Z2 calculation of Dirac semimetals

[Md Islam]

Hi,

I have calculated Z2 invariant for a doped Na3Bi semimetal. The node calculation shows that it has 2 Dirac nodes symmetrically placed about G point on the k3 axis at the Fermi energy. So I was expecting Z2 to be non-zero only in the k3 =0 plane. But WT calculation shows that Z2 is also non-zero in the k2=0 and k1=0 planes. Having a nodes on k3 axis implies that k2=0 and k1=0 planes have band touching points and so the corresponding Z2 should have been 0. In fact, for a pure Na3Bi, where two Dirac nodes are on k3 axis I do get expected result (Z2=0 for k1_0 and k2=0 planes), so I am bit confused why I am getting non-zero Z2 for this case. Please let me know if I am interpreting WT results incorrectly.

 

Thanks,

Fhokrul

[Brook]

Dear Fhokrul,

When you calculate the Z2 number, you have to be sure that there is no band crossing in the k-plane. Otherwise, the results are meaningless even it’s nontrivial. Since there are two Dirac points at k2=0 and k1=0, so you can’t use the value. WannierTools don’t tell you there is a node when you calculate the WCC.

[Author]

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