Two-Dimensional Gas of Massless Dirac Fermions in Graphene

Two-Dimensional Gas of Massless Dirac Fermions in Graphene K. S. Novoselov A. K. Geim S. V. Morozov et al.

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Two-Dimensional Gas of Massless Dirac Fermions in Graphene 2005 Nature / arXiv 10.1038/nature04233 cond-mat/0509330 novoselov2005-dirac-fermions novoselov2005-dirac-fermions.txt, the project's staged copy 372d7244ee6e211aed22cbba07b79964af799d18 arxiv-open materials-science

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0 spans located by searching the stored text for the quote's exact words, allowing any whitespace between them existence Quotation withheld because this record is not cleared for redistribution. massless Dirac fermion transport in graphene Quotation withheld because this record is not cleared for redistribution. experiment experiment Quotation withheld because this record is not cleared for redistribution. mechanisms in graphene the honeycomb lattice makes charge carriers behave as massless Dirac fermions obeying the relativistic Dirac equation rather than the Schrodinger equation Quotation withheld because this record is not cleared for redistribution. Carrier mobility in the devices is probably still limited by defects inherited from the parent graphite, so the measured mobility is not intrinsic. what this limits: the mobility figures as a property of the material: they were PROBABLY STILL LIMITED BY DEFECTS IN PA[rent graphite], so they bound the sample rather than the substance Quotation withheld because this record is not cleared for redistribution. The measured minimum conductivity disagrees with the value most existing theories predict. what this limits: the minimum-conductivity result against theory: THERE IS A BROAD THEORETICAL CONSENSUS THAT A 2D GAS OF DIRAC FERMIONS SHOULD EXHIBIT A MINIMUM CONDUCTIVITY OF ABOUT e2/h ... AND MOST THEORIES SUGGEST A VALUE that the measurement does not match Quotation withheld because this record is not cleared for redistribution. The description that names the paper stops applying at two layers, and the authors say where. what this limits: the massless Dirac description used here: the authors state that in two-layer graphene the fermions exhibit a finite mass Quotation withheld because this record is not cleared for redistribution. The explanation offered for the anomalous conductivity is qualitative and rests on an assumption the paper flags as an assumption. what this limits: the account given here of the minimum conductivity: it is explained qualitatively, assuming the absence of localization, by invoking Mott's argument that the mean free path can never be shorter than the carrier wavelength Quotation withheld because this record is not cleared for redistribution. The theoretical prediction of the effect arrived from groups who did not know the experiment existed. what this limits: the agreement between this measurement and theory: the half-integer QHE was suggested by two theory groups stimulated by the authors' earlier work on thin graphite films but unaware of the present experiment Quotation withheld because this record is not cleared for redistribution. graphene charge carriers behave as massless Dirac fermions, letting a condensed-matter experiment probe relativistic QED and cosmology-relevant physics Quotation withheld because this record is not cleared for redistribution. the carrier density measured from the Hall coefficient compared against the value calculated from the device geometry as a parallel-plate capacitor eliminates: an experimental artefact in either route - a measured 7.3e10 and a calculated 7.2e10 cm-2/V have no common failure mode, so their agreement is not an assumption either one makes · outcome (stated by the tagger, no quotation): held Quotation withheld because this record is not cleared for redistribution. Dirac fermion Dirac fermion Quotation withheld because this record is not cleared for redistribution. rest mass rest mass Quotation withheld because this record is not cleared for redistribution. cyclotron mass cyclotron mass Quotation withheld because this record is not cleared for redistribution. pseudospin pseudospin about this quote: THE TERM IS NOT IN THE QUOTE - the quote's 'The latter' are the pseudospins named in the sentence just before it ('in the case of graphene it refers to “pseudospins”'). That sentence is not quoted because a displaced formula runs through it. Quotation withheld because this record is not cleared for redistribution. Dirac equation Dirac equation Quotation withheld because this record is not cleared for redistribution. mass - TWO MASSES, ONE ZERO AND ONE NOT, IN THE SAME PARTICLE: the linear spectrum implies zero rest mass while the cyclotron mass is explicitly not zero, so a tag reading 'mass = 0' and one reading 'mass is not 0' are both correct here and neither is usable without saying which mass Quotation withheld because this record is not cleared for redistribution. the plus-or-minus sign - SPINS IN QED, PSEUDOSPINS IN GRAPHENE: the authors carry a formula across from quantum electrodynamics and then state that the quantity it indexes here has nothing to do with real spin, its origin being the two carbon sublattices Quotation withheld because this record is not cleared for redistribution. Dirac fermion - BY MIMICRY, NOT BY IDENTITY: the charge carriers are said to MIMIC relativistic particles with zero mass, under a Dirac equation borrowed from relativistic physics, with an effective speed of light the paper itself puts in scare quotes Quotation withheld because this record is not cleared for redistribution. builds-on → the Dirac equation (relativistic quantum mechanics / particle physics) Quotation withheld because this record is not cleared for redistribution. builds-on → Mott's argument on the minimum mean free path in a metal Quotation withheld because this record is not cleared for redistribution. builds-on → the Atiyah-Singer index theorem Quotation withheld because this record is not cleared for redistribution. builds-on → Berry's phase Quotation withheld because this record is not cleared for redistribution. rest mass —distinct-from→ cyclotron mass rest mass cyclotron mass strength of the relation: 1 Quotation withheld because this record is not cleared for redistribution. c* ≈ 10^6 m/s — effective speed of light of massless charge carriers in graphene Quotation withheld because this record is not cleared for redistribution. half-integer — anomalous filling factors of the graphene quantum Hall effect about this quote: QUOTE REPAIRED: the extractor split a hyphen-space and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. Quotation withheld because this record is not cleared for redistribution. π — Berry phase shift exhibited by the Dirac fermions Quotation withheld because this record is not cleared for redistribution. In graphene, electron transport is governed by the DIRAC equation: charge carriers behave as massless relativistic particles with effective speed c*≈10^6 m/s — a 2D gas of Dirac fermions. Quotation withheld because this record is not cleared for redistribution. The integer quantum Hall effect in graphene is anomalous, occurring at half-integer filling factors, and graphene's conductivity never falls below a minimum value. about this quote: QUOTE REPAIRED: the extractor split a hyphen-space and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. Quotation withheld because this record is not cleared for redistribution. Hall conductivity Hall conductivity Quotation withheld because this record is not cleared for redistribution. massless Dirac fermions massless Dirac fermions Quotation withheld because this record is not cleared for redistribution. quantum Hall effect quantum Hall effect about this quote: QUOTE REPAIRED: the extractor split a hyphen-space and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. Quotation withheld because this record is not cleared for redistribution. mean mean Quotation withheld because this record is not cleared for redistribution.

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