Institut für Theorie der Kondensierten Materie (TKM)
How spectrum-wide quantum criticality protects surface states of topological superconductors from Anderson localization: Quantum Hall plateau transitions (almost) all the way down

TKM Institutsseminar


Jonas Karcher


18.02.2021 14:00






Prof. Dr. Mirlin


Recent numerical studies indicate that two-dimensional (2D) Dirac fermion theories exhibit
an unusual mechanism of topological protection against Anderson localization. These describe
surface-state quasiparticles of time-reversal invariant, three-dimensional (3D) topological superconductors
(TSCs), subject to the effects of quenched disorder. Numerics reveal a surprising
connection between 3D TSCs in classes AIII, CI, and DIII, and 2D quantum Hall effects in
classes A, C, and D. Conventional arguments derived from the non-linear -model picture imply
that most TSC surface states should Anderson localize for arbitrarily weak disorder (CI, AIII),
or exhibit weak antilocalizing behavior (DIII). The numerical studies reviewed here instead indicate
spectrum-wide surface quantum criticality, characterized by robust eigenstate multifractality
throughout the surface-state energy spectrum. In other words, there is an “energy stack” of critical
wave functions. For class AIII, multifractal eigenstate and conductance analysis reveals identical
statistics for states throughout the stack, consistent with the class A integer quantum-Hall
plateau transition (QHPT). Class CI TSCs exhibit surface stacks of class C spin QHPT states.
Critical stacking of a third kind, possibly associated to the class D thermal QHPT, is identified for
nematic velocity disorder of a single Majorana cone in class DIII. The Dirac theories studied here
can be represented as perturbed 2D Wess-Zumino-Novikov-Witten sigma models; the numerical
results link these to Pruisken models with the topological angle $\Theta = \pi$. Beyond applications to
TSCs, all three stacked Dirac theories (CI, AIII, DIII) naturally arise in the effective description
of dirty d-wave quasiparticles, relevant to the high-$T_c$ cuprates.