Dissipation-enabled fractional Josephson effect

Abstract

The anomalous $4\pi$-periodic ac Josephson effect, a hallmark of topological Josephson junctions, was experimentally observed in a quantum spin Hall insulator. This finding is unexpected due to time-reversal symmetry preventing the backscattering of the helical edge states and therefore suppressing the $4\pi$-periodic component of the Josephson current. Here we analyze the two-particle inelastic scattering as a possible explanation for this experimental finding. We show that a sufficiently strong inelastic scattering restores the $4\pi$-periodic component of the current beyond the short Josephson junction regime. Its signature is an observable peak in the power spectrum of the junction at half the Josephson frequency. We propose to use the exponential dependence of the peak width on the applied bias and the magnitude of the dc current as means of verifying that the inelastic scattering is indeed the mechanism responsible for the $4\pi$-periodic signal.

17 pages, 16 figures

References in corpus (10)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Gapless Andreev bound states in the quantum spin Hall insulator HgTe
• Josephson radiation from gapless Andreev bound states in HgTe-based topological junctions
• Time-Reversal-Invariant $Z_4$ Fractional Josephson Effect
• Non-Abelian parafermions in time-reversal invariant interacting helical systems
• Josephson junction dynamics in the presence of $2\pi$- and $4\pi$-periodic supercurrents
• Detecting topological superconductivity using low-frequency doubled Shapiro steps
• Parity anomaly and spin transmutation in quantum spin Hall Josephson junctions
• $8\pi$-periodic dissipationless ac Josephson effect on a quantum spin-Hall edge via a Quantum magnetic impurity

Cited by in corpus (14)

• Transport in two-dimensional topological materials: recent developments in experiment and theory
• Joule overheating poisons the fractional ac Josephson effect in topological Josephson junctions
• Transport signatures of Majorana bound states in superconducting hybrid structures
• Signatures of the Majorana spin in electrical transport through a Majorana nanowire
• Tomography of zero-energy end modes in topological superconducting wires
• Survival of the fractional Josephson effect in time-reversal-invariant topological superconductors
• Period-doubling in the phase dynamics of a shunted HgTe quantum well Josephson junction
• Josephson radiation from nonlinear dynamics of Majorana zero modes
• Interplay of quantum spin Hall effect and spontaneous time-reversal symmetry breaking in electron-hole bilayers II: Zero-field topological superconductivity
• Probing Majorana bound states via a pn-junction containing a quantum dot
• Microwave signatures of ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_4$ fractional Josephson effects
• Interedge backscattering in time-reversal symmetric quantum spin Hall Josephson junctions
• Tunable effective length of fractional Josephson junctions
• Limits of Thermal Conductance Quantization in Chiral Topological Josephson Junctions