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- W3115655330 endingPage "034007" @default.
- W3115655330 startingPage "034007" @default.
- W3115655330 abstract "This paper provides a pedagogical introduction to recent developments in geometrical and topological band theory following the discovery of graphene and topological insulators. Amusingly, many of these developments have a connection to contributions in high-energy physics by Dirac. The review starts by a presentation of the Dirac magnetic monopole, goes on with the Berry phase in a two-level system and the geometrical/topological band theory for Bloch electrons in crystals. Next, specific examples of tight-binding models giving rise to lattice versions of the Dirac equation in various space dimension are presented: in 1D (Su-Schrieffer-Heeger and Rice-Mele models), 2D (graphene, boron nitride, Haldane model) and 3D (Weyl semi-metals). The focus is on topological insulators and topological semi-metals. The latter have a Fermi surface that is characterized as a topological defect. For topological insulators, the two alternative view points of twisted fiber bundles and of topological textures are developed. The minimal mathematical background in topology (essentially on homotopy groups and fiber bundles) is provided when needed. Topics rarely reviewed include: periodic versus canonical Bloch Hamiltonian (basis I/II issue), Zak versus Berry phase, the vanishing electric polarization of the Su-Schrieffer-Heeger model and Dirac insulators." @default.
- W3115655330 created "2021-01-05" @default.
- W3115655330 creator A5013516678 @default.
- W3115655330 creator A5084757149 @default.
- W3115655330 date "2021-04-23" @default.
- W3115655330 modified "2023-10-16" @default.
- W3115655330 title "Topological and geometrical aspects of band theory" @default.
- W3115655330 cites W1484947792 @default.
- W3115655330 cites W1512882214 @default.
- W3115655330 cites W1514707913 @default.
- W3115655330 cites W1524641833 @default.
- W3115655330 cites W1538825449 @default.
- W3115655330 cites W1601700513 @default.
- W3115655330 cites W1878730722 @default.
- W3115655330 cites W1903493486 @default.
- W3115655330 cites W1904914631 @default.
- W3115655330 cites W1948123192 @default.
- W3115655330 cites W1963706680 @default.
- W3115655330 cites W1965675553 @default.
- W3115655330 cites W1965798740 @default.
- W3115655330 cites W1968626831 @default.
- W3115655330 cites W1968755463 @default.
- W3115655330 cites W1969558316 @default.
- W3115655330 cites W1970188810 @default.
- W3115655330 cites W1970271794 @default.
- W3115655330 cites W1973808410 @default.
- W3115655330 cites W1978762857 @default.
- W3115655330 cites W1979015793 @default.
- W3115655330 cites W1979276597 @default.
- W3115655330 cites W1980366548 @default.
- W3115655330 cites W1980451122 @default.
- W3115655330 cites W1981651287 @default.
- W3115655330 cites W1982391957 @default.
- W3115655330 cites W1983970619 @default.
- W3115655330 cites W1986508321 @default.
- W3115655330 cites W1987403044 @default.
- W3115655330 cites W1988195577 @default.
- W3115655330 cites W1989250610 @default.
- W3115655330 cites W1990265804 @default.
- W3115655330 cites W1991050432 @default.
- W3115655330 cites W1991260972 @default.
- W3115655330 cites W1993382772 @default.
- W3115655330 cites W1993896628 @default.
- W3115655330 cites W1994897752 @default.
- W3115655330 cites W1995696119 @default.
- W3115655330 cites W2000250098 @default.
- W3115655330 cites W2000564135 @default.
- W3115655330 cites W2003397144 @default.
- W3115655330 cites W2007408209 @default.
- W3115655330 cites W2008188057 @default.
- W3115655330 cites W2008791564 @default.
- W3115655330 cites W2009417367 @default.
- W3115655330 cites W2010019866 @default.
- W3115655330 cites W2010284368 @default.
- W3115655330 cites W2013877283 @default.
- W3115655330 cites W2016333013 @default.
- W3115655330 cites W2017470368 @default.
- W3115655330 cites W2017901233 @default.
- W3115655330 cites W2019740372 @default.
- W3115655330 cites W2020332193 @default.
- W3115655330 cites W2020595981 @default.
- W3115655330 cites W2025113759 @default.
- W3115655330 cites W2026237155 @default.
- W3115655330 cites W2027394310 @default.
- W3115655330 cites W2028948400 @default.
- W3115655330 cites W2029258203 @default.
- W3115655330 cites W2030028233 @default.
- W3115655330 cites W2030164271 @default.
- W3115655330 cites W2030655062 @default.
- W3115655330 cites W2034398864 @default.
- W3115655330 cites W2035743770 @default.
- W3115655330 cites W2037807652 @default.
- W3115655330 cites W2038286405 @default.
- W3115655330 cites W2038531793 @default.
- W3115655330 cites W2041354171 @default.
- W3115655330 cites W2042938036 @default.
- W3115655330 cites W2043175787 @default.
- W3115655330 cites W2044642597 @default.
- W3115655330 cites W2045462689 @default.
- W3115655330 cites W2047648575 @default.
- W3115655330 cites W2054225720 @default.
- W3115655330 cites W2056404648 @default.
- W3115655330 cites W2058122340 @default.
- W3115655330 cites W2059115869 @default.
- W3115655330 cites W2059929193 @default.
- W3115655330 cites W2060115196 @default.
- W3115655330 cites W2061000251 @default.
- W3115655330 cites W2062089197 @default.
- W3115655330 cites W2063397682 @default.
- W3115655330 cites W2064989124 @default.
- W3115655330 cites W2067785597 @default.
- W3115655330 cites W2072413444 @default.
- W3115655330 cites W2072703702 @default.
- W3115655330 cites W2073047667 @default.
- W3115655330 cites W2074159413 @default.
- W3115655330 cites W2074950413 @default.
- W3115655330 cites W2077896911 @default.
- W3115655330 cites W2078822726 @default.