Inhibiting klein tunneling in a graphene pn junction without an external magnetic field hyungju oh,1,2, sinisa coh,1,2 youngwoo son,1,2,3 and marvin l. Tunneling electrons and phonon interaction leads to. Synthesis of ndoped graphene by chemical vapor deposition. Quantum tunnelling is a phenomenon which becomes relevant at the nanoscale and below. Aug 20, 2006 the socalled klein paradoxunimpeded penetration of relativistic particles through high and wide potential barriersis one of the most exotic and counterintuitive consequences of quantum. Utilizing this property, we further investigate the effect of electron collimation in 3lg.
The authors present an overview of the main theoretical approaches used to describe tunnel processes in graphene nanoelectronics. Allgraphene fieldeffect transistor based on lateral. Both the incoming and transmitted wave functions are associated with positive group velocity blue lines in fig. Klein paradox and resonant tunneling in a graphene superlattice article pdf available. Klein paradox in the graphenebased doublebarrier structures. Pasupathy1 1department of physics, columbia university, new york, new york 10027, usa 2department of chemistry and chemical biology, cornell university, ithaca, new york 14853,usa. Abstract for nanoelectronics applications of graphene a mass gap in its energy spectrum is needed like a conventional semiconductor. The transport properties of the relativistic electron through graphene based double barrier structures have been investigated based on the realspace noninteracting green function. Both the kleingordon and the dirac equation are no 1particle waveequations, but relativistic. Pdf klein paradox and resonant tunneling in a graphene. 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. Inhibiting klein tunneling in a graphene p n junction.
Chiral tunneling and the klein paradox in graphene wolfram. Pdf chiral tunneling and the klein paradox in graphene. The absence of states at the fermi level suggests that the p. Chiral tunneling and the klein paradox in graphene arxiv vanity. We begin with a summary of the dirac equation in one dimension in the presence of a potential v x and show. Quantum simulation of the klein paradox quantum optics and.
At high enough adatoms concentrations, such clusters merge into percolative pathways, effectively partitioning the graphene sheet into weaklycoupled graphene dot arrays, or gm. Since highquality, largearea, and continuous cvd graphene was grown, it enabled the fabrication of large device arrays with 40 individually addressable nonlocal spin valves exhibiting 83. The klein paradox role of chirality klein tunneling in singlelayer graphene klein tunneling and conductivity klein tunneling in bilayer graphene. Graphene also is a solidstate equivalent of a system of relativistic particles. The former is caused by the strong scattering under a high efield, and the latter is due to the appearance of a tunneling barrier in graphene channel induced by a structural transformation from crystalline graphene to disordered.
The socalled klein paradox unimpeded penetration of relativistic particles through high and wide potential barriersis one of the most exotic and counterintuitive consequences of quantum. 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. Klein tunneling in weyl semimetals under the influence of magnetic field. Chiral tunnelling and the klein paradox in graphene. Modeling klein tunneling and caustics of electron waves in. Tunable fewelectron double quantum dots and klein tunnelling in ultraclean carbon nanotubes g. Nov 07, 2011 however, the dirac electrons found in graphene can tunnel through energy barriers regardless of their width and energy height. Here we investigate the klein tunneling effect in weyl semimetals under the. Allgraphene fieldeffect transistor based on lateral tunnelling. Published 12 february 2014 2014 iop publishing ltd journal of physics d. Graphene is composed of singleatom thick sheets of sp2 bonded carbon atoms that are arranged in a perfect twodimensional 2d honeycomb lattice.
Due to the difference in the berrys phase, we show. The socalled klein paradox unimpeded penetration of relativistic particles through high and wide potential barriersis one of the most exotic and counterintuitive consequences of quantum electrodynamics. Dynamic tunneling junctions at the atomic intersection of. Synthesis and nitrogen doping of graphene by chemical vapor deposition controllable carrier transport due to charged impurities in the graphene lattice is still lacking. The chirality originates from the diatomic unit cell of the graphene crystal lattice and means that the amplitude of the electron. Optimized cvd graphene was demonstrated to have idg. An electron moving through the hexagonal crystal structure of graphene is not only quasirelativistic but also exhibits chirality 1. Controllable double quantum dots and klein tunneling in nanotubes. Massless dirac fermions in graphene allow a close realization of kleins gedanken experiment whereas massive chiral fermions in bilayer graphene offer an.
We study the effect of chiraltunneling in bernal and rhombohedral stacked trilayergraphene 3lg. Doping of graphene by foreign atoms leads to modify its band structure and electro chemical properties. Here we show that the effect can be tested in a conceptually simple condensedmatter experiment using electrostatic barriers in single and bilayer graphene. The klein paradox was first described by oskar klein in 1928 when investigating. 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. In particular, they have unique properties that make. The essential features of klein tunneling of massless fermions in graphene may be treated in one dimension without the need for dirac spinors. It is a paradox from the classical point of view as it enables elementary particles and atoms to permeate an energetic barrier without the need for sufficient energy to overcome it. Simulating quantum transport through mesoscopic, ringshaped graphene structures, we address various quantum coherence and interference phenomena.
Chiral tunneling and the klein paradox in graphene. 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. However, the dirac electrons found in graphene can tunnel through energy barriers regardless of their width and energy height. Design, synthesis, and characterization of graphene. Cohen1,2 1department of physics, university of california, berkeley, california 94720, usa 2materials sciences division, lawrence berkeley national laboratory, berkeley, california 94720, usa 3korea institute for advanced study, hoegiro 85. Twistcontrolled resonant tunnelling between monolayer and. Chiral tunnelling and the klein paradox in graphene author s. Chiral tunnelling and the klein paradox in graphene nature.
Detection of graphene chirality using achiral liquid. Chiral tunnelling and the klein paradox in graphene nasaads. Chiral tunneling and the klein paradox in graphene article pdf available in nature physics 29. Resonant tunnelling between the chiral landau states of. The peculiarities of chiral tunneling are naturally explained in terms of the classical phase space. One way to inhibit the klein tunneling is to open a band gap in graphene and consequently change the linear dispersive. Tunnelling spectroscopy of andreev states in graphene. Highquality chemical vapor deposition graphenebased. In graphene, the quasiparticle excitations around the dirac point obey linear diraclike energy dispersion law, which can be described by a twodimensional dirac equation. In nonrelativistic quantum mechanics, electron tunneling into a barrier is. Klein tunneling in weyl semimetals under the influence of magnetic. This determines the presence of the klein paradox in graphene1 which manifests itself in the fact that tunnel barriers inside graphene are transparent for electrons that are incident on them at a right angle. A major obstacle for graphene based electronics is the inability to confine dirac electrons by electrostatic potentials, because of a unique characteristic of relativistic massless electrons known as klein tunneling 15.
Based on the chirality of the electronic bands, at the kpoint, rhombohedral bernal3lg exhibits 100% 50% transparency across a heterojunction. Recent experiments have shown that the sic layer immediately below the graphene is itself a carbonrich layer, with an inplane, graphenelike network of sp2derived. However, when the bias voltage between the tip and graphene sample increased above a special threshold of 63 millivolts, then each tunneling electron is able to create a phonon vibration in the graphene sheet, which allows the electron to get into the graphene much easier, crommie says. 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. Jain 1department of physics, 104 davey lab, pennsylvania state university, university park, pennsylvania 16802, usa. 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 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. One of the main reasons for this attention is that the potential barrier. Falko12 1national graphene institute, the university of manchester, manchester, m9pl, uk 2school of physics and astronomy, the university of manchester, manchester, m9pl, uk thomas. Katsnelson, and shengjun yuan radboud university of nijmegen, institute for molecules and materials, heijendaalseweg 5, 6525 aj nijmegen, the netherlands. Negative differential conductance and tunneling characteristics of twoterminal graphene devices are observed before and after electric breakdown, respectively. Chiral tunnelling and the klein paradox in graphene condensed. Klein tunneling and electron trapping in nanometrescale graphene quantum dots christopher guti. Geim, chiral tunnelling and the klein paradox in graphene, nature physics, 2, 2006 pp. Fall 2008 department of physics and astronomy, the university of tennessee at knoxville, 37996. The socalled klein paradoxunimpeded penetration of relativistic particles through high and wide potential barriersis one of the most exotic and counterintuitive consequences of quantum.
Currently the growth and development of high quality, largearea cvd graphene on catalytic metal. Dynamic tunneling junctions at the atomic intersection of two. The 2d honeycomb lattice structure of singlelayer graphene is a possible physical environment for testing kleintunneling experimentally and the behavior of this type of fermions in this context can be modeled by the equation i t i f. Using a selfconsistent description of the devices electrostatic configuration, we relate the current to three distinct tunable voltages across the system and. Klein tunneling and dirac potentials in trapped ions. Klein tunneling of massive dirac fermions in singlelayer. Several examples are used to illustrate the specific. Multiple virtual tunneling of dirac fermions in granular. Whilst studying the double quantum dot, the researchers discovered a new type of tunnelling that is analogous to tunnelling according to the klein paradox. The ndoped graphene were removed from the substrate by scratching and sonicating in 0. Klein tunneling and dirac potentials in trapped ions j. Quantitative comparison between theory and experiment ajit c. This fact makes the control of the current in graphene by the external electrostatic.
Geim, chiral tunneling and the klein paradox in graphene, nature phys. In this paper, motivated by mass production of graphene, by the use of 2d massive diraclike equation we obtain the exact solution for the transmission probability corresponding to the klein tunneling of massive dirac fermions through a twodimensional barrier. However, klein s result showed that if the potential is of the order of the electron mass. The investigation of the transport properties of single molecules by flowing tunneling currents across extremely narrow gaps is relevant for challenges as diverse as the development of molecular electronics and sequencing of dna. Klein tunneling in graphene systems under the influence of. This paper studies the transport properties of charge carriers through graphene superlattices consisting of monolayer or bilayer graphene on. In nonrelativistic quantum mechanics, electron tunneling into a barrier is observed, with exponential damping. Our tunnelling spectroscopy study provides fundamental insights into how the josephson effect develops in graphene, and it can be extended to other 2d materials. Because of this structure, graphene is characterized by a number of unique and exceptional structural, optical, and electronic properties.
Controllable double quantum dots and klein tunneling in. D svintsov 1,2, v vyurkov 1,2, a orlikovsky 1,2, v ryzhii 3 and t otsuji 3. Falko 12 1 national graphene institute, the university of manchester, manchester, m9pl, uk. Modeling klein tunneling and caustics of electron waves in graphene r. The achievement of welldefined electrode architectures remains a technical challenge, especially due to the necessity of high precision fabrication processes and the. But comparing cvd graphene properties to exfoliated graphene, the latter goes on exhibiting better quality so far. Although the extreme chemical stability of graphene is the origin of its strong. Aug 30, 20 we study klein tunneling across a pn junction in monolayer graphene mlg and the abbilayer graphene blg under the effect of a perpendicular magneticfield bfield.
Chiral tunnelling and the klein paradox in graphene, published online. 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. Nov 17, 2015 we investigate the currentvoltage characteristics of a fieldeffect tunnelling transistor comprised of both monolayer and bilayer graphene with wellaligned crystallographic axes, separated by three layers of hexagonal boron nitride. Diraclike quasiparticles ingraphene graphene is a single layer of carbon atoms densely packed in a. Synthesis of large area and high quality graphene has been demonstrated by this method 6,7. The parameters for graphene given in that paper have been used. In recent years, there has been increased interest in studying the physical properties of graphene and graphenebased microstructures since their experimental realization. In this paper, an analytical form of the realspace noninteracting green function of graphene material is developed.
Inhibiting klein tunneling in a graphene p n junction without. Klein paradox and resonant tunneling in a graphene superlattice. 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. Pdf chiral tunnelling and the klein paradox in graphene. In the klein tunneling process, normally incident electrons in mlg blg are fully transmissive reflective upon hitting the junction barrier. Quantum tunnelling to the origin and evolution of life. Thus, the problem of klein tunneling of relativistic particles across a potential barrier and the socalled klein paradox, which recently has gained more attention can be put to the test. Recently, chemical functionalization of graphene 15 was reported to be a viable method to produce granular graphene 16, due to the tendency of adatoms to form electrically insulating clusters.
The ndoped graphene was dispersed in ethanol by mild sonication, and then. Supporting material for synthesis of ndoped graphene by chemical vapor deposition and its electrical properties dacheng wei, yunqi liu, yu wang, hongliang zhang, liping huang, and gui yu beijing national laboratory for molecular sciences, key laboratory of organic solids, institute of. May 14, 2009 whilst studying the double quantum dot, the researchers discovered a new type of tunnelling that is analogous to tunnelling according to the klein paradox. The discovery of graphene has enabled the experimental realization of this effect. Here we show a new and unique incarnation of the klein paradox. Massless dirac fermions in graphene allow a close realization of kleins gedanken experiment, whereas massive chiral fermions in bilayer. Many experiments in electron transport in graphene rely on the klein paradox for massless. 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. At nonnormal incidence, this tunneling problem for 2d massless fermions can be represented as a 1d problem for massive dirac. 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. When a finite bfield is applied, transmission of the normally incident electrons. Dec 19, 2017 simulating quantum transport through mesoscopic, ringshaped graphene structures, we address various quantum coherence and interference phenomena.
Tunable fewelectron double quantum dots and klein tunnelling. Twistcontrolled resonant tunnelling between monolayer and bilayer graphene t. Chiral tunneling in singlelayer and bilayer graphene. First, a perpendicular magnetic field, penetrating the graphene ring, gives rise to aharonovbohm oscillations in the conductance as a function of the magnetic flux, on top of the universal conductance fluctuations. Klein paradox, which constitutes one of the most interesting.
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