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<div class=tx-hanmail-content-wrapper style="font-size: 10pt; font-family: 돋움; color: #333333; line-height: 1.5; background-color: transparent; browser: msie"><P><SPAN style="FONT-FAMILY: Arial">Dear experts</SPAN></P>
<P><BR>
<SPAN style="FONT-FAMILY: Arial">I am trying to use Wannier90 for the quantum spin Hall (QSH) phase in graphene and silicene.</SPAN></P>
<P><SPAN style="FONT-FAMILY: Arial">According to Kane and Melle, the Berry curvature sould be integrated over the half Brillouin zone </SPAN></P>
<P><SPAN style="FONT-FAMILY: Arial">(but not over the full Brillouin zone) for the spin Chern number or spin Hall conductivity in the QSH phase.</SPAN></P>
<P><BR>
<SPAN style="FONT-FAMILY: Arial">Wannier90 calculates the anomalous Hall conductivity (AHC) by integrating the Berry curvature over </SPAN></P>
<P><SPAN style="FONT-FAMILY: Arial">the full Brillouin zone. Since the quantized AHC is the Chern number in units of e^2/h, I expect that </SPAN></P>
<P><SPAN style="FONT-FAMILY: Arial">the AHC calculated by integration of the Berry curvature over the half Brillouin zone gives the spin Chern </SPAN></P>
<P><SPAN style="FONT-FAMILY: Arial">number in the QSH phase. </SPAN></P>
<P><BR>
<SPAN style="FONT-FAMILY: Arial">The problem is how to integrate the Berry curvature over the half Brillouin zone </SPAN><SPAN style="FONT-FAMILY: Arial">(but not over the full Brillouin zone) in Wannier90.</SPAN></P>
<P><SPAN style="FONT-FAMILY: Arial">How can i overcome the problem? Is there a tricky way or a simple modification of the code?</SPAN></P>
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<SPAN style="FONT-FAMILY: Arial">Thanks in advance for every tips.</SPAN></P>
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<SPAN style="FONT-FAMILY: Arial">Best regards,</SPAN></P>
<P><SPAN style="FONT-FAMILY: Arial">Kyu Won Lee</SPAN></P></div></td></tr>
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