Anomalous topological pumps and fractional Josephson effects
Fan Zhang, C. L. Kane
DOI 10.1103/PhysRevB.90.020501 · Physical Review B
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Abstract
We discover novel topological pumps in the Josephson effects for superconductors with time-reversal symmetry. The phase difference, which is odd under the chiral symmetry defined by the product of time-reversal and particle-hole symmetries, acts as an anomalous adiabatic parameter. In contrast to topological pumps with conventional parameters, these pumps are characterized by Z×Z or Z2×Z2 strong invariants. We determine the general classifications in class AIII, and those in class DIII with a single anomalous parameter. For the Z2×Z2 topological pumps in class DIII, the first Z2 invariant describes the coincidence of fermion parity and spin pumps whereas the second Z2 invariant reflects the non-Abelian statistics of Majorana Kramers pairs, leading to three distinct fractional Josephson effects.
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