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Updated: Sep 19, 2025

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
Published on: October 12, 2019
Band and Curie limit symmetry groups
1Department of Geology and Geoecology, Herzen Russian State Pedagogical University, 48, Moika Emb., St. Petersburg, 191186, Russian Federation.
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The paper discusses the contradiction between the 7 band (on a cylinder with infinite radius) symmetry groups and the 5 uniaxial Curie limit symmetry groups. Logical difficulties in understanding the symmetry axis ∞ as a true crystallographic one are shown. The formula n → ∞ is proposed to be understood as if the order n of the axis becomes as large as desired, but retains the properties of a natural number (even, odd etc.). In this way, the true inversion axes of symmetry and one-to-one correspondence of bands and limit groups are restored. Such an analysis may be useful in teaching a university course in crystallography.
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