^{1}, M. V. Fistul

^{2}and A. V. Ustinov

^{3,a)}

### Abstract

We report an experimental and theoretical study of low-voltage resistive states observed in small tunnel Josephson junctions subject to microwave radiation. The observed features result from Shapiro steps in the current–voltage characteristics and appear when both thermal fluctuations and high frequency dissipation are strong. Without microwave radiation, Josephson junctions have a phase diffusion supercurrent branch characterized by a finite small resistance and hysteretic switching to a higher voltage range under these conditions. When microwave radiation is applied, three different types of resistive states are observed in the current-voltage characteristics. First, a phase diffusion branch steadily evolves and its maximum voltage increases with the microwave power. Another interesting observed feature is a zero-crossing resistive state characterized by a negative resistance. Finally, we find that the low-voltage resistive state can split into numerous hysteretic fine branches resembling incoherent Shapiro-like steps. The appearance of a particular resistive state depends on the interrelations among the Josephson energy , the energy of thermal fluctuations, and the microwave frequency . A theoretical analysis based on incoherent multi-photon absorption by a junction biased in the Josephson phase diffusion regime is in good agreement with the experimental observations.

M.V.F. acknowledges the financial support by SFB 491. This work was supported by the DFG-Center for Functional Nanostructures (CFN) and the EU project SCOPE.

I. INTRODUCTION

II. SAMPLE PREPARATION AND EXPERIMENTAL DETAILS

III. MICROWAVE INDUCED CURRENT-VOLTAGE CHARACTERISTICS: EXPERIMENTS

IV. MICROWAVE INDUCED CURRENT–VOLTAGE CHARACTERISTICS: THEORY

V. DISCUSSION AND CONCLUSIONS

### Key Topics

- Josephson junctions
- 78.0
- Microwaves
- 49.0
- Diffusion
- 34.0
- Josephson effect
- 30.0
- Microwave power transmission
- 11.0

## Figures

The steps in the fabrication of the samples (a–g) and the electrical circuit for the measurements (h).

The steps in the fabrication of the samples (a–g) and the electrical circuit for the measurements (h).

A typical I–V curve of a Josephson junction biased in the Josephson phase diffusion regime. The area of the Josephson junction is , and the temperature is .

A typical I–V curve of a Josephson junction biased in the Josephson phase diffusion regime. The area of the Josephson junction is , and the temperature is .

I–V curves (only the low voltage part is shown) of a small Josephson junction at different microwaves powers. The I–V curves are measured at different temperatures T, K: 5 (a); 2.8 (b); 1.5 (c); 0.3 (d). The area of the Josephson junction is and the microwave frequency is . Different colors correspond to different microwave powers.

I–V curves (only the low voltage part is shown) of a small Josephson junction at different microwaves powers. The I–V curves are measured at different temperatures T, K: 5 (a); 2.8 (b); 1.5 (c); 0.3 (d). The area of the Josephson junction is and the microwave frequency is . Different colors correspond to different microwave powers.

I–V curves (only the low voltage part is shown) of a small Josephson junction at different microwave powers. The I–V curves are measured at different microwave frequencies , GHz: 40 (a); 10 (b); 5 (c); 1 (d). The area of the Josephson junction is and the temperature was fixed at . Different colors correspond to the different microwave powers.

I–V curves (only the low voltage part is shown) of a small Josephson junction at different microwave powers. The I–V curves are measured at different microwave frequencies , GHz: 40 (a); 10 (b); 5 (c); 1 (d). The area of the Josephson junction is and the temperature was fixed at . Different colors correspond to the different microwave powers.

(a) I–V curves displaying fine branching, for different microwave powers. The arrows indicate the direction of the voltage switching during current sweeping. (b) The maximum voltage for the main branch and the first fine branch as functions of the microwave power. (c) The variations in the switching current for the first fine branch. The area of the Josephson junction is , the frequency , and the temperature .

(a) I–V curves displaying fine branching, for different microwave powers. The arrows indicate the direction of the voltage switching during current sweeping. (b) The maximum voltage for the main branch and the first fine branch as functions of the microwave power. (c) The variations in the switching current for the first fine branch. The area of the Josephson junction is , the frequency , and the temperature .

I–V curves of BSCCO (2212) containing intrinsic Josephson junctions for different microwave powers. The area of the BSCCO sample is . The microwave frequency is . The measurements were made at .

I–V curves of BSCCO (2212) containing intrinsic Josephson junctions for different microwave powers. The area of the BSCCO sample is . The microwave frequency is . The measurements were made at .

Numerically calculated I–V curves (Eqs. (7) and (5)) for different microwave powers: enhanced phase diffusion regime. Here .^{6}

Numerically calculated I–V curves (Eqs. (7) and (5)) for different microwave powers: enhanced phase diffusion regime. Here .^{6}

Numerically calculated I–V curves (Eqs. (7) and (5)) for different microwave powers: “zero crossing step” regime. Here .

Numerically calculated I–V curves (Eqs. (7) and (5)) for different microwave powers: “zero crossing step” regime. Here .

Numerically calculated I–V curves (Eqs. (7) and (5)) for different microwave powers showing the fine branching state regime. Here .

Numerically calculated I–V curves (Eqs. (7) and (5)) for different microwave powers showing the fine branching state regime. Here .

## Tables

Parameters of Josephson junctions of different area. All data are obtained at .

Parameters of Josephson junctions of different area. All data are obtained at .

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