 Then, it turns out that \[[@CR23]\]:$$\documentclass[12pt]{minimal}
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                \begin{document}$$\begin{aligned} \sigma _{11} = 0\;,\qquad \sigma _{12} = -\sigma _{21} = \frac{\nu }{2\pi }\;,\qquad \nu = \mathrm{sign}(m_{+}) - \mathrm{sign}(m_{-})\;. \end{aligned}$$\end{document}$$The integer $\documentclass[12pt]{minimal}
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                \begin{document}$$\nu $$\end{document}$ is the Chern number of the Bloch bundle associated to $\documentclass[12pt]{minimal}
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                \begin{document}$${{\hat{H}}}({\vec {k}})$$\end{document}$. The zeros of $\documentclass[12pt]{minimal}
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                \begin{document}$$m_{\omega }=W+\omega 3\sqrt{3} t_2\sin \phi $$\end{document}$, with $\documentclass[12pt]{minimal}
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