Pattern of odd-denominator fractional quantum Hall states (IMAGE)
Caption
Each filling factor ν = p/q is represented by a dot in a polar form with angle θ = 2πp/q. The radial axis represents the denominator q in an inverted manner: q = 1 is at the outermost edge, and larger denominators lie progressively closer to the center (up to q = 55). In general, the distance to the origin is chosen as r(q) = 55 − q. As a consequence, simpler fractions appear near the rim, whereas higher-denominator fractions cluster toward the center. For example, ν = 1/3 is located at angle 2π/3 and radius 52. Red dots are fractional quantum Hall (FQH) states found in their measurements, black dots are FQH states that have been reported in the literature , and blue dots are all possible fractions with odd denominators smaller than 52 but not yet observed in experiments. Black, green, blue, pink, and orange lines are used to connect fractions that correspond to integer quantum Hall (IQH) states of composite fermions (CFs) with 2, 4, 6, 8, and 10 attached fluxes, respectively. Blue shaded areas enclose the fractions that cannot be understood as IQH states of CFs. Green shaded area encloses ν > 2/3 fractions that may be particle-hole conjugates of certain states at ν < 1/3 or FQH states of CFs.
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