We investigate the roles of the pseudospin and the valley degeneracy in electron scattering at graphene edges. Ting1 1texas center for superconductivity, university of houston, houston, texas 77204, usa 2institute of physics, chinese academy of sciences, p. Electronic properties of curved fewlayers graphene. Mar 14, 2012 designer dirac fermions and topological phases in molecular graphene. Berry phase and pseudospin winding number in bilayer graphene. It is found that they are strongly correlated with charge density modulations of shortwavelength oscillations and slowly decaying beat patterns in the electronic density profile. The first part concerns the effect of the lattice pseudospin, an analog of a relativistic electron spin, on the scattering properties of.
The former occurs due to the bipartite honeycomb lattice, which has two distinct sublattices. Weak localisation magnetoresistanceand valley symmetry in graphene e mccann, k kechedzhi, vi falko, h suzuura, t ando, and bl altshuler, phys rev lett. K, k while the coupling of the electron spin sto its momentum p is a relativistic effect, and. The presence of spin, however, introduces a pseudovector. Many of the interesting physical phenomena appearing in graphene are gov. Nov 27, 2012 the potential use of graphene in spintronic devices is limited by its weak spinorbit coupling. At an open boundary, the edge potential u 0 is shown to turn on pseudospin. Graphene s spin equivalent, pseudospin, arises from the degeneracy introduced by the honeycomb. Graphene and relativistic quantum physics bourbaphy. In section 3, we discuss various graphene quantum dots and their associated spin relaxation times. Ever since the novel quantum hall effect in bilayer graphene was discovered, and explained by a berry phase of 2. Note on lattice spin in graphene and spin from isospin phenomenon.
Pseudospin and chirality the particles described by the dirac hamiltonian of monolayer graphene have yet another property. Graphenes spin equivalent, pseudospin, arises from the degen eracy introduced. Phase coherence in graphene ubc library open collections. In the original edition of this book, composite bosons. Spin and valley quantum hall ferromagnetism in graphene a. Bound states and magnetic field induced valley splitting in gate. Formation of unconventional standing waves at graphene edges. We show that pseudospin 12 degrees of freedom can be categorized in two types according to their behavior under time reversal. Graphenes spin equivalent, pseudospin, arises from the degeneracy introduced by the honeycomb lattices two inequivalent atomic sites per unit cell. Hierarchy of fillings for the fqhe in monolayer graphene. Box 9506, 2300 ra leiden, the netherlands published 6 october 2008 a colloquiumstyle introduction to two electronic processes in a carbon monolayer graphene is. Catalan institute of nanoscience and nanotechnology the prospect of transporting spin information over. Also, one may need to take into account an additional real spin degeneracy of all states p. Tuning the pseudospin polarization of graphene by a.
Graphene offers a rich platform for this research 4, 5, because the conduction electrons have three distinct spin quantum numbers. Formation of unconventional standing waves at graphene. Aug 16, 2012 graphene s spin equivalent, pseudospin, arises from the degeneracy introduced by the honeycomb lattices two inequivalent atomic sites per unit cell. The two dimensional charge carriers in mono and bilayer graphene are described by massless and massive chiral dirac hamiltonians, respectively. Whenever the direction of motion of the electron changes, the sublattice pseudospin also has to change and realign to the new direction of motion 2. The pseudospin behaves in many aspects like a true electron spin and can be seen as an internal angular momentum see fig. Graphene sublattice symmetry and isospin determined by. Singleelectron transport in graphenelike nanostructures. In the case of graphene, the landau quantization resulting from this pseudomagnetic field has been measured using scanning tunneling microscopy.
It is shown that these magnetic defects are also partly. Spin and valley quantum hall ferromagnetism in graphene. Designer dirac fermions and topological phases in molecular graphene. We study graphene monolayer charge carriers irradiated by an electromagnetic vortex. In graphene science, i dont understand how one interprets pseudospin as a vector. Weak localization in monolayer and bilayer graphene. Band structure of graphene, massless dirac fermions as low. Pseudospinorbital coupling for pseudospintronic device in. For instance, valleys are fully mixed for armchair graphene nanoribbons, while they are polarized for zigzag graphene nanoribbons 48,49. Pseudospin driven spin relaxation mechanism in graphene 12 november 2014, by icn2 credit. Katsnelson,5 and francisco guinea6 1center for statistical and theoretical condensed matter physics and department of physics, zhejiang normal university, jinhua 321004, peoples republic of china 2beijing computational science research center, beijing 84, peoples republic of.
Giant valley isospin conductance oscillations in ballistic graphene. Beenakker instituutlorentz, universiteit leiden, p. In the su4 kondo effect, the screening of the local magnetic moment requires, on average, three. Pseudospin filter for graphene via laser irradiation. Magnetoplasmons and su4 symmetry in graphene andrea m fischer1, rudolf a r omer1 and alexander b dzyubenko2. Graphene s spin equivalent, pseudospin, arises from the degeneracy introduced by the honeycomb lattices two inequivalent atomic sites per unit cell.
Pseudospindriven spin relaxation mechanism in graphene. Manipulation of valley isospins in strained graphene for. The phase coherent properties of electrons in low temperature graphene are measured and analyzed. Valley isospin of interface states in a graphene pn junction in the quantum hall regime. Transmission of chiral electrons through the pn junction in graphene. This means that the rate of pseudospin relaxation in graphene in the nonrelativistic limit can potentially be much greater than that of electron spin in a semiconductor quantum well. Weak localization of dirac fermions in graphene xinzhong yan1,2 and c. Tunable orbital pseudospin and multilevel kondo effect in carbon nanotubes. In graphene, the strong coulomb interactions and approximate spinpseudo spin symmetry are predicted to lead to a variety of quantum hall ferromagnetic ground states and excitations which manifest as integer quantum hall plateaus appearing within a graphene. Furthermore, graphene electrons couple to the electromagnetic. Valleymomentum locking in a graphene superlattice with y. Unlike isospin, however, pseudospin is intimately connected to rotations in real space. We shall start with analyzing general properties of the twoterminal conductance for graphene mono and bilayer samples.
Weak localisation in graphene trigonal warping and. The su4 symmetry of graphene arising from spin and valley pseudospin degrees of freedom is explored. These metrics are regularly updated to reflect usage leading up to the last few days. Changes in the substrate of epitaxial graphene give a smooth potential that conserves the pseudospin of chiral electrons. The quantum hall effect qhe is one of the most fascinating and beautiful phenomena in all branches of physics. Here we report the observation of a number of these quantum hall isospin ferromagnetic qhifm states, which we classify according to their real spin structure using tilted. Giant rashba splitting in graphene due to hybridization. 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.
Although graphene linear spectrum is important, it is not the only essential feature. Chiu1, yang xu2 1department of physics, massachusetts institute of technology, cambridge, ma 029, usa and 2institute of microelectronics and optoelectronics, college of information science and electronic engineering, zhejiang university, 310027 p. This thesis describes low temperature transport experiments designed to probe the consequences of this basic fact. They characterize the pseudospin valve in terms of the pseudomagneto resistance ratio, pmr. Weaklocalization magnetoresistance and valley symmetry in. The promise of graphene and graphenederived structures. We study magnetoplasmons or neutral collective excitations of graphene in a strong perpendicular magnetic eld, which can be modelled as bound electronhole pairs. Rudolf roemer university of warwick, coventry, uk dr.
Conclusions and outlook 10 acknowledgments 10 references 10 1. Helical scattering and valleytronics in bilayer graphene henning schomerus department of physics, lancaster university, lancaster la1 4yb, united kingdom received 18 august 2010. Rr ap par p where r apr p is the resistance for the pseudospin antiparallel structure pseudospin parallel structure and finds a large onoff ratio in their. On the other hand, it also lifts pseudospin symmetry, leading to modi cations of wl. Nov 12, 2014 the prospect of transporting spin information over long distances in graphene, possible because of its small intrinsic spinorbit coupling and vanishing hyperfine interaction, has stimulated. Generation of pure bulk valley current in graphene yongjin jiang,1,2, tony low,3 kai chang,4,2, mikhail i. Altshuler4 1department of physics, lancaster university, lancaster, la1 4yb, united kingdom 2division of applied physics, graduate school of engineering, hokkaido university, sapporo 0608628, japan. Entangled spinvalley texture states in graphene in the. Theoretical analyses using nearestneighbor tightbinding methods and firstprinciples density. Graphene and relativistic quantum physics philip kim department of physics columbia university new york new york 10027, usa 1 introduction graphene is one atom thick layer of carbon atoms arranged in a honeycomb lattice. In this thesis we consider several topics in electronic and spin properties of graphene, with a particular emphasis on the quantum hall effect qhe regime, where this material exhibits most interesting behavior. Esr spectroscopy of graphene with adsorbed nacl particles.
In the next section, we give an overview over spintronics in quantum dots and motivate the use of graphene. Electronic properties of bilayer graphene, from high to low energies. Full effective hamiltonian for lowenergy properties 8components wavefunction. Graphene sublattice symmetry and isospin determined by circular dichroism in angleresolved photoemission spectroscopy article in nano letters 128. Altshuler4 1department of physics, lancaster university, lancaster, la1 4yb, united kingdom 2division of applied physics, graduate school of engineering, hokkaido university, sapporo 0608628, japan 3department of physics, tokyo institute of.
Recent theoretical advances in graphene spintronics. Moessner cnrs, paris, france entangled spinvalley texture states in graphene in the quantum hall regime. Weaklocalization magnetoresistance and valley symmetry in graphene e. Probing quantum interference effects in epitaxial graphene. Of these, two of the pseudospin triplet modes are intravalley cooperons while the remaining triplet and the singlet are intervalley cooperons. Theoretical analyses using nearestneighbor tightbinding methods and firstprinciples densityfunctional. Quantum hall effects world scientific publishing company. One of the intriguing characteristics of honeycomb lattices is the appearance of a pseudomagnetic field as a result of mechanical deformation. Graphenes spin equivalent, pseudospin, arises from the degeneracy. Pseudospin and spin dynamics are usually perceived as decoupled from each other, with pseudospin lifetimes being much shorter and pseudospin dynamics much faster than those for spins. Pseudospin and deformationinduced gauge field in graphene. When the leads are, respectively, of the n and p type, we find that electron elastic cotunneling and local andreev reflection are both eliminated even in the absence of any valleyisospin or spin polarizations. Apparently this happens because 2d diracweyl equation leaves out certain angular momenta, i.
Oct 10, 2011 in addition to spin and pseudospin, a third quantum label for graphene electrons is the twocomponent isospin degree of freedom, also called the valley index. Such valleymixing behavior is well characterized by introducing the concept of valley isospin in a bloch sphere as if describing the singlet spin state. Changes in the substrate of epitaxial graphene give a smooth potential that conserves the pseudospin of. Designer dirac fermions and topological phases in molecular.
A quantum critical point emergent relativistic quantum mechanics. Graphenes conduction and valence bands are defined by two inequivalent sets of dirac cones, which sit at the points k and k. Tunable orbital pseudospin and multilevel kondo effect in. Singleelectron transport in graphenelike nanostructures k. The dirac equation insights about graphene from relativistic qm insights about relativistic qm from graphene quantum hall effect in graphene. One is called sublattice pseudospin and the other valley isospin. Here, we use a direct product of isospin ab lattice space matrices. One type exhibits the properties of ordinary spin whose three cartesian components are all odd under time reversal. Note on lattice spin in graphene and spin from isospin. Recent theoretical advances in graphene spintronics phantoms.
Helical scattering and valleytronics in bilayer graphene. Box 603, beijing 80, china received 24 january 2008. Here we show that a signature of the pseudomagnetic field is a local sublattice symmetry breaking observable. Quantum theory of graphene graphenes electronic structure. Tremendous theoretical and experimental developments are still being made in this sphere. Graphene is a oneatomthick sheet of carbon and produced by gently pushing small graphite crystals along a hard surface.
In a way, pseudospin in graphene can be considered to more readily undergo adiabatic relaxation in an analogously dyakonov manner. Nov 15, 2011 we investigate the roles of the pseudospin and the valley degeneracy in electron scattering at graphene edges. Pdf note on lattice spin in graphene and spin from isospin. The natural conclusion is that the pseudospin is a real angular momentum. Quantum transport in graphene heterostructures academic. Above zero energy, the current carrying states in graphene are, as usual, electronlike and negatively charged. Giant rashba splitting in graphene due to hybridization with. I demonstrate that graphene is able to coherently transport spinpolarized electrons over micrometer distances, and prove that magnetic defects in the graphene sheet are responsible for limiting spin transport over longer distances. We investigate the crossed andreev reflections between two graphene leads connected by a narrow superconductor. In addition to spin and pseudospin, a third quantum label for graphene electrons is the twocomponent isospin degree of freedom, also called the valley index. The potential use of graphene in spintronic devices is limited by its weak spinorbit coupling. Quantum pumping of layer pseudospin current in biased bilayer.
Giant valleyisospin conductance oscillations in ballistic. Effects of edge potential on an armchairgraphene open. I thought pseudospin was the vector of pauli matrices. Chiu1, yang xu2 1department of physics, massachusetts institute of technology, cambridge, ma 029, usa and 2institute of microelectronics and optoelectronics.
Symmetries and optics alexander b dzyubenko california state university bakersfield, usa general physics institute, russian academy of sciences, moscow, russia plmcn14 crete, greece may 20 prof. However despite the often claimed fact that it just resembles spin, it seems that pseudospin actually does carry some real angular momentum arxiv. So how can it be a vector that one can plot for example in the image below. Singleelectron transport in graphene like nanostructures k.