TY - JOUR
T1 - Possibility of adiabatic transport of a Majorana edge state through an extended gapless region
AU - Rajak, Atanu
AU - Nag, Tanay
AU - Dutta, Amit
N1 - Publisher Copyright:
© 2014 American Physical Society.
PY - 2014/10/3
Y1 - 2014/10/3
N2 - In the context of slow quenching dynamics of a p-wave superconducting chain, it has been shown that a Majorana edge state cannot be adiabatically transported from one topological phase to the other separated by a quantum critical line. On the other hand, the inclusion of a phase factor in the hopping term, which breaks the effective time-reversal invariance, results in an extended gapless region between two topological phases. We show that for a finite chain with an open boundary condition, there exists a nonzero probability that a Majorana edge state can be adiabatically transported from one topological phase to the other across this gapless region following a slow quench of the superconducting term; this happens for an optimum transit time, which is proportional to the system size and diverges for a thermodynamically large chain. We attribute this phenomenon to the mixing of the Majorana only with low-lying inverted bulk states. Remarkably, the Majorana state always persists with the same probability even after the quenching is stopped. For a periodic chain, on the other hand, we find a Kibble-Zurek scaling of the defect density with a renormalized rate of quenching.
AB - In the context of slow quenching dynamics of a p-wave superconducting chain, it has been shown that a Majorana edge state cannot be adiabatically transported from one topological phase to the other separated by a quantum critical line. On the other hand, the inclusion of a phase factor in the hopping term, which breaks the effective time-reversal invariance, results in an extended gapless region between two topological phases. We show that for a finite chain with an open boundary condition, there exists a nonzero probability that a Majorana edge state can be adiabatically transported from one topological phase to the other across this gapless region following a slow quench of the superconducting term; this happens for an optimum transit time, which is proportional to the system size and diverges for a thermodynamically large chain. We attribute this phenomenon to the mixing of the Majorana only with low-lying inverted bulk states. Remarkably, the Majorana state always persists with the same probability even after the quenching is stopped. For a periodic chain, on the other hand, we find a Kibble-Zurek scaling of the defect density with a renormalized rate of quenching.
UR - http://www.scopus.com/inward/record.url?scp=84907855903&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.90.042107
DO - 10.1103/PhysRevE.90.042107
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AN - SCOPUS:84907855903
SN - 1539-3755
VL - 90
JO - Physical Review E
JF - Physical Review E
IS - 4
M1 - 042107
ER -