Characterization of Shapiro steps in the presence of a 4π-periodic Josephson current

Abstract

The Majorana zero-energy modes (MZMs) residing at the boundary of topological superconductors have attracted a great deal of interest recently, as they provide a platform to explore fundamental physics such as non-Abelian statistics, as well as fault-tolerant quantum computation. Period doubling of Shapiro steps in a Josephson junction under microwave irradiation has been regarded as strong evidence for the emergence of the MZMs at the junction edges. However, questions remain as to how the Shapiro steps respond to the presence of a 4π-periodic Josephson current. In this study, we investigated the characteristic features of Shapiro steps with respect to the ratio (α) of the 4π-periodic current to the topologically trivial 2π-periodic one, as well as the reduced microwave frequency (Ω) and McCumber parameter (β) of the junction. Our analysis reproduced Shapiro steps similar to those observed experimentally for specific parameter sets of α,Ω ({\lesssim 0.1}), and β ({gtrsim 1.0}). Full suppression of the first lobe of the n=1 step guarantees the presence of a 4π-periodic Josephson current.In addition, we discuss the range of Ω and β needed for full suppression of the first lobe of the {n=1} step, even for small α ({<0.1}). To observe "period-doubled Shapiro steps", even with a small α, the junction should have a large {I_c}{R_N} product and sufficiently large junction capacitance.

References in corpus (12)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Introduction to topological superconductivity and Majorana fermions
• Zero-bias anomaly in a nanowire quantum dot coupled to superconductors
• Multichannel Generalization of Kitaev's Majorana End States and a Practical Route to Realize Them in Thin Films
• Kinetics of non-equilibrium quasiparticle tunneling in superconducting charge qubits
• Missing Shapiro steps in topologically trivial Josephson Junction on InAs quantum well
• Detecting topological superconductivity using low-frequency doubled Shapiro steps
• Optimal Conditions for Observing Fractional Josephson Effect in Topological Josephson Junctions

Cited by in corpus (14)

• The Josephson diode effect in supercurrent interferometers
• Fractional AC Josephson effect in a topological insulator proximitized by a self-formed superconductor
• The hybrid Josephson rhombus: A superconducting element with tailored current-phase relation
• Period-doubling in the phase dynamics of a shunted HgTe quantum well Josephson junction
• AC Josephson effect in a gate-tunable Cd${}_3$As${}_2$ nanowire superconducting weak link
• Non-Hermitian superconducting diode effect
• Edge supercurrent in Josephson junctions based on topological materials
• A particle conserving approach to AC-DC driven interacting quantum dots with superconducting leads
• ${\varphi }_0$-junction and Josephson diode effect in high-temperature superconductor
• Josephson junction of minimally twisted bilayer graphene
• Current-phase relation of a short multi-mode Bi2Se3 topological insulator nanoribbon Josephson junction with ballistic transport modes
• Ubiquitous missing first Shapiro step in Al-InSb nanosheet Josephson junctions
• Unveiling Topological Hinge States in the Higher-Order Topological Insulator WTe${}_2$ Based on the Fractional Josephson Effect
• Numerical analysis of Josephson junction arrays for multi-order quantum voltage steps