Neumann's principle ↩

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shorthands: {}
aliases: [Principle of symmetry]
created: 2021-10-31 18:36:35
modified: 2022-01-10 04:13:02

Neumann's principle states that if a crystal is invariant with respect to certain symmetry operations (such as point group transformations), then any of its physical properties must also be invariant with respect to the same symmetry operations.

Examples

3-fold symmetry in 2D

Let's consider a crystal that is invariant with respect to the symmetry1:

Then due to Neumann's principle, the crystal's conductivity tensor must be invariant as well:

(omitting the calculations)

Due to the symmetry, this condition is fulfilled by the conductivity tensor:

So the conductivity tensor takes this form:

  1. See the example symmetry here
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