Dual Shapiro steps and fundamental transconductance in the dc-driven Bloch transistor

Abstract:We propose a superconducting circuit based on the Bloch transistor, a quantum device consisting of two small-capacitance Josephson junctions, connected in series and having a small superconducting island in between. This device is driven by two dc electrical sources controlling Josephson oscillations of frequency $f_J = 2e\overline{V_J}/h$, related to the average transistor voltage $\overline{V_J}$, and Bloch oscillations of frequency $f_B = \overline{I_B}/2e$, related to the average current $\overline{I_B}$ injected into the transistor island. We show that due to the Bloch transistor properties, these two types of oscillations are coupled and can mutually phase-lock, i.e., $f_J = f_B$. This leads to the formation of a current step on the current-voltage curve at $\overline{I_B} = 2ef_J$, which is similar to the dual Shapiro step, appearing under microwave irradiation of frequency $f$ on the current-voltage curve of a small Josephson Junction at current $I=2ef$. Moreover, the Bloch transistor transconductance $\overline{I_B}/\overline{V_J}$ takes the fundamental value of $1/R_Q$, where $R_Q = h/4e^2$ is the resistance quantum. The obtained results pave the way to an alternative quantum standard of resistance, based on the superconducting circuit and operating without applying a strong magnetic field.

Superconductivity (cond-mat.supr-con); Quantum Physics (quant-ph)

arXiv:2605.14080 [cond-mat.supr-con]

(or arXiv:2605.14080v2 [cond-mat.supr-con] for this version)

https://doi.org/10.48550/arXiv.2605.14080 Focus to learn more arXiv-issued DOI via DataCite

Phys. Rev. B, vol. 114, 134510 (2026)

https://doi.org/10.1103/pfyb-pdk9 Focus to learn more DOI(s) linking to related resources

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.