Time reversal and herring test

[jackychenp]

In the group of Pnnm(58), according to J. O. Dimmock Phys. Rev.(1962), $$\Gamma_{3}^+$$ and $$\Gamma_{4}^+$$ should be time reversal degenerated and that means $$\Sigma\chi\{R^2\}$$ should be 0. I've attached my result using Herring test. I cannot get 0 for these two representations even though I have tried hard. Any suggestions are appreciable!

 

[read]

It seems you are considering the irreps of the double group #58. The \gamma^+ and ^- for 1-4 are the irreps of the simple group #58, and they are 1 dimensional real representations and thus by definition cannot be complex and Herring must be +1. \Gamma_5^+ and - are indeed 2 dimensional and complex and might be have herring=0...

 

[jackychenp]

Yes, that is the same as what I derived, but a lot of workers include D.D. Sell, R. Loudon, and J.O. Dimmock think $$\Gamma_{3}^+$$ and $$\Gamma_{4}^+$$ should be time reversal degenerate. It is really a small chance that they are all wrong.

 

[read]

For any real irrep you will have herring=+1. In case of 1 dimensional irrep characters==matrises, so the irreps \Gamma_3 and 4 are real. No chance to get herring=0...