Bias spectroscopy of one-dimensional subbands ($E_{n+1}-E_n=e|V|$)

In a rigid spectrum, source and drain threshold lines in a bias-versus-gate map satisfy $E_n(V_g)={\mu }_S$ or ${\mu }_D$. Where adjacent thresholds align with opposite edges of the bias window, their spacing equals the window width $e|V|$. For symmetric bias and spin degeneracy, neighboring channel counts at those edges give a differential electrical conductance halfway between integer $2e^2/h$ plateaus. The dc ratio $I/V$ is a different observable; barrier motion and heating can modify the interpretation.