Kavli Affiliate: Natalia Chepiga
| First 5 Authors: Bowy M. La Rivière, Bowy M. La Rivière, , ,
| Summary:
We report the emergence of exact zero modes in junctions of two, three and
four short interacting Majorana wires, equivalent to a chain with an impurity
bond, Y- and X- junctions respectively. These exact zero modes are due to
incommensurate short-range correlations induced by the interacting Majorana
fermions, and they appear as unavoided level crossings between in-gap states
upon continuously tuning the interaction. In a junction of only two chains we
report exact zero modes and parity switching as soon as the coupling between
the chains across a junction is positive. Remarkably, for junctions with
multiple chains the in-gap states group up into sets of parity pairs — pairs
of states with opposite parity and similar energies. We demonstrate that the
formation of these parity pairs are always due to the interaction of the outer
edges of the junction. The behavior within each pair can be efficiently
described by two coupled chains. In the Y-junction, we detect four in-gap
states (two parity pairs) that show exact zero modes not only within each pair
but also between them. This is attributed to an additional Majorana fermion
localized at the center of junction that is protected by symmetry. Therefore,
coupling between the Majorana fermions at the outer edges of the junction is
mediated by that in the center. We argue that this is a generic feature of
junctions with an odd number of arms. In the X-junction we detect eight in-gap
states (four parity pairs) that are the result of two Majorana degrees of
freedom localized at the center of the junction. However, we demonstrate that,
by contrast to the Y-junction, the appearance of Majorana fermions at the
center of the X-junction is not protected and the interaction across the
junction can be tuned to the point where there are only Majorana fermions
localized at the four outer edges of the junction, forming four in-gap states.
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