Gate-Voltage Control of Borophene Structure Formation.

Boron nanostructures are easily charged but how charge carriers affect their structural stability is unknown. We combined cluster expansion methods with first-principles calculations to analyze the dependence of the preferred structure of two-dimensional (2D) boron, or "borophene", on charge doping controlled by a gate voltage. At a reasonable doping level of 3.12×10  cm , the hollow hexagon concentration in the ground state of 2D boron increases to 1/7 from 1/8 in its charge-neutral state. The numerical result for the dependence of hollow hexagon concentration on the doping level is well described by an analytical method based on an electron-counting rule. Aside from in-plane electronic bonding, the hybridization among out-of-plane boron orbitals is crucial for determining the relative stability of different sheets at a given doping level. Our results offer new insight into the stability mechanism of 2D boron and open new ways for the control of the lattice structure during formation.