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

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 4π rather than a 2π periodicity. This effect is a consequence of the conservation of fermion parity—the number of electron mod 2—in a superconducting junction and is closely related to the Z2 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. We predict that the low-frequency noise due these processes diverges exponentially with temperature T as T→0. Possible experiments on HgCdTe quantum wells will be discussed. Disciplines Physical Sciences and Mathematics | Physics Comments Suggested Citation: Fu, L. and C.L. Kane. (2009). "Josephson current and noise at a superconductor/quantum-spin-Hallinsulator/superconductor junction." Physical Review B. 79, 161408(R). © 2009 The American Physical Society http://dx.doi.org/10.1103/PhysRevB.79.161408 This journal article is available at ScholarlyCommons: http://repository.upenn.edu/physics_papers/69 Josephson current and noise at a superconductor/quantum-spin-Hall-insulator/superconductor junction Liang Fu and C. L. Kane Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA Received 28 April 2008; revised manuscript received 11 February 2009; published 28 April 2009 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 rather than a 2 periodicity. This effect is a consequence of the conservation of fermion parity—the number of electron mod 2—in a superconducting junction and is closely related to the Z2 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. We predict that the low-frequency noise due these processes diverges exponentially with temperature T as T→0. Possible experiments on HgCdTe quantum wells will be