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 fJ = 2eVJ̅/h, related to the average transistor voltage VJ̅, and Bloch oscillations of frequency fB = IB̅/2e, related to the average current IB̅ 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., fJ = fB. This leads to the formation of a current step on the current-voltage curve at IB̅ = 2efJ, 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 IB̅/VJ̅ takes the fundamental value of 1/RQ, where RQ = h/4e2 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.
Versions
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BibTeX
@misc{zorin2026dual,
title = {{Dual Shapiro steps and fundamental transconductance in the dc-driven Bloch transistor}},
author = {A. B. Zorin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.14080},
eprint = {2605.14080},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.14080},
}
RIS
TY - UNPB
TI - Dual Shapiro steps and fundamental transconductance in the dc-driven Bloch transistor
AU - A. B. Zorin
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2605.14080
UR - https://arxiv.org/abs/2605.14080
AB - 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 = 2eV_J̅/h, related to the average transistor voltage V_J̅, and Bloch oscillations of frequency f_B = I_B̅/2e, related to the average current I_B̅ 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 I_B̅ = 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 I_B̅/V_J̅ 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.
ER -