Josephson Current and Noise at a Superconductor-Quantum Spin Hall Insulator-Superconductor Junction

Understand

We study junctions between superconductors mediated by the edge states of a quantum spin Hall insulator.

• We show that such junctions exhibit a fractional Josephson effect, in which the current phase relation has a 4\pi, rather than a 2\pi periodicity.
• This effect is a consequence of the conservation of fermion parity - the number of electrons modulo 2 - in a superconducting junction, and is closely related to the Z_2 topological structure of the quantum spin Hall insulator.
• Inelastic processes, which violate the conservation of fermion parity, lead to telegraph noise in the equilibrium supercurrent.