^{1,a)}

### Abstract

The review is devoted to an experimental study of simulation of superconductivity by microwave radiation in superconducting films. An influence of the power, frequency of microwave radiation, as well as temperature and width of superconducting films on behavior of experimental dependencies of stimulated the critical current and the current at which a vortex structure of the resistive state vanishes and the phase-slip first line appears is analyzed. The experimental studies of films with different width reveal that the effect of superconductivity stimulation by microwave field is common and occurs in both the case of uniform (narrow films) and non-uniform (wide films) distribution of superconducting current over the film width. It is shown that stimulation of superconductivity in a wide film increases not only the critical current and the critical temperature, but also the maximum current at which there is a vortex state in the film. The effect of superconductivity stimulation by microwave radiation in wide films can be described by the Eliashberg theory, which was used to explain the same phenomenon in narrow channels. For the first time it was found experimentally that when the film width increases, the range of radiation power, at which the effect of superconductivity stimulation is observed, shrinks abruptly, and hence the probability of its detection decreases.

I. Introduction

II. A microscopic theory of superconductivity of films, stimulated by microwave radiation

III. A non-equilibrium critical current of superconducting films in a microwave field

IV. Stimulation of superconductivity by an external microwave radiation in tin films of different widths

A. The critical current

B. A maximum current of the existence of vortex resistivity

V. Temperature dependencies of currents stimulated by microwave radiation in wide tin films

A. The critical current

B. The current of phase-slip processes

VI. Conclusion

## Figures

A series of current-voltage characteristics of the film sample SnW5 at T = 3.745 K and f = 12.89 GHz for various levels of radiation power: the radiation power is zero (1), with increasing a serial number of the CVC the radiation power increases (2–4).

A series of current-voltage characteristics of the film sample SnW5 at T = 3.745 K and f = 12.89 GHz for various levels of radiation power: the radiation power is zero (1), with increasing a serial number of the CVC the radiation power increases (2–4).

The dependence of the relative critical current Ic (P)/Ic (0) in the sample Sn1 on the reduced microwave radiation power P/PC at T = 3.812 K for different radiation frequencies f, GHz: 15.4 (▲), 8.1 (●), 3.7 (▪) (Ic (0) is the critical current of the film at P = 0; PC is the minimum power of electromagnetic radiation at which Ic (P) = 0).

The dependence of the relative critical current Ic (P)/Ic (0) in the sample Sn1 on the reduced microwave radiation power P/PC at T = 3.812 K for different radiation frequencies f, GHz: 15.4 (▲), 8.1 (●), 3.7 (▪) (Ic (0) is the critical current of the film at P = 0; PC is the minimum power of electromagnetic radiation at which Ic (P) = 0).

The reduced value of exceeding the maximum critical current Ic max(P) over Ic (0) as a function of the radiation frequency for the samples Sn1(▲), SnW10 (▪) and SnW5 (●) at t = T/Tc ≈ 0.99; the values of lower cutoff frequencies of superconductivity stimulation calculated by Eq. (11) for the samples Sn1 , SnW10 and SnW5 .

The reduced value of exceeding the maximum critical current Ic max(P) over Ic (0) as a function of the radiation frequency for the samples Sn1(▲), SnW10 (▪) and SnW5 (●) at t = T/Tc ≈ 0.99; the values of lower cutoff frequencies of superconductivity stimulation calculated by Eq. (11) for the samples Sn1 , SnW10 and SnW5 .

The dependence of the relative critical current Ic (P)/Ic (0) in the sample SnW10 on the reduced microwave radiation power P/PC at T = 3.777 K for different radiation frequencies f, GHz: 12.91 (▪), 6.15 (●), 0.63 (▼); dashed curve 3 is the dependence Ic (P)/Ic (0) (P/PC ) calculated by Eq. (21) .

The dependence of the relative critical current Ic (P)/Ic (0) in the sample SnW10 on the reduced microwave radiation power P/PC at T = 3.777 K for different radiation frequencies f, GHz: 12.91 (▪), 6.15 (●), 0.63 (▼); dashed curve 3 is the dependence Ic (P)/Ic (0) (P/PC ) calculated by Eq. (21) .

The dependence of the relative critical current Ic (P)/Ic (0) in the sample SnW5 on the reduced microwave radiation power P/PC at T = 3.744 К for different radiation frequencies f, GHz: 15.2 (▲), 11.9 (●), 9.2 (▪), 5.6 (▼). The dashed curve 2 is the dependence Ic (P)/Ic (0) (P/PC ) calculated by Eq. (21) .

The dependence of the relative critical current Ic (P)/Ic (0) in the sample SnW5 on the reduced microwave radiation power P/PC at T = 3.744 К for different radiation frequencies f, GHz: 15.2 (▲), 11.9 (●), 9.2 (▪), 5.6 (▼). The dashed curve 2 is the dependence Ic (P)/Ic (0) (P/PC ) calculated by Eq. (21) .

The dependence of the relative critical current Ic (P)/Ic (0) on the reduced microwave radiation power P/PC with the frequency f = 9.2 GHz at t = T/Tc ≈ 0.99 in different samples: SnW5 (▲), SnW6 (●) and SnW10 (▪).

The dependence of the relative critical current Ic (P)/Ic (0) on the reduced microwave radiation power P/PC with the frequency f = 9.2 GHz at t = T/Tc ≈ 0.99 in different samples: SnW5 (▲), SnW6 (●) and SnW10 (▪).

A region of external radiation power ΔP/Pc , where the effect of stimulation of the critical current is observed, as a function of the film width w for the frequency of 9.2 GHz at T/Tc ≈ 0.99.

A region of external radiation power ΔP/Pc , where the effect of stimulation of the critical current is observed, as a function of the film width w for the frequency of 9.2 GHz at T/Tc ≈ 0.99.

The dependence of the critical current Ic (▪) and the maximum current of existence of the vortex resistivity Im (●) for the sample SnW5 on the reduced microwave power P/PC with the frequency f = 12.89 GHz at T = 3.748 K. The inset shows an enlarged fragment of the above-mentioned dependencies.

The dependence of the critical current Ic (▪) and the maximum current of existence of the vortex resistivity Im (●) for the sample SnW5 on the reduced microwave power P/PC with the frequency f = 12.89 GHz at T = 3.748 K. The inset shows an enlarged fragment of the above-mentioned dependencies.

The experimental temperature dependence of the critical currents Ic (P = 0) (▪), Ic (f = 9.2 GHz) (●), and Ic (f = 12.9 GHz) (▼) for the sample SnW10. The theoretical dependence mA calculated by Eq. (19) , 25 ,26 (curve 1); calculated dependence mA (curve 2); theoretical dependence mA calculated by Eq. (27) , 6 (straight line 3); theoretical dependence Ic (f = 9.2 GHz) calculated by Eq. (16) and fitting dependence mA (curve 4); theoretical dependence Ic (f = 12.9 GHz) calculated by Eq. (16) , and fitting dependence mA (curve 5); theoretical dependence Ic (f = 9.2 GHz) calculated by Eq. (16) normalized by the curve 2, and fitting dependence mA (curve 6); calculated dependence mA (straight line 7).

The experimental temperature dependence of the critical currents Ic (P = 0) (▪), Ic (f = 9.2 GHz) (●), and Ic (f = 12.9 GHz) (▼) for the sample SnW10. The theoretical dependence mA calculated by Eq. (19) , 25 ,26 (curve 1); calculated dependence mA (curve 2); theoretical dependence mA calculated by Eq. (27) , 6 (straight line 3); theoretical dependence Ic (f = 9.2 GHz) calculated by Eq. (16) and fitting dependence mA (curve 4); theoretical dependence Ic (f = 12.9 GHz) calculated by Eq. (16) , and fitting dependence mA (curve 5); theoretical dependence Ic (f = 9.2 GHz) calculated by Eq. (16) normalized by the curve 2, and fitting dependence mA (curve 6); calculated dependence mA (straight line 7).

The experimental temperature dependencies of the critical currents Ic (P = 0) (▪), Ic (f = 15.2 GHz) (▲) for the sample SnW8: calculated dependence Ic (T) = 1.0 × 103(1 − T/Tc )3/2 mA (curve 1); theoretical dependence mA calculated by Eq. (27) , 6 (straight line 2); theoretical dependence Ic (f = 15.2 GHz) calculated by Eq. (16) normalized by the curve 1, and fitting dependence Ic (T) = 1.0 × 103(1 − T/3.835)3/2 mA (curve 3); calculated dependence Ic (T) = 1.72 × 102(1 − T/3.835) mA (straight line 4).

The experimental temperature dependencies of the critical currents Ic (P = 0) (▪), Ic (f = 15.2 GHz) (▲) for the sample SnW8: calculated dependence Ic (T) = 1.0 × 103(1 − T/Tc )3/2 mA (curve 1); theoretical dependence mA calculated by Eq. (27) , 6 (straight line 2); theoretical dependence Ic (f = 15.2 GHz) calculated by Eq. (16) normalized by the curve 1, and fitting dependence Ic (T) = 1.0 × 103(1 − T/3.835)3/2 mA (curve 3); calculated dependence Ic (T) = 1.72 × 102(1 − T/3.835) mA (straight line 4).

The experimental temperature dependencies of the maximum current Im of existence of stationary uniform flow of intrinsic vortices of transport current across the film SnW5: Im (T,P = 0) (●), (▼) and (▲). Curve 1 is the theoretical dependence (see Eq. (23) ); curve 2 is the calculated dependence (see Eq. (24) ); curve 3 is the calculated dependence (see Eq. (26) ).

The experimental temperature dependencies of the maximum current Im of existence of stationary uniform flow of intrinsic vortices of transport current across the film SnW5: Im (T,P = 0) (●), (▼) and (▲). Curve 1 is the theoretical dependence (see Eq. (23) ); curve 2 is the calculated dependence (see Eq. (24) ); curve 3 is the calculated dependence (see Eq. (26) ).

The calculated dependencies of the equilibrium (curve 1) and stimulated by microwave field the gap for the sample SnW5 (curve 2, f = 9.2 GHz; curve 3, f = 15.2 GHz).

The calculated dependencies of the equilibrium (curve 1) and stimulated by microwave field the gap for the sample SnW5 (curve 2, f = 9.2 GHz; curve 3, f = 15.2 GHz).

## Tables

Parameters of tin film samples.

Parameters of tin film samples.

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