Fig. 3.

Split Landau-level overlap behavior in experiment and computation. (A and B) Detail of the crossing of split LLs –12 from charge neutrality (s, t = 0, –12) and + 8 from $n/n_s=-4$ (s, t = –4, 8) (A) and –8 from charge neutrality and + 8 from $n/n_s=-4$ (B). The horizontal lines are at the indicated $\mathrm{\Phi }/{\mathrm{\Phi }}_0$, and the lines with steep slopes are the average (s, t) of the crossing LLs. For the case of A, this is the average of (0, –12) and (–4, 8), which is (–2, –2) as indicated. (C and D) Computed inverse density of states for $q=2,999,\hspace{0.17em}{a}_1=3,\hspace{0.17em}{a}_2=a_3=1$, and V = 0.3 near the crossing of the split levels s, t = 2, –6, and 0, 4 (C) and s, t = 0, 4, and 2, –4 (D). Note that if we were to add in an additional factor of 2 to s and t, to account for an additional degeneracy, then the values of s and t in C and D would match those in A and B after shifting the zero point of the density. The color scale for C and D is as in Fig. 4. Stars in B indicate the ends of the faint “extra” LLs originating from the intersections of lower (upper) with upper (lower) split LLs. These features are clearly reproduced in computation in D.