= Spin channel counting in a transmission trace
In the <Landauer formula>, $G=(e^2/h)\operatorname{tr}(t^\dagger t)$ when the <flux-normalized transmission matrix> $t$ includes every incident <spin> channel. The <trace> already sums both <spin> states if both are represented; multiplying this expression by another factor of two would count them twice.
For a <Hamiltonian> independent of <spin> with two identical, uncoupled <spin> sectors, one may instead calculate a single sector $t_0$ and write $G=(2e^2/h)\operatorname{tr}(t_0^\dagger t_0)$. For example, one perfectly transmitted spatial mode gives $2e^2/h$ with both sectors present, and $e^2/h$ when only one sector propagates. With <spin-orbit coupling>, keep the full <matrix> even when its eigenchannels have no definite <spin> projection.
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