Chiral tunnelling and the Klein paradox in graphene

Graphene, a one-atom thick zero gap semiconductor [1,2], has been attracting an increasing interest due to its remarkable physical properties ranging from an electron spectrum resembling relativistic dynamics [3,4,5,6,7,8,9,10,11,12] to ballistic transport under ambient conditions [1,2,3,4]. The latter makes graphene a promising material for future electronics and the recently demonstrated possibility of chemical doping without significant change in mobility has improved graphene's prospects further [13]. However, to find optimal dopants and, more generally, to progress towards graphene-based electronics requires understanding the physical mechanism behind the chemical doping, which has been lacking so far. Here, we present the first joint experimental and theoretical investigation of adsorbates on graphene. We elucidate a general relation between the doping strength and whether or not adsorbates have a magnetic moment: The paramagnetic single NO 2 molecule is found to be a strong acceptor, whereas its diamagnetic dimer N 2 O 4 causes only weak doping. This effect is related to the peculiar density of states of graphene, which provides an ideal situation for model studies of doping effects in semiconductors. Furthermore, we explain recent results on its "chemical sensor" properties, in particular, the possibility to detect a single NO 2 molecule [13].Controlling the type and the concentration of charge carriers is at the heart of modern electronics: It is the ability of combining gate voltages and impurities for locally changing the density of electrons or holes that allows for the variety of nowadays available semiconductor based devices. However, the conventional Si-based electronics is expected to encounter fundamental limitations at the spatial scale below 10 nm, according to the semiconductor industry roadmap, and this calls for novel materials that might substitute or complement Si. Being only one atomic layer thick, graphene exhibits ballistic transport on a submicron scale and can be doped heavily -either by gate voltages or molecular adsorbateswithout significant loss of mobility [1]. In addition, later experiments [13] demonstrated its potential for solid state gas sensors and even the possibility of single molecule detection.We show, that in graphene, aside from the donoracceptor distinction, there are in general two different classes of dopants -paramagnetic and nonmagnetic. In contrast to ordinary semiconductors, the latter type of impurities act generally as rather weak dopants, whereas the paramagnetic impurities cause strong doping: Due to the linearly vanishing, electron-hole symmetric density of states (DOS) near the Dirac point of graphene, localised impurity states without spin polarisation are pinned to the centre of the pseudogap. Thus impurity states in graphene distinguish strongly from their counterparts in usual semiconductors, where the DOS in the valence and conduction bands are very different and impurity levels lie generally far away from the middle of the gap. Impurity effects on t...

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Molecular Doping of Graphene

et al. 2007

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“…The sublattice degree of freedom of the wavefunctions is given by a pseudospin vector that is either parallel or anti-parallel to the wavevector measured from the Dirac point, giving rise to a chirality being 1 or −1, respectively 5,6,7 . These two fundamental properties of graphene, linear energy dispersion and the chiral nature of the quasiparticles, result in interesting phenomenon such as half-integer quantum Hall effect 2,3 , Klein paradox 9 , and suppression of backscattering 6,7,10 , as well as some novel predicted properties such as electron supercollimation in graphene superlattices 11,12,13 .…”

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Making Massless Dirac Fermions from a Patterned Two-Dimensional Electron Gas

2009

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Analysis of the electronic structure of an ordinary two-dimensional electron gas (2DEG) under an appropriate external periodic potential of hexagonal symmetry reveals that massless Dirac fermions are generated near the corners of the supercell Brillouin zone. The required potential parameters are found to be achievable under or close to laboratory conditions. Moreover, the group velocity is tunable by changing either the effective mass of the 2DEG or the lattice parameter of the external potential, and it is insensitive to the potential amplitude. The finding should provide a new class of systems other than graphene for investigating and exploiting massless Dirac fermions using 2DEGs in semiconductors.Graphene 1,2,3,4 , a honeycomb lattice of carbon atoms, is composed of two equivalent sublattices of atoms. The dynamics of the low-energy charge carriers in graphene may be described to a high degree of accuracy by a massless Dirac equation with a two-component pseudospin basis which denotes the amplitudes of the electronic states on these two sublattices. The quasiparticles have a linear energy dispersion near the corners K and K ′ (the Dirac points) of the hexagonal Brillouin zone 5,6,7,8 . Consequently, the density of states (DOS) varies linearly and vanishes at the Dirac point energy. The sublattice degree of freedom of the wavefunctions is given by a pseudospin vector that is either parallel or anti-parallel to the wavevector measured from the Dirac point, giving rise to a chirality being 1 or −1, respectively 5,6,7 . These two fundamental properties of graphene, linear energy dispersion and the chiral nature of the quasiparticles, result in interesting phenomenon such as half-integer quantum Hall effect 2,3 , Klein paradox 9 , and suppression of backscattering 6,7,10 , as well as some novel predicted properties such as electron supercollimation in graphene superlattices 11,12,13 .As a possible realization of another two-dimensional (2D) massless Dirac particle system, theoretical studies on the physical properties of particles in optical honeycomb lattices 14 have been performed 15,16,17,18,19 . The behaviors of ultra-cold atoms in a honeycomb lattice potential were considered, in principle, to be equivalent to those of the low-energy charge carriers in graphene 15 .In this Letter, we propose a different practical scheme for generating massless Dirac fermions. We show through exact numerical calculations within an independent particle picture that applying an appropriate nanometerscale periodic potential with hexagonal symmetry onto conventional two-dimensional electron gases (2DEGs) will generate massless Dirac fermions at the corners of the supercell Brillouin zone (SBZ). We find that the potential configurations needed should be within or close to current laboratory capabilities, and this approach could benefit from the highly developed experimental techniques of 2DEG physics 20 including recent advances in self-assembly nanostructures 21,22,23 .We moreover find that the band velocity and the energy windo...

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“…1b By applying voltages to both top and back gates, we can create pnp junctions with in situ modulation of junction polarity and dopant levels. This in situ creation of pnp or npn junctions in double gated junctions has been extensively studied in single layer graphene (SLG) devices 16,17,[19][20][21][22][23] , and enabled the observation of phenomena such as Klein tunneling [24][25][26] , equilibration of counter-propagating edge modes 16,17,20,21 , and conductance fluctuations induced by charge localization in the quantum Hall regime 21 .…”

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Quantum Transport and Field-Induced Insulating States in Bilayer Graphene pnp Junctions

et al. 2010

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We perform transport measurements in high quality bilayer graphene pnp junctions with suspended top gates. At a magnetic field B=0, we demonstrate band gap opening by an applied perpendicular electric field, with an On/Off ratio up to 20,000 at 260mK. Within the band gap, the conductance decreases exponentially by 3 orders of magnitude with increasing electric field, and can be accounted for by variable range hopping with a gate-tunable density of states, effective mass, and localization length. At large B, we observe quantum Hall conductance with fractional values, which arise from equilibration of edge states between differentially-doped regions, and the presence of an insulating state at filling factor ν=0. Our work underscores the importance of bilayer graphene for both fundamental interest and technological applications.

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Chiral tunnelling and the Klein paradox in graphene

Cited by 3,782 publications

References 27 publications

Molecular Doping of Graphene

Molecular Doping of Graphene

Making Massless Dirac Fermions from a Patterned Two-Dimensional Electron Gas

Quantum Transport and Field-Induced Insulating States in Bilayer Graphene pnp Junctions

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