Geodesic
Application of Singularity Theory to Bifurcation of Band Structures in Crystals
Journal of Singularities, Tome 21 (2020), pp. 268-281

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Starting from the mean-field Hamiltonian of an electron in a crystal, we briefly review some known facts about its spectral structures and how singularities come into play in such spectral structures, and then provide our future perspective. We also estimate lower bounds of codimensions for the case where more than two bands to cross at a point. 
@article{10_5427_jsing_2020_21p,
     author = {H. Teramoto and A. Tsuchida and K. Kondo and S. Izumiya and M. Toda, and T. Komatsuzaki},
     title = {Application of {Singularity} {Theory} to {Bifurcation} of {Band} {Structures} in {Crystals}},
     journal = {Journal of Singularities},
     pages = {268--281},
     publisher = {mathdoc},
     volume = {21},
     year = {2020},
     doi = {10.5427/jsing.2020.21p},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2020.21p/}
}
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H. Teramoto; A. Tsuchida; K. Kondo; S. Izumiya; M. Toda,; T. Komatsuzaki. Application of Singularity Theory to Bifurcation of Band Structures in Crystals. Journal of Singularities, Tome 21 (2020), pp. 268-281. doi: 10.5427/jsing.2020.21p

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