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<p style="margin-top:0;margin-bottom:0">Dear Dominik,</p>
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<p style="margin-top:0;margin-bottom:0">Thanks for your reply! I'm really a rookie in this area.</p>
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<p style="margin-top:0;margin-bottom:0">Now I'm testing silicene(<span>10.1103/PhysRevLett.107.076802</span>) with Z2Pack. I successfully get the edge states by wannier90 calculation. The Z2 invariant should be 1 according to the reference. I set
<i>num_band=num_wann=8</i> to integrate the bands under the fermi level and chose <span style="color: rgb(33, 33, 33); font-family: wf_segoe-ui_normal, "Segoe UI", "Segoe WP", Tahoma, Arial, sans-serif, serif, EmojiFont; font-size: 15px;"><i>lambda s, t: (s,
t, 0)</i><span style="font-family: Calibri, Helvetica, sans-serif, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;"> and to calculate lines along ky.</span></span></p>
<p style="margin-top:0;margin-bottom:0"><span style="color: rgb(33, 33, 33); font-family: wf_segoe-ui_normal, "Segoe UI", "Segoe WP", Tahoma, Arial, sans-serif, serif, EmojiFont; font-size: 15px;"><span style="font-family: Calibri, Helvetica, sans-serif, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;"><br>
</span></span></p>
<p style="margin-top:0;margin-bottom:0"><span style="color: rgb(33, 33, 33); font-family: wf_segoe-ui_normal, "Segoe UI", "Segoe WP", Tahoma, Arial, sans-serif, serif, EmojiFont; font-size: 15px;"><span style="font-family: Calibri, Helvetica, sans-serif, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;">The
result given by Z2Pack shows Z2 = 0. I don't know if there's anything wrong with my calculation?</span></span></p>
<p style="margin-top:0;margin-bottom:0"><span style="color: rgb(33, 33, 33); font-family: wf_segoe-ui_normal, "Segoe UI", "Segoe WP", Tahoma, Arial, sans-serif, serif, EmojiFont; font-size: 15px;"><span style="font-family: Calibri, Helvetica, sans-serif, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;"><br>
</span></span></p>
<p style="margin-top:0;margin-bottom:0"><span style="color: rgb(33, 33, 33); font-family: wf_segoe-ui_normal, "Segoe UI", "Segoe WP", Tahoma, Arial, sans-serif, serif, EmojiFont; font-size: 15px;"><span style="font-family: Calibri, Helvetica, sans-serif, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;">All
the parameters are similar to the Bi example. I changed <i>search_shell</i> in range of 24~96 in order to finish the calculation.</span></span></p>
<p style="margin-top:0;margin-bottom:0"><span style="color: rgb(33, 33, 33); font-family: wf_segoe-ui_normal, "Segoe UI", "Segoe WP", Tahoma, Arial, sans-serif, serif, EmojiFont; font-size: 15px;"><span style="font-family: Calibri, Helvetica, sans-serif, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;"><br>
</span></span></p>
<p style="margin-top:0;margin-bottom:0"><span style="color: rgb(33, 33, 33); font-family: wf_segoe-ui_normal, "Segoe UI", "Segoe WP", Tahoma, Arial, sans-serif, serif, EmojiFont; font-size: 15px;"><span style="font-family: Calibri, Helvetica, sans-serif, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;">Best
regards,</span></span></p>
<p style="margin-top:0;margin-bottom:0"><span style="color: rgb(33, 33, 33); font-family: wf_segoe-ui_normal, "Segoe UI", "Segoe WP", Tahoma, Arial, sans-serif, serif, EmojiFont; font-size: 15px;"><span style="font-family: Calibri, Helvetica, sans-serif, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;">Patric</span></span></p>
<p style="margin-top:0;margin-bottom:0"><span style="color: rgb(33, 33, 33); font-family: wf_segoe-ui_normal, "Segoe UI", "Segoe WP", Tahoma, Arial, sans-serif, serif, EmojiFont; font-size: 15px;"><br>
</span></p>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> Dominik Gresch <greschd@phys.ethz.ch><br>
<b>Sent:</b> Thursday, September 27, 2018 11:22:31 AM<br>
<b>To:</b> Yifan GAO; z2pack@lists.phys.ethz.ch<br>
<b>Subject:</b> Re: topological invariants calculation on 2D system</font>
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<p>Dear Patric,</p>
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<p>When calculating 2D invariants, the only Chern and Z2 invariants that can be calculated are those on the 2D Brillouin zone itself. Since you are using VASP, the 2D system is represented as a 3D system, where one dimension is very long in real space, and
correspondingly very narrow in reciprocal space. As a result, the bands will be almost flat in that direction. So, the surface you need to choose for calculating the 2D invariant should be extended in the remaining two dimensions.</p>
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<p>As a simple examle, if your unit cell is</p>
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<p>a_1 = (1, 0, 0)</p>
<p>a_2 = (0, 1, 0)</p>
<p>a_3 = (0, 0, 200)</p>
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</p>
<p>then you want the surface to span k_x and k_y, e.g. lambda s, t: (s, t, 0) for a Chern number. The k_z value can be chosen to be zero, but it could really be anything since the system should not depend on k_z.</p>
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<p>Best regards,</p>
<p>Dominik<br>
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<br>
<div class="x_moz-cite-prefix">On 27.09.2018 14:38, Yifan GAO wrote:<br>
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<p style="margin-top:0; margin-bottom:0">Hello,</p>
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<p style="margin-top:0; margin-bottom:0">I don't quite understand how can I get the topological <span>invariants, like Z2 and Chern, within a 2D system? I'm feeling puzzled when building the surface. </span></p>
<p style="margin-top:0; margin-bottom:0"><span>BTW I'm using vasp. </span></p>
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<p style="margin-top:0; margin-bottom:0"><span>Thank you,</span></p>
<p style="margin-top:0; margin-bottom:0"><span>Patric</span></p>
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