Lecturer: Dr. Dganit Meidan
Affiliation: Physics Department,
Ben-Gurion University of the Negev
Abstract:
We study the topological classification
of parafermionic chains in the presence
of a modified time reversal symmetry
T^2 = 1. Such chains can be realized in
one dimensional structures embedded in
fractionalized two dimensional states of
matter, e.g. on the edges of a fractional
quantum spin Hall system, where
counter propagating modes may be
gapped either by back-scattering or by
coupling to a superconductor. In the
absence of any additional symmetries, a
chain of Z_m parafermions can belong
to one of several distinct phases
characterized by presence or absence of
Z_m′ parafermions at its ends where m′
is a divisor of m. We find that when the
modified time reversal symmetry is
imposed, the classification becomes
richer. If m is odd, each of the phases
splits into two subclasses. We identify
the symmetry protected phase as a
Haldane phase that carries a Kramers
doublet at each end. When m is even,
each phase splits into four subclasses.
The origin of this split is in the emergent
Majorana fermions associated with even
values of m. We demonstrate the
appearance of such emergent Majorana
zero modes in a system where the
constituents particles are either fermions
or bosons.