Boundary criticality and multifractality at the 2D spin quantum Hall transition

Details Boundary criticality and multifractality at the 2D spin quantum Hall transition Boundary criticality and multifractality at the 2D spin quantum Hall transition

2008-03-10

arxiv.org/abs/0803.1343v2

Phys. Rev. B 78, 245105 (2008)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

v2, 17 pages, 10 figures, published version

Scientific paper

10.1103/PhysRevB.78.245105

Multifractal scaling of critical wave functions at a disorder-driven (Anderson) localization transition is modified near boundaries of a sample. Here this effect is studied for the example of the spin quantum Hall plateau transition using the supersymmetry technique for disorder averaging. Upon mapping of the spin quantum Hall transition to the classical percolation problem with reflecting boundaries, a number of multifractal exponents governing wave function scaling near a boundary are obtained exactly. Moreover, additional exact boundary scaling exponents of the localization problem are extracted, and the problem is analyzed in other geometries.

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