These input parameters correspond to a hexagonal NW with shell side length s = 45 nm, core side length c = 30 nm, and n-type doping density n D = 0.2 × 10 18 cm -3 . For all results depicted in this and the following sections, 50,000 triangular elements were used to accurately capture the oscillating and highly localized wavefunctions at the coreshell interfaces. It is worth noting that the spatial electron density shown in Figs. 5a and 5c is qualitatively different than the spatially uniform electron gas profile typically observed in macroscopic bulk/slab heterojunctions. Indeed, Fig. shows the unique formation of six degenerate quasi-one-dimensional electron gases at vertices of the core-shell interface, which strongly resembles the lowest energy electron wavefunction. Specifically, the E 1 wavefunction corresponds to a highly localized charge distribution near the corners of the core-shell interface. As shown in Fig. , a few of the wavefunctions are doubly degenerate (i.e., E 2 /E 3 , E 4 /E 5 , E 8 /E 9 , and E 10 /E 11 ), which arises from the irreducible representations of the D 6h symmetry group (similar to that observed in benzene molecules). Furthermore, the other higher energy wavefunctions are also localized near the core-shell interface, such that their sum (cf. Eq. ( )) gives rise to a total electron distribution concentrated at the NW heterojunction's six corners. Note that HADOKEN can be used to explore other user-defined parameters; various combinations of core/shell sizes and doping densities can result in qualitatively distinct electron density profiles. Self-consistent calculations with low n D values, for example, tend to give relatively flat band-bending diagrams and a 2DEG localized in the core's center (not shown in Fig. ), rather than near the corners. Conversely, localization near the NW corners generally requires high values of n D , particularly for small core sizes.