Properties of graphene: a theoretical perspective (original) (raw)
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The electronic properties of bilayer graphene
We review the electronic properties of bilayer graphene, beginning with a description of the tight-binding model of bilayer graphene and the derivation of the effective Hamiltonian describing massive chiral quasiparticles in two parabolic bands at low energy. We take into account five tight-binding parameters of the Slonczewski-Weiss-McClure model of bulk graphite plus intra-and interlayer asymmetry between atomic sites which induce band gaps in the low-energy spectrum. The Hartree model of screening and band-gap opening due to interlayer asymmetry in the presence of external gates is presented. The tight-binding model is used to describe optical and transport properties including the integer quantum Hall effect, and we also discuss orbital magnetism, phonons and the influence of strain on electronic properties. We conclude with an overview of electronic interaction effects. CONTENTS
From quantum confinement to quantum Hall effect in graphene nanostructures
2012
We study the evolution of the two-terminal conductance plateaus with a magnetic field for armchair graphene nanoribbons (GNRs) and graphene nanoconstrictions (GNCs). For GNRs, the conductance plateaus of 2e 2 h at zero magnetic field evolve smoothly to the quantum Hall regime, where the plateaus in conductance at even multiples of 2e 2 h disappear. It is shown that the relation between the energy and magnetic field does not follow the same behavior as in "bulk" graphene, reflecting the different electronic structure of a GNR. For the nanoconstrictions we show that the conductance plateaus do not have the same sharp behavior in zero magnetic field as in a GNR, which reflects the presence of backscattering in such structures. Our results show good agreement with recent experiments on high-quality graphene nanoconstrictions. The behavior with the magnetic field for a GNC shows some resemblance to the one for a GNR but now depends also on the length of the constriction. By analyzing the evolution of the conductance plateaus in the presence of the magnetic field we can obtain the width of the structures studied and show that this is a powerful experimental technique in the study of the electronic and structural properties of narrow structures.
The electronic properties of graphene
This article reviews the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. The Dirac electrons behave in unusual ways in tunneling, confinement, and the integer quantum Hall effect. The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers. Edge ͑surface͒ states in graphene depend on the edge termination ͑zigzag or armchair͒ and affect the physical properties of nanoribbons. Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.
Experimental observation of the quantum Hall effect and Berry's phase in graphene
Nature, 2005
When electrons are confined in two-dimensional materials, quantum-mechanically enhanced transport phenomena such as the quantum Hall effect can be observed. Graphene, consisting of an isolated single atomic layer of graphite, is an ideal realization of such a two-dimensional system. However, its behaviour is expected to differ markedly from the well-studied case of quantum wells in conventional semiconductor interfaces. This difference arises from the unique electronic properties of graphene, which exhibits electron-hole degeneracy and vanishing carrier mass near the point of charge neutrality 1,2 . Indeed, a distinctive half-integer quantum Hall effect has been predicted 3-5 theoretically, as has the existence of a non-zero Berry's phase (a geometric quantum phase) of the electron wavefunction-a consequence of the exceptional topology of the graphene band structure 6,7 . Recent advances in micromechanical extraction and fabrication techniques for graphite structures 8-12 now permit such exotic two-dimensional electron systems to be probed experimentally. Here we report an experimental investigation of magneto-transport in a high-mobility single layer of graphene. Adjusting the chemical potential with the use of the electric field effect, we observe an unusual halfinteger quantum Hall effect for both electron and hole carriers in graphene. The relevance of Berry's phase to these experiments is confirmed by magneto-oscillations. In addition to their purely scientific interest, these unusual quantum transport phenomena may lead to new applications in carbon-based electronic and magneto-electronic devices.
Electronic properties of graphene
2007
Graphene is the first example of truly two-dimensional crystals-it's just one layer of carbon atoms. It turns out that graphene is a gapless semiconductor with unique electronic properties resulting from the fact that charge carriers in graphene obey linear dispersion relation, thus mimicking massless relativistic particles. This results in the observation of a number of very peculiar electronic properties-from an anomalous quantum Hall effect to the absence of localization. It also provides a bridge between condensed matter physics and quantum electrodynamics and opens new perspectives for carbon-based electronics.
Toward a theory of the quantum Hall effect in graphene
Low Temperature Physics, 2008
We analyze a gap equation for the propagator of Dirac quasiparticles and conclude that in graphene in a magnetic field, the order parameters connected with the quantum Hall ferromagnetism dynamics and those connected with the magnetic catalysis dynamics necessarily coexist (the latter have the form of Dirac masses and correspond to excitonic condensates). This feature of graphene could lead to important consequences, in particular, for the existence of gapless edge states. Solutions of the gap equation corresponding to recently experimentally discovered novel plateaus in graphene in strong magnetic fields are described.
Graphene: New bridge between condensed matter physics and quantum electrodynamics
Solid State Communications, 2007
Graphene is the first example of truly two-dimensional crystals-it's just one layer of carbon atoms. It turns out to be a gapless semiconductor with unique electronic properties resulting from the fact that charge carriers in graphene demonstrate charge-conjugation symmetry between electrons and holes and possess an internal degree of freedom similar to "chirality" for ultrarelativistic elementary particles. It provides unexpected bridge between condensed matter physics and quantum electrodynamics (QED). In particular, the relativistic Zitterbewegung leads to the minimum conductivity of order of conductance quantum e 2 /h in the limit of zero doping; the concept of Klein paradox (tunneling of relativistic particles) provides an essential insight into electron propagation through potential barriers; vacuum polarization around charge impurities is essential for understanding of high electron mobility in graphene; index theorem explains anomalous quantum Hall effect.
Science (New York, N.Y.), 2014
The nature of fractional quantum Hall (FQH) states is determined by the interplay between the Coulomb interaction and the symmetries of the system. The distinct combination of spin, valley, and orbital degeneracies in bilayer graphene is predicted to produce an unusual and tunable sequence of FQH states. Here, we present local electronic compressibility measurements of the FQH effect in the lowest Landau level of bilayer graphene. We observe incompressible FQH states at filling factors ν = 2p + 2/3, with hints of additional states appearing at ν = 2p + 3/5, where p = -2, -1, 0, and 1. This sequence breaks particle-hole symmetry and obeys a ν → ν + 2 symmetry, which highlights the importance of the orbital degeneracy for many-body states in bilayer graphene.
Unconventional Integer Quantum Hall Effect in Graphene
Physical Review Letters, 2005
Monolayer graphite films, or graphene, have quasiparticle excitations that can be described by 2 + 1 dimensional Dirac theory. We demonstrate that this produces an unconventional form of the quantized Hall conductivity σxy = −(2e 2 /h)(2n + 1) with n = 0, 1, . . ., that notably distinguishes graphene from other materials where the integer quantum Hall effect was observed. This unconventional quantization is caused by the quantum anomaly of the n = 0 Landau level and was discovered in recent experiments on ultrathin graphite films.