  Materials hosting topologically protected non-Abelian zero modes offer the
exciting possibility of storing and manipulating quantum information in a
manner that is protected from decoherence at the hardware level. In this work,
we study the possibility of realizing such excitations along line defects in
certain fractional quantum Hall states in multi-valley systems. Such line
defects have been recently observed experimentally between valley polarized
Hall states on the surface of Bi(111), and excitations near these defects
appear to be gapped (gapless) depending on the presence (absence) of
interaction-induced gapping perturbations constrained by momentum selection
rules, while the position of defects is determined by strain. In this work, we
use these selection rules to show that a hybrid structure involving a
superlattice imposed on such a multi-valley quantum Hall surface realizes
non-Abelian anyons which can then be braided by modulating strain locally to
move line defects. Specifically, we explore such defects in Abelian fractional
quantum Hall states of the form {\nu} = 2/m using a K-matrix approach, and
identify relevant gapping perturbations. Charged modes on these line defects
remain gapped, while charge netural valley pseudospin modes may be gapped with
the aid of two (mutually orthogonal) superlattices which pin non-commuting
fields. When these superlattices are alternated along the line defect,
non-Abelian zero modes result at points where the gapping perturbation changes.
Given that these pseudospin modes carry no net physical charge or spin, the
setup eschews utilizing superconducting and magnetic elements to engineer
gapping perturbations. We provide a scheme to braid these modes using strain
modulation, and confirm that the resulting unitaries satisfy a representation
of the braid group.

Strongly Correlated Electrons