Dynamics of underdamped Josephson junctions with non-sinusoidal current-phase relation

Kornev, V. K.; Karminskaya, T. Yu.; Kislinskiĭ, Yu. V.; Komissinki, P V; Constantinian, K. Y.; Ovsyannikov, G. A.

doi:10.1016/j.physc.2006.01.012

Cited by 14 publications

(5 citation statements)

References 2 publications

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“…Another famous experiment on the behavior of thin-film superconducting bridges in a mi-crowave field by A. H. Dayem and J. J. Wiegand [18] also demonstrates the production of constant-voltage steps in the IV-characteristics. Some experimental results are explained by nonsinusoidal current-phase relation [19,20]. Ben-Jacob with coauthors [10] found the subharmonic steps within the resistively and capacitively shunted junction model (RCSJ) with purely sinusoidal current-phase relation [21,22].…”

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confidence: 99%

Devil's staircases and continued fractions in Josephson junctions

et al. 2013

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The detailed numerical simulations of the IV-characteristics of Josephson junction under external electromagnetic radiation show devil's staircases within different bias current intervals. We have found that the observed steps form very precisely continued fractions. Increasing of the amplitude of radiation shifts the devil's staircases to higher Shapiro steps. The algorithm of appearing and detection of the subharmonics with increasing radiation amplitude is proposed. We demonstrate that subharmonic steps registered in the famous experiments by A. H. Dayem and J. J. Wiegand [Phys. Rev 155, 419 (1967)] and J. Clarke [Phys. Rev. B 4, 2963(1971] also form continued fractions.Josephson junctions are regarded as excellent model systems for studying a variety of nonlinear phenomena in different fields of science [1, 2] such as frequency locking, chaos, charge density waves, transport in superconducting nanowires, interference phenomena and others [3][4][5][6]. These phenomena, and especially properties of the Shapiro steps (SS) [7] in Josephson junctions are very important for technical applications [8].In a Josephson system driven by an external microwave radiation, the so-called devil's staircase (DS) structure has been predicted as a consequence of the interplay of the Josephson plasma frequency, and the applied frequency (see Refs. [9,10] and references therein). To stress the universality in the scenario presented, we note that the devil's staircase appears in other systems including the infinite spin chains with long-range interactions [11], frustrated quasi-two-dimensional spin-dimer system in magnetic fields [12], systems of strongly interacting Rydberg atoms [13], and fractional quantum Hall effect [14]. A series of fractional synchronization regimes (devils staircase) in a spin-torque nano-oscillator driven by a microwave field was experimentally demonstrated [15]. The devil's staircase is considered as an outstanding example of a 'phase diagram' in physics, because it shows a high degree of self-organization [16].A detailed experimental investigation of the subharmonic SS in SNS junctions were made by J.Clarke [17]. He found that the application to a junction of rf electromagnetic radiation of frequency Ω induced constantvoltage current steps at voltages (n/m) Ω/(2e), where n and m are positive integers. The results were explained based on the idea that phase difference in Josephson junction is increasing in time in a uniform manner and current-phase relation is nonsinusoidal. The junction generates harmonics when it biased at some voltage and these harmonics may synchronize with the applied radiation to produce the steps. Another famous experiment on the behavior of thin-film superconducting bridges in a microwave field by A. H. Dayem and J. J. Wiegand [18] also demonstrates the production of constant-voltage steps in the IV-characteristics. Some experimental results are explained by nonsinusoidal current-phase relation [19,20]. Ben-Jacob with coauthors [10] found the subharmonic steps within the resistiv...

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confidence: 99%

Devil's staircases and continued fractions in Josephson junctions

et al. 2013

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“…3 order parameter amplitude d results in unconventional CPR with characteristic product of critical current -normal state resistance Iс2RN Γ Nb/e [58] The contribution of 2 nd harmonic in CPR for a S/Sd junction without interlayer barrier with the same electrical parameters as the discussed S-MS with L=40 m gives Ic2≈20 nA for Γ =210 -4 , Nb/e=0.8 mV and RN =7.1 Ω at T=4.2 K. Note, using theoretical dependence for ratio IC1/IC vs. parameter q [65,89] and the estimated contribution of Ic2 gives negligibly small estimate q  3 10 -3 . The deviation of CPR from sinusoidal may originate due to appearance of low energy states at the SIO/YBCO interface, related to the coherent Andreev reflections [62][63][64]109,110]. Indeed, the S-MS demonstrated the ZBCP at temperatures T=4.2 K and T>TCNb which are associated with Andreev low energy states.…”

Section: Determination Of the 2 Nd Harmonic From Cprmentioning

confidence: 95%

Triplet Superconducting Correlations in Hybrid Superconducting Junctions

Constantinian¹,

Ovsyannikov²,

Petrzhik³

et al. 2023

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We summarize the results on electron transport in hybrid superconducting S/B/S' mesa-structure consisted of the oxide epitaxial S/B heterostructures, where S is the cuprate YBa2Cu3O 7-x superconductor, B – an interlayer with the spin dependent characteristics, and S’ is the Nb top superconductor. Josephson effect was observed manifested in appearance of oscillating Shapiro steps amplitudes with microwave signal power due to synchronization of junction self-generation of electromagnetic radiation and the external microwave probe signal. Triplet component of superconducting correlations emerged when the interlayer comprised two magnetic materials SrRuO3 and La0.7Sr0.3MnO3 with non-collinear magnetizations as well in the case of antiferromagnetic insulator Sr2IrO4 characterized by strong spin-orbit interaction. Thickness of the interlayer in the both cases considerably exceeded the coherence length of the magnetic spin active interlayer hinting on appearance of long-range proximity effect and spin-triplet superconducting current. Magnetic field dependences measured at dc, and the existence of the second harmonic in superconducting current–phase relation revealed by measurements at microwave frequencies will be discussed.

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“…Shapiro steps on the normalized microwave current a=I MW /I C (0) at f e =50 GHz are shown in Fig.5c and Fig.5d, correspondingly. Calculated dependences of i 1 (a) and i 1/2 (a) for different values of q and fixed McCumber parameter β C =f C /f RC =1 (f RC =1/πR N C) using the modified RSJ model [51,53] are also presented in Fig.5c and Fig.5d. However, dependence i 1 =I 1 (a)/I C (0) in Fig.5c hardly helps to estimate q-factor, at the same time as seen from Fig.5d the maximum of half-integer Shapiro step has max(i 1/2 )≈0.3 and fits well enough to the case q=0.3.…”

Section: Figures 3b and 3cmentioning

confidence: 99%

“…Since the characteristic frequency for MS The information on the CPR in MS could be obtained from the dynamics of Shapiro steps varying the power of microwave irradiation in conditions of high frequency limit f e >f C [51]. model [51,53] are also presented in Fig. 5c and Fig.…”

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Superconducting current and low-energy states in a mesa-heterostructure interlayered with a strontium iridate film with strong spin-orbit interaction

et al. 2019

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O x with Sr 2 IrO 4 interlayer thickness d=5 and 7 nm and in-plane sizes L=10-50 µm. A strontium iridate, Sr 2 IrO 4 , is known as a canted antiferromagnetic insulator at low temperatures and characterized also by the strong spin-orbit interaction due to the impact of the IrO 2 plane. The superconducting critical current density j C ≈ 0.3 A/cm 2 for the case d=7 nm was observed at T=4.2K. The temperature dependences of the superconducting critical current I C (T) and the voltage position on the I-V curve of the gap singularity of the Nb electrode V ∆ (T) show an increase with decreasing temperature and corresponds to the expected BCS behavior of the Nb energy gap ∆ Nb (T). The critical current is very sensitive to the influence of an external magnetic field and reduces twice at an external magnetic field (H≈0.2 Oe for L=40-50 µm) comparable with the earth magnetic field; The magnetic field dependence I C (H) at low H was narrower than the Fraunhofer pattern about 1.5 times. Both the integer and fractional Shapiro steps at voltages V m,n =(m/n)(h/2e)f e were observed under microwave radiation at frequencies f e =38 GHz and f e =50 GHz. Fractional Shapiro steps (m/n=1/2, 3/2) may point on the presence of the second harmonic in the superconducting current-phase relation.The spin-triplet superconducting pairing induced at the interface of a superconductor and a material with the strong spin-orbit interaction (SOI) gives promising opportunities for superconducting spintronics applications [1][2][3]. It has been shown theoretically, that the SOI in a ferromagnet of the superconductor-ferromagnet-superconductor junction can result in a spintriplet pairing [4][5][6][7]. Rashba proximity states in superconducting tunnel junctions, tuning of a magnetization, the proximity-induced triplet superconductivity, and the anomalous Josephson effect have been predicted as well [8][9][10][11][12][13][14][15][16][17]. Coulomb repulsion and Pauli quenching affect the superconducting current in tunnel junction with SOI interlayer but do not destroy the possibility to tune it by changing the strength of the spin-orbit interaction [18][19][20][21]. So, a lot of very

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Dynamics of underdamped Josephson junctions with non-sinusoidal current-phase relation

Cited by 14 publications

References 2 publications

Devil's staircases and continued fractions in Josephson junctions

Devil's staircases and continued fractions in Josephson junctions

Triplet Superconducting Correlations in Hybrid Superconducting Junctions

Superconducting current and low-energy states in a mesa-heterostructure interlayered with a strontium iridate film with strong spin-orbit interaction

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