CoChat
Sign Up
Cited by 75Topological Materials and PhenomenaQuantum and electron transport phenomenaAdvanced Condensed Matter Physics

Noncommutative geometry and non-Abelian Berry phase in the wave-packet dynamics of Bloch electrons

Open access
Shindou, Ryuichi, Imura, Ken-Ichiro·2005·Nuclear Physics B
DOI 10.1016/j.nuclphysb.2005.05.019
Open this paper in CoChat — free accountOpen PDF

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1016/j.nuclphysb.2005.05.019

Cites

52 of 52 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • The Jones and Stokes representations characterize the polarization state of light by the complex two-component vector ψ and the real three-component vector S, respectively; in the generic case, they obey SU(2) and SO(3) evolutions and correspond to the Schrödinger and Heisenberg representations of spin in quantum mechanics.

    “The Jones and Stokes representations characterize the polarization state of light, respectively, by the complex two-component vector ψ and the real three-component vector S arrowrightnosp . In the generic case, they obey ( ) SU 2 and ( ) SO 3 evolutions and correspond, respectively, to the Schrödinger and Heisenberg representations of spin in quantum mechanics [34,98].”

    From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [98]

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

Flagged first, then by citations

Research works printed but not linked: 38

  1. [1][1] P.A.M. Dirac, Proc. R. Soc. London 133, 60 (1931). -
  2. [2][2] G. 't Hooft, Nucl. Phys. B 79, 276 (1974); A.M. Polyakov, JETP Lett. 20, 194 (1974). -
  3. [3][3] M. Onoda, N. Nagaosa, J. Phys. Soc. Jpn. 71, 19 (2002). -
  4. [4][4] Z. Fang, et al., Science 302, 92 (2003). -
  5. [5][5] See also, G.E. Volovik, JETP Lett. 46, 98 (1987), and references therein. -
  6. [6][6] M.C. Chang, Q. Niu, Phys. Rev. Lett. 75, 1348 (1995); ibid., Phys. Rev. B 53, 7010 (1996). -
  7. [7][7] G. Sundaram, Q. Niu, Phys. Rev. B 59, 14915 (1999). -
  8. [8][8] J.E. Hirsch, Phys. Rev. Lett. 83, 1834 (1999). -
  9. [9][9] S. Zhang, Phys. Rev. Lett. 85, 393 (2000). -
  10. [10][10] S. Murakami, N. Nagaosa, S.C. Zhang, Science 301, 1348 (2003); ibid., Phys. Rev. B 69, 235206 (2004). -
  11. [11][11] J. Sinova, et al., Phys. Rev. Lett. 92, 126603 (2004). -
  12. [12][12] D. Culcer, et al., Phys. Rev. Lett. 93, 046602 (2004). -
  13. [13][13] S. Datta, B. Das, Appl. Phys. Lett. 56, 665 (1990). -
  14. [14][14] D. J. Thouless, Phys. Rev. B 27, 6083 (1983); Q. Niu, Phys. Rev. Lett. 64, 1812 (1990). -
  15. [15][15] [R. Shindou, cond-mat/0312668.](http://arxiv.org/abs/cond-mat/0312668) - · arXiv
  16. [16][16] M.V. Berry, Proc. R. Soc. London, A 392, 45 (1984). -
  17. [17][17] C.A. Mead, Chem. Phys. 49, 23 (1980) -
  18. [18][18] R. Karplus, J.M. Luttinger, Phys. Rev. 95, 1154 (1954). -
  19. [19][19] J. Zak, Phys. Rev. B 15, 771 (1977); ibid., 16, 4154 (1977). -
  20. [21][21] D.J. Thouless, et al., Phys. Rev. Lett. 49, 405 (1982). -
  21. [22][22] R.D. King-Smith, D. Vanderbilt, Phys. Rev. B 47, 1651 (1993); R. Resta, Europhys. Lett. 22, 133 (1993). See also, R. Resta, Rev. Mod. Phys. 66, 899 (1994), and references therein. -
  22. [23][23] K. Ohgushi, S. Murakami, N. Nagaosa, Phys. Rev. B 62, 6065 (2000). -
  23. [24][24] R. Shindou, N. Nagaosa, Phys. Rev. Lett. 87, 116801 (2001). -
  24. [25][25] T. Jungwirth, Q. Niu, A.H. MacDonald, Phys. Rev. Lett. 88, 207208 (2002). -
  25. [26][26] Y. Yao et al. Phys. Rev. Lett. 92, 037204 (2004). -
  26. [28][28] J. Inoue, G.E.W. Bauer, L.W. Molenkamp, Phys. Rev. B 70, R041303 (2004). -
  27. [29][29] J. Schliemann, D. Loss, Phys. Rev. B 69, 165315 (2004). -
  28. [30][30] H. Koizumi, Y. Takada, Phys. Rev. B 65, 153104 (2002). -
  29. [31][31] A. Berard, H. Mohrbach, Phys. Rev. D 69, 127701 (2004). -
  30. [32][32] N. Seiberg, E. Witten, J. High Energy Phys. 9909, 32 (1999). -
  31. [33][33] A. Connes, M.R. Douglas, A. Schwarz, J. High Energy Phys. 9802, 3 (1998). -
  32. [34][34] N. Marzari, D. Vanderbilt, Phys. Rev. B 56, 12847 (1997). -
  33. [35][35] K. Ishikawa, T. Matsuyama, Z. Phys. C 33, 41 (1986); ibid., Nucl. Phys. B 280, 523 (1987). -
  34. [36][36] S.C. Zhang, T.H. Hansson, S. Kivelson, Phys. Rev. Lett. 62, 82 (1989). See also, S.C. Zhang, Int. J. Mod. Phys. 6, 25 (1992). -
  35. [37][37] G.E. Volovik, JETP 67, 1804 (1988); J. Goryo, K. Ishikawa, Phys. Lett A 260, 294 (1999); A. Furusaki, M. Matsumoto, M. Sigrist, Phys. Rev. B 64, 054514 (2001). -
  36. [38][38] G.E. Volovik, V.M. Yakovenko, J. Phys.: Condens. Matter 1, 5263 (1989); T. Senthil, J.B. Marston, M.P.A. Fisher, Phys. Rev. B 60, 4245 (1999). -
  37. [39][39] N. Sai, K.M. Rabe, D. Vanderbilt, Phys. Rev. B 66, 104108 (2002). -
  38. [40][40] D. Culcer, Y. Yao, Q. Niu, cond-mat/0411285. | invariance | T | I | |------------------------------------|-----|-----| | charge : 1 | + | + | | spin : 〈 S 〉 ( k ) | - | + | | parity : 〈 Π 〉 ( k ) | + | - | | Hall-type current: F k µ k ν ( k ) | - | + | | polarization current: k µ t ( k ) | + | | F - Table 1: Transformation properties under time reversal T and spatial inversion I - A negative (positive) sign indicates whether a matrix element in question at k reverses its sign (or not) in comparison with that of -k when the system is invariant under a certain symmetry operation, such as T or I . For example, the negative sign for 〈 S 〉 ( k ) in the T -invariant case means that the spin matrix 〈 S α 〉 ( k ) is identical to -( 〈 S α 〉 ( -k ) ) t upto a certain SU ( N ) gauge transformation as given in Eq.(68). | type of current | Hall-type | Hall-type | polarization | polarization | |-------------------|-------------|-------------|----------------|----------------| | invariance | T | I | T | I | | charge | - | + | + | - | | spin | + | + | - | - | | parity | | | + | + | - - Table 2: Cancellation rules for charge/spin/parity Hall-type/polarization currents -A negative (positive) sign indicates that contributions to the total charge/spin/parity (vertical axis) Hall-type/polarization (horizontal axis) current from k and -k electrons (do not) cancel each other when the system is invariant under either T or I . This table can be deduced from Table 1. For example, in the T -invariant case, a negative sign for the spin in Table 1 gives, together with another negative sign for the Hall-type current, a positive sign for the spin Hall current in Table 2, correspoinding, respectively, to Eqs. (68,66) and (79). · arXiv

Cited by

Sorted by citations

Related

Authors
Shindou, R., & Imura, K.-I.
Affiliations
  • The University of Tokyo (JP)
  • RIKEN (JP)
Corresponding author
Imura, Ken-Ichiro
ORCID
Venue
Nuclear Physics B
Publisher
Elsevier BV
Published
2005-08
Volume
720
Issue
3
Pages
399-435
ISSN
0550-3213 (ISSN-L)
DOI
10.1016/j.nuclphysb.2005.05.019
OpenAlex
W2032484576
Cited by
75
References
52
Citations by year
2026: 3 · 2025: 2 · 2024: 1 · 2022: 5 · 2021: 5 · 2020: 8 · 2019: 7 · 2018: 4 · 2017: 6 · 2016: 1 · 2015: 1 · 2014: 2 · 2013: 3 · 2012: 2
FWCI
3.48
Type
journal article
Language
en
Open access
Licence
Locations
  • Nuclear Physics B (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • 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
  • Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
Keywords
noncommutative geometry, non-Abelian Berry phase, wave packet dynamics, Bloch electrons, Yang-Mills fields, Ehrenfest theorem, Hall current, polarization current, topological current, orbital currents, spintronics

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 ›

Are you an author, or do you see a problem with this page? Request a review