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<p>Dear Patric,</p>
<p><br>
</p>
<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>
<p><br>
</p>
<p>As a simple examle, if your unit cell is</p>
<p><br>
</p>
<p>a_1 = (1, 0, 0)</p>
<p>a_2 = (0, 1, 0)</p>
<p>a_3 = (0, 0, 200)</p>
<p><br>
</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>
<p><br>
</p>
<p>Best regards,</p>
<p>Dominik<br>
</p>
<br>
<div class="moz-cite-prefix">On 27.09.2018 14:38, Yifan GAO wrote:<br>
</div>
<blockquote type="cite"
cite="mid:TY2PR0101MB23022B73D7851B1CED9B0638AF140@TY2PR0101MB2302.apcprd01.prod.exchangelabs.com">
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<p style="margin-top:0;margin-bottom:0">Hello,</p>
<p style="margin-top:0;margin-bottom:0"><br>
</p>
<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>
<p style="margin-top:0;margin-bottom:0"><span><br>
</span></p>
<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>
<p style="margin-top:0;margin-bottom:0"><span><br>
</span></p>
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