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<div><span></span>Hi Xiangru,</div><div><br></div><div>I have asked the same question to Dominik. Please see the following reply from him. I hope it will be helpful.</div><div><br></div><div><p style="font-size: 16px; line-height: 24px;">1. The symmetry operations are given with respect to the reduced coordinate system, with the basis being the one described in eq. (2). While C2y is obviously [-1 0 0 ; 0 1 0 ; 0 0 -1 ] in cartesian coordinates, this transforms to [ 0 1 0 ; 1 0 0; 0 0 -1]. The matrix T = [[a, -a, -c], [b, b, 0], [0, 0, d]] transforms from reduced to cartesian coordinates. So to get the C2y matrix in reduced coordinates you need to compute the basis transformation<br></p><p style="font-size: 16px; line-height: 24px;"> <br></p><p style="font-size: 16px; line-height: 24px;"> C_2y_reduced = T^-1 C_2y_cartesian T</p><p style="font-size: 16px; line-height: 24px;"><br></p><p style="font-size: 16px; line-height: 24px;">The same is also done for the other symmetries, but only mirror and rotation change under the basis transformation.</p><p style="font-size: 16px; line-height: 24px;"><br></p><p style="font-size: 16px; line-height: 24px;">Best,</p><p style="font-size: 16px; line-height: 24px;">Heng</p></div>
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<div><span><div style="margin: 10px; font-size: 10pt;"><p class="MsoPlainText" style="font-family: Simsun; line-height: normal; widows: 1; font-size: 15px;"><font face="Times New Roman, serif">Heng Gao</font></p><p class="MsoPlainText" style="line-height: normal; widows: 1; font-size: 15px;"><font face="Times New Roman, serif">Ph.D. candidate</font></p><p class="MsoPlainText" style="font-family: verdana; line-height: normal; widows: 1; font-size: 15px;"><span style="font-family: 'Times New Roman', serif;">Department of </span><span style="font-family: 'Times New Roman', serif; background-color: window;">Physics</span><span style="font-family: 'Times New Roman', serif; background-color: window;">, and </span></p><p class="MsoPlainText" style="font-family: verdana; line-height: normal; widows: 1; font-size: 15px;"><span style="font-family: 'Times New Roman', serif;">International Centre for Quantum and Molecular Structures, </span></p><p class="MsoPlainText" style="font-family: verdana; line-height: normal; widows: 1; font-size: 15px;"><span style="font-family: 'Times New Roman', serif;">Shanghai </span><span style="font-family: 'Times New Roman', serif;">University,<o:p></o:p></span></p><p class="MsoPlainText" style="font-family: verdana; line-height: normal; widows: 1; font-size: 15px;"><span style="font-family: 'Times New Roman', serif;">99 <span class="SpellE">Shangda</span> Road, Shanghai</span><span style="font-family: 'Times New Roman', serif;">, </span><span style="font-family: 'Times New Roman', serif;">200444 China</span></p><p class="MsoPlainText" style="font-family: verdana; line-height: normal; widows: 1; font-size: 15px;"><span style="line-height: 19px; font-family: 'Times New Roman', serif;">E-mail: gaoheng1015</span><span style="line-height: 19px; font-family: 'Times New Roman', serif;">@</span><span style="line-height: 19px; font-family: 'Times New Roman', serif;">shu.edu.cn</span></p></div></span></div>
<blockquote style="margin-top: 0px; margin-bottom: 0px; margin-left: 0.5em;"><div> </div><div style="border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0cm 0cm 0cm"><div style="PADDING-RIGHT: 8px; PADDING-LEFT: 8px; FONT-SIZE: 12px;FONT-FAMILY:tahoma;COLOR:#000000; BACKGROUND: #efefef; PADDING-BOTTOM: 8px; PADDING-TOP: 8px"><div><b>From:</b> <a href="mailto:kongxru@gmail.com">xiangru kong</a></div><div><b>Date:</b> 2017-10-19 04:30</div><div><b>To:</b> <a href="mailto:z2pack@lists.phys.ethz.ch">z2pack</a></div><div><b>Subject:</b> about the real-space matrices for C2y in the example of kdotp-symmetry</div></div></div><div><div class="FoxDiv20171019093025139422"><div dir="ltr">Dear Dominik,<div><br></div><div>What is the basis for the the real-space matrices for C2y in the example of kdotp-symmetry?</div><div><br></div><div>In my opinion, the real-space matrices for C2y should be reasonable for diag{-1,1,-1}.</div><div><br></div><div><br></div><div>Thanks </div><div>Xiangru Kong</div><div><br></div><div><br></div></div>
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