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Berry curvature vanishes in TRS system
In spin 1/2 system with TR symmetry , the Berry curvature must vanish. Because Berry curvature is odd. How to prove it?
\begin{equation}
\langle\partial_{-k_x}u^{I}(-k)|\partial_{-k_y}u^{I}(-k)\rangle-...
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Derivation of expression for Berry curvature
Many texts quote the expression for the Berry curvature for a two-level system, with Hamiltonian $\mathbf{h}(\mathbf{k})=(h_x,h_y,h_z)$ in terms of $\mathbf{k}=(k_x,k_y)$, as something like
\begin{...
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