Fig. 3: Threshold drift velocity for gain.
a The gain metric g(α, u) is shown as a 2D color plot. A clear linear boundary between regions with and without plasmonic gain is observed. The red dashed line is a linear fitting to the transition boundary that gives α = 50.99 u/v − 6.508. b A slice of the 2D color plot at α = 8 eVÅ2 (white dashed line in Fig. 3a) is shown. The inset band structures schematically show the transitions responsible for u/v = 0.165 and u/v = 0.33 which are below and above uth respectively. The inset loss functions are scaled to only represent the regions over which g(α, u) is integrated as defined by \(g(\alpha,u)=\left|{\int}_{L < 0}L(q,\omega )dqd\omega \right|\). A black dashed line is drawn at uth/v = 0.285.
