In nonrelativistic quantum mechanics, electron tunneling into a barrier is observed, with exponential damping. Negative differential conductance and chiral effects in. Apr 12, 2006 the socalled klein paradox unimpeded penetration of relativistic particles through high and wide potential barriers is one of the most exotic and counterintuitive consequences of quantum electrodynamics qed. May 30, 2009 an armchair graphene nanoribbon switch has been designed based on the principle of the klein paradox. Klein paradox tunnelling and tsc fusion of d in pd. Chiral tunneling and the klein paradox in graphene wolfram. Chiral tunnelling and the klein paradox in graphene nature. Chiral tunnelling and the klein paradox in graphene. 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. Klein tunneling in graphene graphene is a single layer graphite. Statistical magnitudes and the chiral tunneling in bilayer. Comment on chiral tunnelling and the klein paradox in graphene by m.
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 phenomenon is discussed in many contexts in particle, nuclear, and astrophysics, but direct tests of the klein paradox. When a massless chiral fermion mcf encounters a potential barrier, reflection is completely suppressed due the forbidden spinflipping transition, a phenomenon known as klein tunneling 3. Owing to the chiral nature of their quasiparticles, quantum. 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. Aug 14, 2019 chiral tunneling and the klein paradox in graphene. Massless dirac fermions in graphene allow a close realization of kleins gedanken experiment, whereas massive chiral fermions in bilayer. Chiral tunneling and the klein paradox in graphene arxiv vanity. Pdf klein paradox and resonant tunneling in a graphene. Chiral tunneling and the klein paradox in graphene article pdf available in nature physics 29.
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. Pdf chiral tunnelling and the klein paradox in graphene. Geim2 1institute 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. Pdf chiral tunneling and the klein paradox in graphene. Here we show that the effect can be tested in aconceptuallysimplecondensedmatterexperimentusing electrostatic barriers in single and bilayer graphene. Massless dirac fermions in graphene allow a close realization of klein s gedanken experiment whereas massive chiral fermions in bilayer graphene offer an. 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. Geim, chiral tunneling and the klein paradox in graphene, nature phys.
Rqm can be consistently formulated only in terms of fields rather than individual particles. Graphene klein tunnel transistors for high speed analog rf. Both the incoming and transmitted wave functions are associated with positive group velocity blue lines in fig. Klein tunneling across a graphene pn junction is driven by the conservation of pseudospin, which in turn is set by the phase coherent superposition of the dimer p z basis sets. The parameters for graphene given in that paper have been used. This treatment allows us to compute the statistical complexity and fishershannon information for each angle of incidence. Chiral tunnelling and the klein paradox in graphene m. Quantum interference and klein tunnelling in graphene. This is interpreted as the creation of particleantiparticle pairs, where the negative transmission coefficient just shows the flux of antiparticles to the right. Lattice, symmetry and band structure of monolayer graphene. Chiral tunnelling and the klein paradox in graphene pdf pdf the socalled klein paradoxunimpeded penetration of relativistic particles through high and wide potential barriersis one of the most. Chiral tunneling and the klein paradox in graphene.
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 gpnj acts as an efficient momentum filter, transmitting electrons that are injecting perpendicularly to the junction regardless of the barrier height across the. In graphene carbon atoms are sp2 bonded to their nearest neighbors, and thus form a honeycomb lattice made of. Researchers find electron chirality in graphene impacts. Both the kleingordon and the dirac equation are no 1particle waveequations, but relativistic. This is one of the key phenomena determining the peculiar electronic properties of graphene. The proper use of negative energy solution in the barrier region is also key to the introduction of klein tunneling in graphene. We have studied the tunneling of dirac fermions through magnetic barriers in graphene. Klein paradox and resonant tunneling in a graphene superlattice. The socalled klein paradox unimpeded penetration of relativistic particles through high and wide potential barriers is one of the most exotic and counterintuitive consequences of quantum electrodynamics qed. Katsnelson institute for molecules and materials, radboud university nijmegen, 6525 ed nijmegen.
Massless dirac fermions in graphene allow a close realization of kleins gedanken experiment, whereas massive chiral fermions in bilayer graphene offer an. Chirallike tunneling of electrons in twodimensional. Chiral tunneling in singlelayer and bilayer graphene. Due to the chiral nature of their quasiparticles, quantum tunneling in these materials becomes highly. The conservation of spin therefore leads to a perfect transmission of electrons through a high and wide potential barrier at normal incidence fig.
Resonant tunnelling between the chiral landau states of twisted graphene lattices, nature physics 2015. The resulting switch displays an excellent onoff ratio performance. 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. Chiral selective tunneling induced graphene nanoribbon switch. Tunneling of dirac fermions through magnetic barriers in graphene. Klein paradox chiral tunneling if the potential is on the order of the electron mass, the barrier is nearly transparent. If i hadnt called, my money walmart oil change coupons nov coupon code for adobe export pdf would still be in limbo. Katsnelson m i, novoselov k s and geim a k 2006 chiral tunneling and the klein paradox in graphene nat. Pdf the socalled klein paradoxunimpeded penetration of relativistic particles through high and wide potential barriersis one of the most. Chiral tunneling and the klein paradox in graphene by m. 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.
Geim, chiral tunneling and the klein paradox in graphene. 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. Quantum interference and klein tunnelling in graphene heterojunctions. Dragoman, negative differential resistance of electrons in graphene barrier, appl. Klein tunneling in singlelayer graphene transmission probabilities through a 100nmwide barrier as a function of the angle of incidence for single layer grahene. 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. Suppressing klein tunneling in graphene using a onedimensional.
Chiral tunneling and the klein paradox in graphene, nat. Chiral tunnelling and the klein paradox in graphene author s. Verkin institute for low temperature physics and engineering of the national academy of sciences of ukraine. Evidence against klein paradox in graphene iopscience.
Jun 19, 2015 the problem of the chiral kleinlike tunneling across a potential barrier in bilayer graphene is addressed. Chiral tunnelling and the klein paradox in graphene condensed. Comment on chiral tunnelling and the klein paradox in graphene. Rqm can be consistently formulated only in terms of. 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. The electron wave functions are treated as massive chiral particles. Chiral tunneling and the klein paradox in graphene core. In light of possible applications, klein tunneling protects high charge carrier mobility despite unavoidable inhomogeneities. The peculiarities of chiral tunneling are naturally explained in terms of the classical phase space. Due to the chiral nature of their quasiparticles, quantum tunneling in these materials becomes highly anisotropic, qualitatively different from the case of normal, nonrelativistic electrons. 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.
Chiral tunneling and the klein paradox in graphene m. Magnetic barriers are produced via delta functionlike inhomogeneous magnetic fields in which dirac fermions in graphene experience the tunneling barrier in the real sense in contrast to klein paradox caused by electrostatic barriers. Jun 30, 2019 pdf the socalled klein paradoxunimpeded penetration of relativistic particles through high and wide potential barriersis one of the most. Here we show that the effect can be tested in a conceptually simple condensedmatter experiment using electrostatic barriers in single and bilayer graphene.