SFB Extra Seminar

Normally quantum Hall plateau transition (QHPT) states occur only at isolated energies; accessing them requires fine-tuning. We show that QHPT states can be realized throughout an energy continuum, i.e. as an “energy stack” of critical states where each state exhibits QHPT phenomenology. This occurs at the surface of a 3D class AIII topological phase, where it is protected by U(1) and (anomalous) chiral or time-reversal symmetries. Spectrum-wide criticality is diagnosed by comparing numerics on a 2D surface effective theory to universal results for the longitudinal conductivity and wave function multifractality at the QHPT. We demonstrate that the stacking occurs both for AIII topological phases with both odd and even winding numbers. This may have important implications for the still poorly-understood logarithmic conformal field theory believed to describe the QHPT