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The electronic properties of graphene
Open accessAbstract
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 (surface) states in graphene depend on the edge termination (zigzag or armchair) 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.
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“Recently, the non-relativistic electrons in graphene monolayer were found to obey the massless relativistic dispersion known as the Dirac cone, leading to the realization of analogies to Zitterbewegung and Klein tunneling in low-energy condensed-matter physics and atom optics 4 -19 .”
From Observation of interaction-induced phenomena of relativistic quantum mechanics (2021) · cites this paper as [12]
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“Dirac points in graphene1–3 or photonic graphene12 belong to the first type, which occur in lattices with unbroken T. These occur in pairs and are stabilized by a symmetry of the underlying lattice.”
From Observation of an unpaired photonic Dirac point (2020) · cites this paper as [3]
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“In the isotropic graphene, c v = c d , the lattice is hexagonal and the tunnelling is equivalent in all directions, which is preserved by the six-fold symmetry [1].”
From Observing movement of Dirac cones from single-photon dynamics (2021) · cites this paper as [1]
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“A second relevant feature of the eigenfunctions is their nontrivial Berry phase: if the eigenfunctions are transported adiabatically on a closed loop in momentum space around one of the Dirac points, the eigenfunctions change sign (Castro Neto et al., 2009).In other words, they get a Berry phase of Æπ, the sign being opposite for the K and K 0 points.”
From Topological photonics (2019) · cites this paper as Castro Neto et al., 2009
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“photonic Dirac points are known to occur in pairs in “photonic graphene” and other similar photonic crystals”
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“The DO model is obtained from the free Dirac equation by the introduction of the external potential via a non-minimal coupling [57,59,63].”
From Classical simulation of relativistic quantum mechanics in periodic optical structures (2011) · cites this paper as [57]
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“The relativistic extension of the quantum harmonic oscillator, the so-called Dirac oscillator (DO) [57,58,59], provides a paradigmatic and exactly solvable model in relativistic quantum mechanics.”
From Classical simulation of relativistic quantum mechanics in periodic optical structures (2011) · cites this paper as [57]
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“Interestingly, the analogy of Hamiltonian (2) with the JaynesCummings model allows us to relate ZB and Rabi oscillations, as other authors have pointed out 7,29,30 .”
From Revivals, classical periodicity, and zitterbewegung of electron currents in monolayer graphene (2009) · cites this paper as [30]
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“We are also able to create approximately quadratic electric potentials which, due to Klein tunneling, are nonconfining in the relativistic limit [18].”
From Quantum Simulation of the Klein Paradox with Trapped Ions (2011) · cites this paper as [18]
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“The main consequence is the emergence of Landau levels in the vicinity of the Dirac points (Castro Neto et al., 2009).”
From Topological photonics (2019) · cites this paper as Castro Neto et al., 2009
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Colloquium : Topological insulators
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Electronics and optoelectronics of two-dimensional transition metal dichalcogenides
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Qi, X.-L., & Zhang, S.-C. (2011) · Reviews of Modern Physics · doi:10.1103/revmodphys.83.1057 · Cited by 14,394
Graphene: Status and Prospects
Geim, A. K. (2009) · Science · doi:10.1126/science.1158877 · Cited by 13,942
Self-citationGraphene and Graphene Oxide: Synthesis, Properties, and Applications
Zhu, Y., Murali, S., Cai, W., Li, X., Suk, J. W., Potts, J. R., & Ruoff, R. S. (2010) · Advanced Materials · doi:10.1002/adma.201001068 · Cited by 10,653
Metadata
- Authors
- Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S., & Geim, A. K.
- Affiliations
- Boston University (US)
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 2009-01-14
- Volume
- 81
- Issue
- 1
- Pages
- 109-162
- ISSN
- 0034-6861 (ISSN-L)
- 1539-0756
- OpenAlex
- W2105685140
- Cited by
- 24,803
- References
- 459
- Citations by year
- 2026: 853 · 2025: 1031 · 2024: 1100 · 2023: 1204 · 2022: 1363 · 2021: 1537 · 2020: 1727 · 2019: 1637 · 2018: 1709 · 2017: 1741 · 2016: 1787 · 2015: 1711 · 2014: 1637 · 2013: 1542 · 2012: 1544
- FWCI
- 673.10
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Reviews of Modern Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Research Explorer (The University of Manchester) (submittedVersion)
- DIGITAL.CSIC (Spanish National Research Council (CSIC)) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Funders
- National Science Foundation (0343790)
- Ministerio de Economía y Competitividad
- Engineering and Physical Sciences Research Council
- Division of Materials Research
- Topics
- Physical Sciences › Materials Science › Materials Chemistry › Graphene research and applications
- Physical Sciences › Materials Science › Materials Chemistry › 2D Materials and Applications
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Quantum and electron transport phenomena
- Keywords
- graphene, Dirac fermions, two-dimensional Dirac materials, quantum Hall effect, tunneling, confinement, stacking sequence, multilayer graphene, edge states, armchair and zigzag edges, nanoribbons, disorder, electron-electron interaction, electron-phonon coupling, transport properties, spectral properties
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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