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Cited by 31Graphene research and applicationsTopological Materials and PhenomenaQuantum and electron transport phenomena

Physics of Graphene: Zero-Mode Anomalies and Roles of Symmetry

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Ando, Tsuneya·2008·Progress of Theoretical Physics Supplement
DOI 10.1143/ptps.176.203
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Abstract

A brief review is given on electronic and transport properties of monolayer graphene from a theoretical point of view. The topics include the effective-mass description of electronic states, topological anomaly associated with Berry's phase, singular diamagnetic susceptibility, zero-mode anomalies and their removal due to level broadening effects, the symmetry crossover among symplectic, unitary, and orthogonal due to the presence of special time reversal symmetry, and interaction with acoustic, optical, and zone-boundary phonons.

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  • The phase shift delta in the LK formula is determined by dimensionality: zero for two dimensions and plus or minus one eighth for three dimensions.

    “The phase shift δ in Equation 9, which is determined by the dimensionality of the Fermi surface, is 0 for the 2D case and ±1/8 for the 3D case.”

    From Transport of Topological Semimetals (2019) · cites this paper as [204]

    Section §3, “Topological anomaly and Berry’s phase” (page unavailable), discusses a Berry phase and its cancellation of a 1/2 factor in graphene’s Landau levels. Searches for the Lifshitz–Kosevich phase shift and ±1/8 found no passage in our copy assigning δ = 0 to two dimensions or δ = ±1/8 to three dimensions. (LLM, conf=0.76)

    Experimental — accuracy not yet measured

  • For a perfectly two-dimensional system, the LK formula has been modified by Shoenberg and others.

    “For a perfectly 2D system, the above LK formula has been modified by Shoenberg and others (203,204,214,215):”

    From Transport of Topological Semimetals (2019) · cites this paper as [204]

    The passages on magnetic susceptibility (§4, page unavailable) discuss graphene’s susceptibility but do not address a two-dimensional modification of the LK formula. Searches for Shoenberg, the LK formula, and two-dimensional magnetic oscillations found no passage in our copy stating the attributed claim. (LLM, conf=0.74)

    Experimental — accuracy not yet measured

  • The general formula for three-dimensional magnetization oscillations derived by Lifshitz and Kosevich is the LK formula.

    “Given several damping factors, the general formula of the magnetization oscillations for a 3D system, derived by Lifshitz & Kosevich (the LK formula) (203,204,212), is (in SI units)”

    From Transport of Topological Semimetals (2019) · cites this paper as [204]

    Section §4, “Singular diamagnetism” (page unavailable), derives magnetization and susceptibility for graphene but does not discuss the Lifshitz–Kosevich formula or a general formula for three-dimensional magnetization oscillations. Searches for “Lifshitz Kosevich” and “de Haas van Alphen three dimensional oscillatory magnetization” found no passage addressing the claim. (LLM, conf=0.72)

    Experimental — accuracy not yet measured

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Authors
Ando, T.
Affiliations
Tokyo Institute of Technology (JP)
Corresponding author
Ando, Tsuneya
Venue
Progress of Theoretical Physics Supplement
Publisher
Oxford University Press (OUP)
Published
2008
Volume
176
Pages
203-226
ISSN
0375-9687 (ISSN-L)
DOI
10.1143/ptps.176.203
OpenAlex
W1975180034
Cited by
31
References
2
Citations by year
2023: 1 · 2022: 1 · 2021: 2 · 2020: 3 · 2019: 1 · 2018: 1 · 2017: 1 · 2016: 1 · 2015: 2 · 2014: 3 · 2013: 4 · 2012: 3
FWCI
1.36
Type
journal article
Language
en
Open access
Locations
Progress of Theoretical Physics Supplement (publishedVersion)
Funders
  • Ministry of Education, Culture, Sports, Science and Technology
  • Japan Society for the Promotion of Science
Topics
  • Physical Sciences › Materials Science › Materials Chemistry › Graphene research and applications
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
Keywords
monolayer graphene, electronic properties, transport properties, Berry phase, topological anomalies, diamagnetic susceptibility, zero modes, level broadening, time-reversal symmetry, electron-phonon coupling, acoustic phonons, optical phonons, zone-boundary phonons

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