A.C. Quantum interference in superconducting films with periodically modulated thickness

Martinoli, P.; Daldini, O.; Leemann, Ch.; Stocker, Erich Franz

doi:10.1016/0038-1098(75)90043-5

Cited by 77 publications

(43 citation statements)

References 6 publications

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“…Shapiro step phenomena also arise in dc and ac driven charge density waves [7][8][9] , spin density waves 10 , and Frenkel-Kontorova models consisting of commensurate or incommensurate arrangements of particles moving over ordered or disordered substrates [11][12][13] . In the case of vortex motion in type-II superconductors, Martinoli et al reported the first observation of Shapiro steps for dc and ac driven vortices interacting with a periodic one-dimensional (1D) substrate created by periodic thickness modulations of the sample 14,15 , while similar effects were observed for vortices driven over 1D 16,17 or two-dimensional (2D) 18,19 periodic substrates. More recently, Shapiro steps have been found for ac and dc driven colloidal particles moving over a quasi-1D periodic substrate 20 .…”

Section: Introductionmentioning

confidence: 92%

“…In this work we examine Shapiro steps for skyrmions moving over a quasi-1D periodic washboard substrate similar to the geometry considered by Martinoli et al for vortices moving over substrates with a periodic thickness modulation [14][15][16] . We consider the motion of single skyrmions and collectively interacting skyrmions over a periodic substrate, as illustrated in Fig.…”

Section: Introductionmentioning

confidence: 99%

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Shapiro steps for skyrmion motion on a washboard potential with longitudinal and transverse ac drives

Reichhardt

2015

Phys. Rev. B

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We numerically study the behavior of two-dimensional skyrmions in the presence of a quasi-onedimensional sinusoidal substrate under the influence of externally applied dc and ac drives. In the overdamped limit, when both dc and ac drives are aligned in the longitudinal direction parallel to the direction of the substrate modulation, the velocity-force curves exhibit classic Shapiro step features when the frequency of the ac drive matches the washboard frequency that is dynamically generated by the motion of the skyrmions over the substrate, similar to previous observations in superconducting vortex systems. In the case of skyrmions, the additional contribution to the skyrmion motion from a non-dissipative Magnus force shifts the location of the locking steps to higher dc drives, and we find that the skyrmions move at an angle with respect to the direction of the dc drive. For a longitudinal dc drive and a perpendicular or transverse ac drive, the overdamped system exhibits no Shapiro steps; however, when a finite Magnus force is present we find pronounced transverse Shapiro steps along with complex two-dimensional periodic orbits of the skyrmions in the phaselocked regimes. Both the longitudinal and transverse ac drives produce locking steps whose widths oscillate with increasing ac drive amplitude. We examine the role of collective skyrmion interactions and find that additional fractional locking steps occur for both longitudinal and transverse ac drives. At higher skyrmion densities, the system undergoes a series of dynamical order-disorder transitions, with the skyrmions forming a moving solid on the phase locking steps and a fluctuating dynamical liquid in regimes between the steps.

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Section: Introductionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Shapiro steps for skyrmion motion on a washboard potential with longitudinal and transverse ac drives

Reichhardt

2015

Phys. Rev. B

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“…The ML phenomenon occurs due to coupling between, on the one hand, collective lattice modes of frequency f int = qv dc /a, with q an integer and a the lattice periodicity, which occur when a VA moves coherently with velocity v dc through a pinning potential [10,17], and, on the other hand, a superimposed rf-drive of frequency f at an integer fraction 1/p of f int . This coupling produces steps in the dc-transport (IV ) curves when v dc = (p/q)f a [7,[18][19][20][21], similar to ML steps in sliding charge density waves (CDW's) [22,23] and giant Shapiro steps in Josephson junction arrays [24]. However, on decreasing the velocity v dc or increasing the temperature, incoherent velocity fluctuations due to quenched and thermal disorder suppress the collective lattice mode and reduce the width of the ML steps.…”

Section: Introductionmentioning

confidence: 99%

Dynamic ordering and frustration of confined vortex rows studied by mode-locking experiments

2004

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The flow properties of confined vortex matter driven through disordered mesoscopic channels are investigated by mode locking (ML) experiments. The observed ML effects allow to trace the evolution of both the structure and the number of confined rows and their match to the channel width as function of magnetic field. From a detailed analysis of the ML behavior for the case of 3-rows we obtain (i) the pinning frequency fp, (ii) the onset frequency fc for ML (∝ ordering velocity) and (iii) the fraction LML/L of coherently moving 3-row regions in the channel. The field dependence of these quantities shows that, at matching, where LML is maximum, the pinning strength is small and the ordering velocity is low, while at mismatch, where LML is small, both the pinning force and the ordering velocity are enhanced. Further, we find that fc ∝ f 2 p , consistent with the dynamic ordering theory of Koshelev and Vinokur. The microscopic nature of the flow and the ordering phenomena will also be discussed.

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“…The step widths oscillate with the ac amplitude A, with the nth step varying as the modified Bessel function J n (A/ω). Shapiro step-like phase locking is also observed for dc and ac drives in sliding charge-density wave systems [19], as well as vortex motion in superconductors with periodic substrates [20][21][22].…”

Section: Introductionmentioning

confidence: 71%

Nonlinear dynamics, rectification, and phase locking for particles on symmetrical two-dimensional periodic substrates with dc and circular ac drives

Reichhardt

Hastings

2004

Phys. Rev. E

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We investigate the dynamical motion of particles on a two-dimensional symmetric periodic substrate in the presence of both a dc drive along a symmetry direction of the periodic substrate and an additional circular ac drive. For large enough ac drives, the particle orbit encircles one or more potential maxima of the periodic substrate. In this case, when an additional increasing dc drive is applied in the longitudinal direction, the longitudinal velocity increases in a series of discrete steps that are integer multiples of aω/(2π), where a is the lattice constant of the substrate. Fractional steps can also occur. These integer and fractional steps correspond to distinct stable dynamical orbits. A number of these phases also show a rectification in the positive or negative transverse direction where a non-zero transverse velocity occurs in the absence of a dc transverse drive. We map out the phase diagrams of the regions of rectification as a function of ac amplitude, and find a series of tongues. Most of the features, including the steps in the longitudinal velocity and the transverse rectification, can be captured with a simple toy model and by arguments from nonlinear maps. We have also investigated the effects of thermal disorder and incommensuration on the rectification phenomena, and find that for increasing disorder, the rectification regions are gradually smeared and the longitudinal velocity steps are no longer flat but show a linearly increasing velocity.

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A.C. Quantum interference in superconducting films with periodically modulated thickness

Cited by 77 publications

References 6 publications

Shapiro steps for skyrmion motion on a washboard potential with longitudinal and transverse ac drives

Shapiro steps for skyrmion motion on a washboard potential with longitudinal and transverse ac drives

Dynamic ordering and frustration of confined vortex rows studied by mode-locking experiments

Nonlinear dynamics, rectification, and phase locking for particles on symmetrical two-dimensional periodic substrates with dc and circular ac drives

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