Valley-isospin dependence of the quantum Hall effect in a graphene p − n junction

@article{Tworzydo2007ValleyisospinDO,
  title={Valley-isospin dependence of the quantum Hall effect in a graphene p − n junction},
  author={Jakub Tworzydło and Izak M. Snyman and A. Akhmerov and C. W. J. Beenakker},
  journal={Physical Review B},
  year={2007},
  volume={76},
  pages={035411}
}
We calculate the conductance $G$ of a bipolar junction in a graphene nanoribbon, in the high-magnetic-field regime where the Hall conductance in the $p$-doped and $n$-doped regions is $2{e}^{2}∕h$. In the absence of intervalley scattering, the result $G=({e}^{2}∕h)(1\ensuremath{-}\mathrm{cos}\phantom{\rule{0.2em}{0ex}}\ensuremath{\Phi})$ depends only on the angle $\ensuremath{\Phi}$ between the valley isospins ($=\text{Bloch}$ vectors representing the spinor of the valley polarization) at the… 
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TLDR
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    3) is invariant under the transformation ν → −ν, θ → θ + π. This freedom is used to choose the sign of ν such that the electron-like edge channel has isospin +ν