  In a blueprint for topological electronics, edge state transport in a
topological insulator material can be controlled by employing a gate-induced
topological quantum phase transition. Here, by studying the width dependence of
electronic properties, it is inferred that zigzag-Xene nanoribbons are
promising materials for topological electronics with a display of unique
physical characteristics associated with the intrinsic band topology and the
finite-size effects on gate-induced topological switching. First, due to
intertwining with intrinsic band topology-driven energy-zero modes in the
pristine case, spin-filtered chiral edge states in zigzag-Xene nanoribbons
remain gapless and protected against backward scattering even with finite
inter-edge overlapping in ultra-narrow ribbons, i.e., a 2D quantum spin Hall
material turns into a 1D topological metal. Second, mainly due to width- and
momentum-dependent tunability of the gate-induced inter-edge coupling, the
threshold-voltage required for switching between gapless and gapped edge states
reduces as the width decreases, without any fundamental lower bound. Third,
when the width of zigzag-Xene nanoribbons is smaller than a critical limit,
topological switching between edge states can be attained without bulk bandgap
closing and reopening. This is primarily due to the quantum confinement effect
on the bulk band spectrum which increases the nontrivial bulk bandgap with
decrease in width. The existence of such protected gapless edge states and
reduction in threshold-voltage accompanied by enhancement in the bulk bandgap
overturns the general wisdom of utilizing narrow-gap and wide channel materials
for reducing the threshold-voltage in a standard field effect transistor
analysis and paves the way toward low-voltage topological devices.
