphene film transferred on a 35inch pet sheet. Chiral tunneling and the klein paradox in graphene article pdf available in nature physics 29. It is shown that a potential well or barrier in the dirac equation can become supercritical and emit positrons. Mod01 lec11 the klein paradox, pair creation process and examples duration. In graphene the same condition is satisfied rather more easily.

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. Pdf chiral tunneling and the klein paradox in graphene. However, no link between the klein paradox and the negative refraction has been found in graphene. This is interpreted as the creation of particleantiparticle pairs, where the negative transmission coefficient just shows the flux of. Chiral tunneling and the klein paradox in graphene m. Both these results can be identified as fine examples of the klein paradox. Carbon materials karyn le hur, yale university cpht, ecole. Both the incoming and transmitted wave functions are associated with positive group velocity blue lines in fig. The explanation of this effect in terms of electronpositron production is reassessed. Chiral tunneling and the klein paradox in graphene. Leggett such sheets have long been known to exist in disguised forms in graphite many graphene sheets stacked on top of one another, c nanotubes a graphene sheet rolled into a. Graphene klein tunnel transistors for high speed analog rf. Electricfield control of magnetism in graphene quantum. Shot noise generated by graphene pn junctions in the quantum hall effect.

Klein paradox tunnelling and tsc fusion of d in pd nanoclusters frank dodd tony smith jr september 2015 vixra 1509. In this thesis, we report transport studies performed on cvdgrown graphene. In nonrelativistic quantum mechanics, electron tunneling into a barrier is observed, with exponential damping. Pdf the socalled klein paradoxunimpeded penetration of relativistic particles through high and wide potential barriersis one of the most exotic and. Of particular interest is the case of a graphene layer in contact with a superconducting electrode, where the in terplay between superconductivity and the relativistic behavior of charge carriers in graphene can be tested 3. Klein noted that pauli had pointed out to him that for x0, the particle momentum is given by p2 v. 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. 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. We find that for particular directions the transmission probability, t, is equal to 1, in particular t1 for forward scattering. Both the kleingordon and the dirac equation are no 1particle waveequations, but relativistic. Comment on chiral tunnelling and the klein paradox in. In 1929, physicist oskar klein obtained a surprising result by applying the dirac equation to the familiar problem of electron scattering from a potential barrier. Antiparticles klein paradox and zitterbewegung spin orbit coupling.

He has a particular annne in the field of language assessment and has designed both oral and written test instruments for a number of institutions. Dirac materials materials whose low energy electronic properties are a. The resulting switch displays an excellent onoff ratio performance. Shot noise generated by graphene p nature communications. Klein tunnel fet based on dual tilted graphene pn junctions gpnj. It becomes feasible therefore to test the klein paradox at a steplike potential discontinuity. Applications to graphene systems are also discussed. A graphene flake is sandwiched between hbn and then transferred on top of sio 2 to make sure high quality graphene is achieved 7. This is what many articles and books call the klein paradox. Transport studies on cvdgrown graphene miriam hanna huntley. Chiral selective tunneling induced graphene nanoribbon switch. Localization of dirac electrons in rotated graphene bilayers. In 1929, it was discovered by physicist oskar klein 11, 9. Relativistic quantum mechanics with trapped ions csic.

Pdf we study the dynamics of carriers in graphene subjected to an. Owing to the chiral nature of their quasiparticles, quantum tunnelling in these materials becomes highly anisotropic, qualitatively different from the case of normal, nonrelativistic electrons. Combining the two equations in 4 we obtain the decoupled equations. In graphene heterostructures, the modulation of conductance as functions of electron trajectory and electrostatic potential profile has previously.

Implications klein tunneling times high frequency graphene devices advances in engineering duration. Geim, chiral tunneling and the klein paradox in graphene. Electricfield control of magnetism in graphene quantum dots. Negative refraction gives rise to the klein paradox. Perfect andreev reflection due to the klein paradox in a. Here we show that the effect can be tested in a conceptually simple condensedmatter experiment using electrostatic barriers in single and bilayer graphene. Klein tunneling from 2 perfect transmission for monolayer graphene for arbitary width of the tunnel barrier transmission decays exponentially for bilayer graphene semiclassical behaviour oscillating transmission for nonchiral semiconductor even though the dispersion for both bilayer graphene and conventional semiconductor are. Pdf hosted at the radboud repository of the radboud. The essential features of klein tunneling of massless fermions in graphene may be treated in one dimension without the need for dirac spinors.

Geim2 1 institute for molecules and materials, radboud university nijmegen, 6525 ed nijmegen, the netherlands 2manchester centre for mesoscience and nanotechnology, university of manchester, manchester m 9pl, uk abstract. Quantum simulation of the klein paradox quantum optics. Here we show that the effect can be tested in a conceptually simple condensedmatter experiment by using electrostatic barriers in single and bilayer graphene. The klein paradox was first described by oskar klein in 1928 when investigating scattering of relativistic particles described by the dirac equation. Both the klein gordon and the dirac equation are no 1particle waveequations, but relativistic. Graphene is the thinnest known material, a sheet of carbon atoms arranged in hexagonal cells a single atom thick, and yet stronger than diamond.

Two dimensions needs a spinor treatment and is investigated numerically, which lets us compare tunneling through smooth potential barriers with that through idealized step potentials. An appendix treats klein tunneling in 1d using a toy model that allows us to easily compare mono and bilayer graphene. Graphene nanoscale ribbons and patches exhibit magnetic properties. Klein found that a relativistic particle encountering a potential step larger than its kinetic energy has a probability to be transmitted, whereas intuition would have this particle reflect.

Anton ramsak ljubljana, december 2010 abstract in this seminar i present graphene, a new material with promising application possibilities and important fundamental physics aspects. Andrei rutgers university 2d materials background carbon allotropes graphene structure and band structure electronic properties electrons in a magnetic field onsager relation. 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. It has potentially significant applications in nanotechnology, beyondsilicon electronics, solidstate realization of highenergy phenomena and as a prototype membrane which could revolutionise soft matter and 2d physics. V4 so if the transmitted particle moved from left to right, v. Relativistic quantum mechanics with trapped ions core. Pdf the klein paradox, which relates to the ability of relativistic particles to pass through extreme potential barriers, could. The klein paradox refers to the amplification of the tunnelling probability in relativistic systems if the potential barrier is increased. What we see is that the negative energy solutions of the dirac equation become accessible on the barrier side thus allowing both reflection and transmissi. Despite these imperfections, the charge carriers can move. Massless dirac fermions in graphene allow a close realization of klein s gedanken experiment. 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.

Screen printing process of silver paste electrodes on graphene pet film. Elementary electronic properties of graphene 112 a. These pn junctions incorporate a potential step for graphene diraclike fermions allowing us to investigate klein tunneling in graphene. Graphene therefore offers the prospect of testing some aspects of qed, usually requiring large, highenergy particle accelerators, in cheaper tabletop experiments. Klein paradox tunnelling and tsc fusion of d in pd nano. An armchair graphene nanoribbon switch has been designed based on the principle of the klein paradox. If i hadnt called, my money walmart oil change coupons nov coupon code for adobe export pdf would still be in limbo.

Klein paradox in chaotic dirac billiards sciencedirect. Klein paradox if we solve the dirac equation in presence of a potential barrier. The klein paradox allows electrons to move through a graphene layer as if it were ideal. Finally, we also discuss the existence of pn junctionlike structures between metal contacts and graphene, a topic that has an impact on. The phenomenon is discussed in many contexts in particle, nuclear, and astrophysics, but direct tests of the klein paradox. An anomalous tunneling phenomenon, in which electrons do not pass through the graphene nanoribbon junction even when the conventional resonance condition is satisfied, is observed in our numerical simulations. Graphene a new form of carbon with scientific impact and. Generally, the klein paradox in graphene can be understood as tunneling of quasiparticles dirac fermions through a high and wide potential barrier 20.

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