1
$\begingroup$

I'm reading C.L. Kane and E.J. Mele's original paper of QSHE(DOI:https://doi.org/10.1103/PhysRevLett.95.226801). When proving the existence of edge state, they use the Laughlin's gauge argument which I am familiar with. However, they also say that the gauge argument is only true when the Hamiltonian conserves $\sigma_z$. This makes me feel confused. I don't know why gauge argument can only be used when $\sigma_z$ is conserved.

$\endgroup$
3
$\begingroup$

If I remember correctly they use the gauge argument for each spin component separately --- as if spin-up and spin-down both had their own gauge field and U(1) group. This will only work if there really are two conserved charges, so $\sigma_z$ must commute with the hamiltonian.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.