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 4πperiodic 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 2πperiodic 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 ≲ 0.1 , and 𝛽 ≳ 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 𝑅 product and sufficiently large junction capacitance.

Particle conserving approach to ac-dc driven interacting quantum dots with superconducting leads

“…Beyond the weak-coupling limit, such setups are known to host Shapiro steps, which are commonly investigated within the semiclassical picture [26,[92][93][94][95]. As recent experiments on topological Josephson junctions hint at signatures of Majorana zero modes in the pattern of Shapiro steps [30,32,96], a microscopic description of such setups [97][98][99] is highly desirable.…”

A particle conserving approach to AC-DC driven interacting quantum dots with superconducting leads

“…Moreover, recent experiments on topological Josephson junctions hint at signatures of Majorana zero modes in the pattern of Shapiro steps for junctions made from topological superconductors, which makes such a microscopic description highly desirable. Although there exist several treatments based on the semiclassical picture [78][79][80], there is surprisingly little literature [81][82][83] on the problem from a microscopic point of view, even a detailed characterization is fundamental in order to differentiate trivial and topological modes [32]. The methodology as presented here could shed light on the properties of the fractional Josephson effect and the associated even-odd pattern in the Shapiro steps, beyond what is understood from the semiclassical treatment.…”

Current through a hybrid four-terminal Josephson junction with Majorana nanowires

“…This situation was predicted by Kitaev [19] using an idealized model. The 4π-periodic current had been proved by many groups in theoretical calculation and experiment measurement [38][39][40][41][42][43]. However, the structure of the experimental device with the fractional Josephson effect is mostly simple.…”