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We demonstrate the locking by external electromagnetic radiation of magnetic precession in the $ \varphi_0 $ Josephson junction through Josephson oscillations in the region of ferromagnetic resonance. This leads to a step in the dependence of the magnetization on the bias current, the position of which is determined by the radiation frequency and the shape of the resonance curve. In junctions with a strong spin-orbit coupling, states with negative differential resistance appear on the IV-characteristic, resulting in an additional locking step. A detailed study of the time dependence of voltage and magnetization and their Fourier transforms shows that the corresponding oscillations have the same frequency as the oscillations at the first step, but they have a different amplitude and different dependence on the radiation frequency. This makes it possible to control not only the frequency, but also the amplitude of the magnetic precession in the locking region. It opens up unique perspectives for the control and manipulation of magnetic moment in hybrid systems such as anomalous Josephson junctions., Comment: 6 pages, 4 figures

The dynamics of a nanomagnet coupled to a Josephson junction has been studied. Although a magnetic field induced by the superconducting current in the Josephson junction is very weak, an applied voltage can generate the nonlinear dynamics of the nanomagnet, which gives a number of interesting phenomena. It has been shown that a ferromagnetic resonance can occur when the frequency of Josephson oscillations becomes equal to the eigenfrequency of the magnetic system. It has been demonstrated that the easy axis of the nanomagnet is reoriented at an increase in the Josephson-to-magnetic energy ratio, as well as in the coupling parameter between the Josephson current and the magnetic moment and in the frequency of Josephson oscillations. It has been shown that a current pulse can turn the magnetic moment of the nanomagnet, which opens new prospects for the application of this system in superconducting spintronics.

The appearance of parametric resonance and the excitation of a longitudinal plasma wave in a system of coupled Josephson junctions with topologically trivial and nontrivial barriers have been demonstrated. The voltage at resonance as a function of the dissipation parameter has a minimum at which the parametric resonance condition changes from ωJ = 2ωLPWtoωJ = ωLPW, where is the Josephson frequency and ωLPW is the frequency of the formed longitudinal plasma wave. The position of this minimum for the system with nontrivial barriers is shifted from that for the system with trivial barriers. This shift can be used to identify the appearance of Majorana states.

The properties of a Josephson junction with the 2π- and 4π-periodic superconducting current component have been analyzed. In the range of low voltages, such a junction exhibits the 4π periodicity of the phase difference for the Majorana current amplitude much smaller than the Josephson current, which makes it possible to observe Josephson current oscillations with a fractional period for small dissipation β < 1 in the hysteresis region. The effect the 4π-periodic Majorana current component is also manifested in a change in the sequence of steps in the ladder structure emerging on the current–voltage (I–V) characteristic of the junction. We have determined the interval of external electromagnetic radiation amplitudes, in which the manifestation of the fractional Josephson effect on the I–V characteristic is most significant.

Synchronization properties of model systems containing large numbers of phase oscillators have many potential biophysical and other applications. Biophysical examples include networks of pacemaker cells in the heart and suprachiasmatic nucleus of the brain. In physical systems the phase dynamics of high-Tc superconducting materials continue to attract attention, since systems of intrinsic Josephson junctions form natural arrays of coupled phase oscillators. As such, they have the potential to act as systems in which various exotic synchronization effects, such as the relatively recently discovered chimera states, may be naturally observed. In this study we make a detailed exploration of the wider parameter space containing regions of chaos synchronization in the CCJJ+DC model of intrinsic Josephson junctions. Extensive regions of phase synchronization - corresponding to the Shapiro steps with zero charge density in the S-layers - are found through numerical simulation. By computing the Lyapunov exponent spectra, we see that chaos synchronization occurs only within certain sub-regions that overlap with 'uncharged' steps in the IV-characteristics. Such chaos synchronization may be useful in applications requiring more powerful, high-frequency, chaotic signals.

We investigate stationary charge imbalance effect in the system of coupled overdamped Josephson junctions. We show that coupling between junction and nonzero stationary charge imbalance in the resistive state bring to a decrease of the Josephson frequency in the Josephson junctions of the stack. The formed difference in Josephson frequency leads to the nonuniform switch to the Shapiro step regime in the presence of external electromagnetic radiation and appearance of kinks of voltage on the IV-characteristics of the stack. We also show that stationary charge imbalance brings to the slope of the Shapiro step due to the difference of the charge imbalance potential on the edges of the step. The theoretical and experimental results for voltage bias coupled Josephson junctions have been compared with the current bias case.

The effect of LC shunting on the phase dynamics of coupled Josephson junctions has been examined. It has been shown that additional (rc) branches appear in the current-voltage characteristics of the junctions when the Josephson frequency ωJ is equal to the natural frequency of the formed resonance circuit ωrc. The effect of the parameters of the system on its characteristics has been studied. Double resonance has been revealed in the system at ωJ = ωrc = 2ωLPW, where ωLPW is the frequency of a longitudinal plasma wave appearing under the parametric-resonance conditions. In this case, electric charge appears in superconducting layers in the interval of the bias current corresponding to the rc branch. The charge magnitude is determined by the accuracy with which the double resonance condition is satisfied. The possibility of the experimental implementation of the effects under study has been estimated.

The influence of the charge imbalance effect on a system of intrinsic Josephson junctions of high temperature superconductors under external electromagnetic radiation is investigated. We find that the charge imbalance is responsible for the slope of the Shapiro step in the IV-characteristic. The nonperiodic boundary conditions shift the Shapiro step from the canonical position which is determined by the frequency of the external radiation. We also find how the system parameters influence the shift of the Shapiro step.

Resonance phenomena in a model of intrinsic Josephson junctions shunted by LC-elements (L-inductance, C-capacitance) are studied. The phase dynamics and IV-characteristics are investigated in detail when the Josephson frequency approaches the frequency of the resonance circuit. A realization of parametric resonance through the excitation of a longitudinal plasma wave, within the bias current interval corresponding to the resonance circuit branch, is demonstrated. It is found that the temporal dependence of the total voltage of the stack, and the voltage measured across the shunt capacitor, reflect the charging of superconducting layers, a phenomenon which might be useful as a means of detecting such charging experimentally. Thus, based on the voltage dynamics, a novel method for the determination of charging in the superconducting layers of coupled Josephson junctions is proposed. A demonstration and discussion of the influence of external electromagnetic radiation on the IV-characteristics and charge-time dependence is given. Over certain parameter ranges the radiation causes an interesting new type of temporal splitting in the charge-time oscillations within the superconducting layers.

Detailed numerical simulations of intrinsic Josephson junctions of high temperature superconductors under external electromagnetic radiation are performed taking into account a charge imbalance effect. We demonstrate that the charge imbalance is responsible for a slope in the Shapiro step the value of which increases with a nonequilibrium parameter. Coupling between junctions leads to the distribution of the slope's values along the stack. The nonperiodic boundary conditions shift the Shapiro step in IV-characteristics from the canonical position determined by $V_{ss}=\hbar f /(2e)$, where $f$ is a frequency of external radiation. This fact makes ambiguous the interpretation of the experimentally found Shapiro step shift by the charge imbalance effect., Comment: 5 pages, 4 figures

We study an effect of external radiation on the dynamics of Josephson junction shunted by an LC circuit. When the Josephson frequency is equal to the frequency of the circuit, additional stable resonant circuit branches appear in the IV-characteristic of the junction. The branches occur on the stable side of a narrow resonance peak, while the other peak side has a negative slope and is unstable. We show that the amplitude dependence of the Shapiro step width crucially changes when the Shapiro step is on the resonant circuit branch. These effects might give very important advantages for methods and technologies that exploit the response of Josephson junctions to microwave fields.

We study the phase dynamics and the resonance features of coupled Josephson junctions in layered superconductors and their manifestations in the current- voltage characteristics and temporal dependence of the electric charge in the superconducting layers. Results on the effect of the external radiation and shunting of the stack of Josephson junctions by LC-elements are presented. We discuss the ideas concerning the experimental observation of these resonances.