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The Electronic Spectrum of Fullerenes from the Dirac Equation
Condensed Matter · Submitted 7 Aug 1992
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In particular the $C_{60}$ and related molecules are well described by the Dirac equation on the surface of a sphere coupled to a color monopole sitting at its center.
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The abstract, sentence by sentence
The electronic spectrum of sheets of graphite (plane honeycomb lattice) folded into regular polihedra is studied. A continuum limit valid for sufficiently large molecules and based on a tight binding approximation is derived. It is found that a Dirac equation describes the flat graphite lattice. Curving the lattice by insertion of odd numbered rings can be mimicked by coupling effective gauge fields. In particular the $C_{60}$ and related molecules are well described by the Dirac equation on the surface of a sphere coupled to a color monopole sitting at its center.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The electronic spectrum of sheets of graphite (plane honeycomb lattice) folded into regular polihedra is studied. | contribution 0.87 | 0.76 | 0.04 | asserted 0.93 |
| s1 | A continuum limit valid for sufficiently large molecules and based on a tight binding approximation is derived. | method 0.91 | 0.91 | 0.06 | asserted 0.99 |
| s2 | It is found that a Dirac equation describes the flat graphite lattice. | result 1.00 | 0.84 | 0.21 | asserted 1.00 |
| s3 | Curving the lattice by insertion of odd numbered rings can be mimicked by coupling effective gauge fields. | result 0.70 | 0.77 | 0.12 | asserted 0.70 |
| s4 | In particular the $C_{60}$ and related molecules are well described by the Dirac equation on the surface of a sphere coupled to a color monopole sitting at its center. | result 0.97 | 0.83 | 0.73 | asserted 0.93 |
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The paper
Original abstract
The electronic spectrum of sheets of graphite (plane honeycomb lattice) folded into regular polihedra is studied. A continuum limit valid for sufficiently large molecules and based on a tight binding approximation is derived. It is found that a Dirac equation describes the flat graphite lattice. Curving the lattice by insertion of odd numbered rings can be mimicked by coupling effective gauge fields. In particular the $C_{60}$ and related molecules are well described by the Dirac equation on the surface of a sphere coupled to a color monopole sitting at its center.
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2 arXiv papers cite this in 2 sentences
Papers citing it · 1 sentence without a confident label
Cites it as background 1 paper
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The simplest version of the quantum Hamiltonian is the following (for details and generalizations, see, e.g., [ref] , [ref] , [ref] ):
Graphene as a quantum surface with curvature-strain preserving dynamics · Graphene algebra · 0.90
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