Extended Data Fig. 5: Fractional mode density in large systems.
From: Trapped fractional charges at bulk defects in topological insulators
Tight-binding simulation of fractional mode density in large systems (15 unit cells per side) with Frank angles Ω = ±90°. We set the intercell coupling strength to be 1 and intracell coupling strength to be 0.2. a, Simulated DOS spectrum and real-space distribution of in-gap modes for a Frank angle Ω = −90°. On-site potentials are applied to the corner sites to pull the corner states into the bulk bandgap. b, Fractional portion of the mode density for each band. The colour of each unit cell indicates the fractional portion of mode density in that cell, and the area of each dot is proportional to the mode density of the corresponding resonator. The fractional part of the integrated mode density around the central unit cell is 3/4 for bands 1 and 3 and 1/2 for band 2. c, d, Same as a and b but for Frank angle Ω = +90°. The fractional part of the integrated mode density around the central unit cell is 1/4 for bands 1 and 3 and 1/2 for band 2.
