Multilayer graphene synthesized by cvd using liquid hexane as. The klein paradox, referring to ideal tunneling of dirac particles through rectangular potential barriers leads to extensive mobility of charge carriers in graphene, which is experimentally observed even near dirac point being the fermi level at the border between electrons and holes if the the gate voltage is not included. Both the klein gordon and the dirac equation are no 1particle waveequations, but relativistic. 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. Buckling a graphene sheet in this final section you will learn how to buckle a graphene sheet using the quantumatk buckler plugin. Pdf klein paradox and resonant tunneling in a graphene.
This catalogue gives an overview of the companies performing work on graphene. Massless dirac fermions in graphene allow a close realization of kleins gedanken experiment, whereas massive chiral fermions in bilayer graphene offer an. Comment on chiral tunnelling and the klein paradox in graphene by m. This time, repeat the nanosheet 30 times in the c direction. The resulting switch displays an excellent onoff ratio performance. Pdf chiral tunneling and the klein paradox in graphene. These pn junctions in corporate a potential step for graphene diraclike fermions allowing us to investigate klein tunneling in graphene.
Mar 14, 2012 the extremely short transition between the p and ntype regions makes this device a suitable candidate in which to study phenomena such as the klein paradox 18 or to create a veselago lens 19. Jun 19, 2019 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. Designer dirac fermions and topological phases in molecular. Chiral tunnelling and the klein paradox in graphene core. 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. Emphasis is placed on the relation ship between the klein paradox. 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. Effect of boron nitrogendivacancy complex defects on. B 76, 075430 2007 2 chiral tunnelling and klein paradox, zitterbewegung. We designed an optical device to measure the transmittance of the carbon films.
Effect of boron nitrogendivacancy complex defects on the. These pn junctions incorporate a potential step for graphene diraclike fermions allowing us to investigate klein tunneling in graphene. The phenomenon is discussed in many contexts in particle, nuclear, and astrophysics, but direct tests of the klein paradox. 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 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. From experimental points of view, fieldeffect transistors 8 9, micromechanical resonators 10, gassensors of graphene have already been proposed 11. 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. Such tunneling from an electronlike to holelike state is called as interband tunneling or klein tunneling. Graphene and carbon nanotubes 20 band structure of graphene conduction and valence band along the first brillouin zone band structure along the highsymmetry direction k. Elementary electronic properties of graphene 112 a. Today, the availability of high mobility graphene up to room temperature makes ballistic transport in nanodevices achievable. However, kleins result showed that if the potential is of the order of the electron mass.
Klein paradox and resonant tunneling in a graphene superlattice chunxu bai and xiangdong zhang department of physics, beijing normal university, beijing 100875, china. Klein paradox if we solve the dirac equation in presence of a potential barrier. The klein paradox describes a tunneling phenomenon of a relativistic electron through a high potential barrier. Chiral tunnelling and the klein paradox in graphene condensed. Chiral tunnelling and the klein paradox in graphene.
The graphene handbook provides a great introduction to the world of graphene and covers everything you need to know about the graphene industry, market and technology. Chiral tunneling and the klein paradox in 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. Mechanical and electrical properties of graphene sheets joseph scott bunch, ph. Perfect andreev reflection due to the klein paradox in a. We report the effect of boron nitrogendivacancy complex defects on the electronic properties of graphene nanoribbon by means of density functional theory. Cornell university 2008 this thesis examines the electrical and mechanical properties of graphene sheets.
Graphene companies catalogue graphene 2020 june 02. Finally, we also discuss the existence of pn junction. This element is unique in that its unique electronic structure allows for hybridization to build up sp3,sp2, and sp networks and, hence, to form more known stable allotropes than any. Massless dirac fermions in graphene allow a close realization of kleins gedanken experiment whereas massive chiral fermions in bilayer. Since its discovery in 2004, graphene has been a great sensation due to its unique structure and unusual properties, and it has only taken 6 years for a noble prize to be awarded for the field of graphene research. 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. First, create a nanosheet as shown above in section build a graphene sheet. Fall 2008 department of physics and astronomy, the university of tennessee at knoxville, 37996. Pdf the socalled klein paradoxunimpeded penetration of relativistic particles through high and wide potential barriersis one of the most. The left and the right electrodes are separated from the central g by two barrier potential v 1 and v 2 with width d 1 and d 2, respectively. The power of graphene lesson explores graphene and its electrical properties and applications at the nano scale. In nonrelativistic quantum mechanics, electron tunneling into a barrier is observed, with exponential damping. The essential features of klein tunneling of massless fermions in graphene may be treated in one dimension without the need for dirac spinors. Graphene therefore offers the prospect of testing some aspects of qed, usually requiring large, highenergy particle accelerators, in cheaper tabletop experiments.
Such a local barrier can be implemented by either using the. It is an invaluable guide for material engineers, business developers, researchers, equipment vendors, graphene material companies, private investors and anyone who wants to. Chiral tunnelling and the klein paradox in graphene core reader. A kleintunneling transistor with ballistic graphene. The physical properties of graphene materials 1 the quasiparticle excitations around the dirac point obey linear diraclike energy dispersion rev. Massless dirac fermions in graphene allow a close realization of kleins gedanken experiment, whereas massive chiral. The fets were also fabricated using the doped graphene as channel material between source and drain electrodes as illustrated in figure 2a left.
An armchair graphene ribbon switch has been designed based on the principle of the klein paradox. Klein paradox and resonant tunneling in a graphene superlattice. We perform low temperature electrical transport measurements on gated, quasi2d graphite quantum dots. 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. Comment on chiral tunnelling and the klein paradox in. We consider a doublebarrier resonant structure giggigg in a monolayer graphene sheet occupying the xy plane, where the schematic potentials of the model are shown in fig. 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. Diraclike quasiparticles ingraphene graphene is a single layer of carbon atoms densely packed in a. The triggering role of carrier mobility in the fractional. Chiral tunneling and the klein paradox in graphene wolfram. The string type is most often used by graphql to represent freeform humanreadable text. Both the kleingordon and the dirac equation are no 1particle waveequations, but relativistic. It serves mainly as a valuable source to investors, enduser companies, policymakers, etc. Jun 30, 2019 pdf the socalled klein paradox unimpeded penetration of relativistic particles through high and wide potential barriersis one of the most.
It predicts that the electron can pass through the high potential barrier to approach the perfect transmission in contrast to the conventional nonrelativistic tunneling where the transmission probability exponentially decays with. We find that for particular directions the transmission probability, t, is equal to 1, in particular t1 for forward scattering. We find that in the case of potential well, the bound states. Katsnelson mi, novoselov ks, geim ak 2006 chiral tunnelling and the klein paradox in graphene. Multilayer graphene synthesized by cvd using liquid hexane as the carbon precursor abstract fulltext html xml download as pdf. Klein tunneling in quantum mechanics, an electron can tunnel from the conduction into the valence band.
The extremely short transition between the p and ntype regions makes this device a suitable candidate in which to study phenomena such as the klein paradox 18 or to create a veselago lens 19. Many experiments in electron transport in graphene rely on the klein paradox for. Chiral tunneling and the klein paradox in graphene article pdf available in nature physics 29. Geim, chiral tunneling and the klein paradox in graphene, nature phys. Many experiments in electron transport in graphene rely on the klein paradox for massless particles. Perfect andreev reflection due to the klein paradox. To resolve a paradox requires that the paradox should still be confusing at the time of publication. String represents textual data, represented as utf8 character sequences. Multilayer graphene synthesized by cvd using liquid hexane.
Historically, the klein paradox was important in demonstrating that a singleparticle dirac equation is inconsistent, and antiparticles are really required. The main goal is to have a source in hand where it would be possible in just one file to have an overall view of which companies develop their work on the field. Comment on chiral tunnelling and the klein paradox in graphene. In 1929, physicist oskar klein obtained a surprising result by applying the dirac equation to the. Teams evaluate their test results, develop new theoretical applications for graphene. It is found that the defective subbands appear in the conduction band and valence band in accordance with boron nitrogendivacancy defect, respectively. A kleintunneling transistor with ballistic graphene iopscience. Klein paradox for a pn junction in multilayer graphene article pdf available in epl europhysics letters 102. In particular, pnp transistors in the ballistic regime give access to klein tunneling physics and allow the realization of devices exploiting the opticslike behavior of dirac fermions dfs as in the veselago lens or the fabryperot cavity. Int represents nonfractional signed whole numeric values. 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 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. Anomalous tunneling phenomena are observed in our numerical simulations.
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. Twodimensional massive dirac equation in both potential well and linear potential is discussed. 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. Among these are charge carriers behaving as massless dirac fermions 2, klein tunneling 3 4, ballistic transport at room temperature 5 6, and anomalous quantum hall effects 7. Students work in teams to test graphene using a simple circuit set up and consider how this remarkable material is impacting many industries. Klein paradox in the graphenebased doublebarrier structures. Pdf klein paradox for a pn junction in multilayer graphene. This monograph gives a wellbalanced overview on all areas of. Graphene a new form of carbon with scientific impact and.
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