Optimizing Topological Switching in Confined 2D-Xene Nanoribbons via Finite-Size Effects

In a blueprint for topological quantum electronics, edge state transport in a topological insulator material can be controlled by employing a gate-induced topological quantum phase transition. While finite-size effects have been widely studied in 2D-Xenes, less attention has been devoted to finite-size effects on the gate-induced topological switching in spin-orbit coupled 2D-Xene nanoribbons. Here, by studying width dependence of electronic properties via a tight binding model, we demonstrate that finite-size effects can be used to optimize both the spin-orbit interaction induced barrier in the bulk and the gate-controlled quantized conductance on the edges of zigzag-Xene nanoribbons. The critical electric field required for switching between gapless and gapped edge states reduces as the width decreases, without any fundamental lower bound. This size dependence of the threshold voltage stems from a unique feature of zigzag-Xene nanoribbons: width and momentum dependent tunability of the gate-induced coupling between overlapping spin-filtered chiral states on the two edges. Furthermore, when the width of zigzag-Xene nanoribbons is smaller than a critical limit, topological switching between edge states can be attained without bulk band gap closing and reopening. This is primarily due to the quantum confinement effect on the bulk band spectrum which increases nontrivial bulk band gap with decrease in width. Such reduction in threshold voltage accompanied by enhancement in bulk band gap overturns the conventional wisdom of utilizing wide channel and narrow gap semiconductors for reducing threshold voltage in standard field effect transistor analysis and paves the way towards next-generation low-voltage topological quantum devices.