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Kevin Lee edited The_integer_QHE_has_a__.tex
over 8 years ago
Commit id: d81f7f0c39710acbff5b9f59d049145033416973
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diff --git a/The_integer_QHE_has_a__.tex b/The_integer_QHE_has_a__.tex
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--- a/The_integer_QHE_has_a__.tex
+++ b/The_integer_QHE_has_a__.tex
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ă„“The The integer QHE has a deep connection with the topology and berry phase. We can calculate the current in the following equation. Consider 2D time dependent system with translation symmetry in x and y directions.
\begin{equation}
\textit{I}_x\sim\langle{u_k}|\frac{\partial{H(k(t))}}{\partial{k_x}}|u_k\rangle
=\partial_x\textit{E}_k-\langle{\partial_x{u_k}}|\textit{H(k)}|u_k\rangle-\langle{u_k}|\textit{H(k)}|\partial_x{u_k}\rangle