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