  Two classes of topological superconductors and Majorana modes in condensed
matter systems are known to date: one, in which impurity disorder strongly
suppresses topological superconducting gap and is detrimental to Majorana
modes, and the other, where Majorana fermions are protected by disorder-robust
superconductor gap. In this work we predict a third class of topological
superconductivity and Majorana modes, in which they appear exclusively in the
presence of impurity disorder. Observation and control of Majorana fermions and
other non-Abelions often requires a symmetry leading to a gap in a
single-particle spectra. Disorder introduces states into the gap and enables
conductance and proximity-induced superconductivity via the in-gap states. We
show that disorder-enabled topological superconductivity can be realized in a
quantum Hall ferromagnet, when helical domain walls are coupled to an s-wave
superconductor. Solving a general quantum mechanical problem of impurity bound
states in a system of spin-orbit coupled Landau levels, we show that
disorder-induced Majorana modes emerge in a setting of the quantum Hall
ferromagnetic transition in a CdMnTe quantum wells at a filling factor $\nu=2$.
Recent experiments on transport through electrostatically controlled single
domain wall in this system indicated the vital role of disorder in conductance,
but left an unresolved question whether this could intrinsically preclude
generation of Majorana fermions. The proposed resolution of the problem,
demonstrating emergence of Majorana fermions exclusively due to impurity
disorder, opens a path forward. We show that electrostatic control of domain
walls in an integer quantum Hall ferromagnet allows manipulation of Majorana
modes. Similar physics can emerge for ferromagnetic transitions in the
fractional quantum Hall regime leading to the formation and control of higher
order non-Abelian excitations.
