$8\pi$-periodic dissipationless ac Josephson effect on a quantum spin-Hall edge via a Quantum magnetic impurity

Abstract

Time-reversal invariance places strong constraints on the properties of the quantum spin Hall edge. One such restriction is the inevitability of dissipation in a Josephson junction between two superconductors formed on such an edge without the presence of interaction. Interactions and spin-conservation breaking are key ingredients for the realization of dissipationless ac Josephson effect on such quantum spin Hall edges. We present a simple quantum impurity model that allows to create a dissipationless fractional Josephson effect on a quantum spin Hall edge. We then use this model to substantiate a general argument that shows that any such non-dissipative Josephson effect must necessarily by $8\pi$-periodic.

8 pages, 6 figures

References in corpus (7)

• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Fermion-parity anomaly of the critical supercurrent in the quantum spin-Hall effect
• Time-Reversal-Invariant $Z_4$ Fractional Josephson Effect
• Resistance of helical edges formed in a semiconductor heterostructure
• Interaction effects on 1D fermionic symmetry protected topological phases
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Cited by in corpus (2)

• ${\mathbb{Z}}_4$ Parafermions in an interacting quantum spin Hall Josephson junction coupled to an impurity spin
• Survival of the fractional Josephson effect in time-reversal-invariant topological superconductors