Transverse ac-driven and geometric ratchet effects for vortices in conformal crystal pinning arrays

Reichhardt, Charles; Reichhardt, Cynthia Jane Olsen

doi:10.1103/PhysRevB.93.064508

Transverse ac-driven and geometric ratchet effects for vortices in conformal crystal pinning arrays

Journal Article · Wed Feb 10 23:00:00 EST 2016 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.93.064508· OSTI ID:1337094

Reichhardt, Charles ^[1]; Reichhardt, Cynthia Jane Olsen ^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division

A conformal pinning array is created by taking a conformal transformation of a uniform hexagonal lattice to create a structure in which the sixfold ordering of the original lattice is preserved but which has a spatial gradient in the pinning site density. With a series of conformal arrays it is possible to create asymmetric substrates, and it was previously shown that when an ac drive is applied parallel to the asymmetry direction, a pronounced ratchet effect occurs with a net dc flow of vortices in the same direction as the ac drive. Here, in this article, we show that when the ac drive is applied perpendicular to the substrate asymmetry direction, it is possible to realize a transverse ratchet effect where a net dc flow of vortices is generated perpendicular to the ac drive. The conformal transverse ratchet effect is distinct from previous versions of transverse ratchets in that it occurs due to the generation of non-Gaussian transverse vortex velocity fluctuations by the plastic motion of vortices, so that the system behaves as a noise correlation ratchet. The transverse ratchet effect is much more pronounced in the conformal arrays than in random gradient arrays and is absent in square gradient arrays due the different nature of the vortex flow in each geometry. We show that a series of reversals can occur in the transverse ratchet effect due to changes in the vortex flow across the pinning gradient as a function of vortex filling, pinning strength, and ac amplitude. We also consider the case where a dc drive applied perpendicular to the substrate asymmetry direction generates a net flow of vortices perpendicular to the dc drive, producing what is known as a geometric or drift ratchet that again arises due to non-Gaussian dynamically generated fluctuations. The drift ratchet is more efficient than the ac driven ratchet and also exhibits a series of reversals for varied parameters. Lastly, our results should be general to a wide class of systems undergoing nonequilibrium dynamics on conformal substrates, such as colloidal particles on optical traps.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1337094

Alternate ID(s):: OSTI ID: 1237784

Report Number(s):: LA-UR--15-29312

Journal Information:: Physical Review B, Journal Name: Physical Review B Journal Issue: 6 Vol. 93; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Separation quality of a geometric ratchet Keller, C.; Marquardt, Florian; Bruder, C. Physical Review E, Vol. 65, Issue 4 https://doi.org/10.1103/PhysRevE.65.041927	journal	April 2002
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Vortex Core Deformation and Stepper-Motor Ratchet Behavior in a Superconducting Aluminum Film Containing an Array of Holes Van de Vondel, J.; Gladilin, V. N.; Silhanek, A. V. Physical Review Letters, Vol. 106, Issue 13 https://doi.org/10.1103/PhysRevLett.106.137003	journal	March 2011
Strongly Enhanced Pinning of Magnetic Vortices in Type-II Superconductors by Conformal Crystal Arrays Ray, D.; Olson Reichhardt, C. J.; Jankó, B. Physical Review Letters, Vol. 110, Issue 26 https://doi.org/10.1103/PhysRevLett.110.267001	journal	June 2013
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Microfabricated Sieve for the Continuous Sorting of Macromolecules Duke, T. A. J.; Austin, R. H. Physical Review Letters, Vol. 80, Issue 7 https://doi.org/10.1103/PhysRevLett.80.1552	journal	February 1998
Fractal Networks, Braiding Channels, and Voltage Noise in Intermittently Flowing Rivers of Quantized Magnetic Flux Olson, C. J.; Reichhardt, C.; Nori, Franco Physical Review Letters, Vol. 80, Issue 10 https://doi.org/10.1103/PhysRevLett.80.2197	journal	March 1998
Nonequilibrium Dynamic Phase Diagram for Vortex Lattices Olson, C. J.; Reichhardt, C.; Nori, Franco Physical Review Letters, Vol. 81, Issue 17 https://doi.org/10.1103/PhysRevLett.81.3757	journal	October 1998
Hall Noise and Transverse Freezing in Driven Vortex Lattices Kolton, Alejandro B.; Domínguez, Daniel; Grønbech-Jensen, Niels Physical Review Letters, Vol. 83, Issue 15 https://doi.org/10.1103/PhysRevLett.83.3061	journal	October 1999
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Rocking Ratchets in Two-Dimensional Josephson Networks: Collective Effects and Current Reversal Marconi, Verónica I. Physical Review Letters, Vol. 98, Issue 4 https://doi.org/10.1103/PhysRevLett.98.047006	journal	January 2007
Origin of Reversed Vortex Ratchet Motion Gillijns, W.; Silhanek, A. V.; Moshchalkov, V. V. Physical Review Letters, Vol. 99, Issue 24 https://doi.org/10.1103/PhysRevLett.99.247002	journal	December 2007
Artificial Brownian motors: Controlling transport on the nanoscale Hänggi, Peter; Marchesoni, Fabio Reviews of Modern Physics, Vol. 81, Issue 1 https://doi.org/10.1103/RevModPhys.81.387	journal	March 2009
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Separating particles according to their physical properties: Transverse drift of underdamped and overdamped interacting particles diffusing through two-dimensional ratchets Savel’ev, Sergey; Misko, Vyacheslav; Marchesoni, Fabio Physical Review B, Vol. 71, Issue 21 https://doi.org/10.1103/physrevb.71.214303	journal	June 2005
Vortex configurations and critical parameters in superconducting thin films containing antidot arrays: Nonlinear Ginzburg-Landau theory Berdiyorov, G. R.; Milošević, M. V.; Peeters, F. M. Physical Review B, Vol. 74, Issue 17 https://doi.org/10.1103/physrevb.74.174512	journal	November 2006
Transverse rectification of disorder-induced fluctuations in a driven system Kolton, Alejandro B. Physical Review B, Vol. 75, Issue 2 https://doi.org/10.1103/physrevb.75.020201	journal	January 2007
Reversible vortex ratchet effects and ordering in superconductors with simple asymmetric potential arrays Lu, Qiming; Reichhardt, C. J. Olson; Reichhardt, C. Physical Review B, Vol. 75, Issue 5 https://doi.org/10.1103/physrevb.75.054502	journal	February 2007
Current reversal in collective ratchets induced by lattice instability Dinis, L.; González, E. M.; Anguita, J. V. Physical Review B, Vol. 76, Issue 21 https://doi.org/10.1103/physrevb.76.212507	journal	December 2007
Asymmetric weak-pinning superconducting channels: Vortex ratchets Yu, K.; Heitmann, T. W.; Song, C. Physical Review B, Vol. 76, Issue 22 https://doi.org/10.1103/physrevb.76.220507	journal	December 2007
Rocking ratchet induced by pure magnetic potentials with broken reflection symmetry Perez de Lara, D.; Castaño, F. J.; Ng, B. G. Physical Review B, Vol. 80, Issue 22 https://doi.org/10.1103/physrevb.80.224510	journal	December 2009
High-frequency vortex ratchet effect in a superconducting film with a nanoengineered array of asymmetric pinning sites Jin, B. B.; Zhu, B. Y.; Wördenweber, R. Physical Review B, Vol. 81, Issue 17 https://doi.org/10.1103/physrevb.81.174505	journal	May 2010
Vortex ratchet reversal at fractional matching fields in kagomélike array with symmetric pinning centers Perez de Lara, D.; Alija, A.; Gonzalez, E. M. Physical Review B, Vol. 82, Issue 17 https://doi.org/10.1103/physrevb.82.174503	journal	November 2010
Vortex ratchet reversal: Role of interstitial vortices Perez de Lara, D.; Erekhinsky, M.; Gonzalez, E. M. Physical Review B, Vol. 83, Issue 17 https://doi.org/10.1103/physrevb.83.174507	journal	May 2011
Frequency-dependent ratchet effect in superconducting films with a tilted washboard pinning potential Shklovskij, Valerij A.; Dobrovolskiy, Oleksandr V. Physical Review B, Vol. 84, Issue 5 https://doi.org/10.1103/physrevb.84.054515	journal	August 2011
Rectification of vortex motion in a circular ratchet channel Lin, N. S.; Heitmann, T. W.; Yu, K. Physical Review B, Vol. 84, Issue 14 https://doi.org/10.1103/physrevb.84.144511	journal	October 2011
Guided vortex motion in YBa 2 Cu 3 O 7 thin films with collective ratchet pinning potentials Palau, A.; Monton, C.; Rouco, V. Physical Review B, Vol. 85, Issue 1 https://doi.org/10.1103/physrevb.85.012502	journal	January 2012
Magnetic flux pinning in superconductors with hyperbolic-tessellation arrays of pinning sites Misko, V. R.; Nori, Franco Physical Review B, Vol. 85, Issue 18 https://doi.org/10.1103/physrevb.85.184506	journal	May 2012
Evidence of vortex jamming in Abrikosov vortex flux flow regime Karapetrov, G.; Yefremenko, V.; Mihajlović, G. Physical Review B, Vol. 86, Issue 5 https://doi.org/10.1103/physrevb.86.054524	journal	August 2012
Enhancing the critical current of a superconducting film in a wide range of magnetic fields with a conformal array of nanoscale holes Wang, Y. L.; Latimer, M. L.; Xiao, Z. L. Physical Review B, Vol. 87, Issue 22 https://doi.org/10.1103/physrevb.87.220501	journal	June 2013
Pinning, ordering, and dynamics of vortices in conformal crystal and gradient pinning arrays Ray, D.; Reichhardt, C.; Reichhardt, C. J. Olson Physical Review B, Vol. 90, Issue 9 https://doi.org/10.1103/physrevb.90.094502	journal	September 2014
Reversible ratchet effects for vortices in conformal pinning arrays Reichhardt, C.; Ray, D.; Reichhardt, C. J. Olson Physical Review B, Vol. 91, Issue 18 https://doi.org/10.1103/physrevb.91.184502	journal	May 2015
Mechanical equilibrium of conformal crystals Rothen, François; Pierański, Piotr Physical Review E, Vol. 53, Issue 3 https://doi.org/10.1103/physreve.53.2828	journal	March 1996
Separation quality of a geometric ratchet Keller, C.; Marquardt, Florian; Bruder, C. Physical Review E, Vol. 65, Issue 4 https://doi.org/10.1103/physreve.65.041927	journal	April 2002
Separation of suspended particles in microfluidic systems by directional locking in periodic fields Herrmann, John; Karweit, Michael; Drazer, German Physical Review E, Vol. 79, Issue 6 https://doi.org/10.1103/physreve.79.061404	journal	June 2009
Two-dimensional optical thermal ratchets based on Fibonacci spirals Xiao, Ke; Roichman, Yael; Grier, David G. Physical Review E, Vol. 84, Issue 1 https://doi.org/10.1103/physreve.84.011131	journal	July 2011
Rectification of Swimming Bacteria and Self-Driven Particle Systems by Arrays of Asymmetric Barriers Wan, M. B.; Olson Reichhardt, C. J.; Nussinov, Z. Physical Review Letters, Vol. 101, Issue 1 https://doi.org/10.1103/physrevlett.101.018102	journal	July 2008
Vortex Core Deformation and Stepper-Motor Ratchet Behavior in a Superconducting Aluminum Film Containing an Array of Holes Van de Vondel, J.; Gladilin, V. N.; Silhanek, A. V. Physical Review Letters, Vol. 106, Issue 13 https://doi.org/10.1103/physrevlett.106.137003	journal	March 2011
Strongly Enhanced Pinning of Magnetic Vortices in Type-II Superconductors by Conformal Crystal Arrays Ray, D.; Olson Reichhardt, C. J.; Jankó, B. Physical Review Letters, Vol. 110, Issue 26 https://doi.org/10.1103/physrevlett.110.267001	journal	June 2013
Forced thermal ratchets Magnasco, Marcelo O. Physical Review Letters, Vol. 71, Issue 10 https://doi.org/10.1103/physrevlett.71.1477	journal	September 1993
Nonequilibrium fluctuation-induced transport Doering, Charles R.; Horsthemke, Werner; Riordan, Jason Physical Review Letters, Vol. 72, Issue 19 https://doi.org/10.1103/physrevlett.72.2984	journal	May 1994
Dynamic Melting of the Vortex Lattice Koshelev, A. E.; Vinokur, V. M. Physical Review Letters, Vol. 73, Issue 26 https://doi.org/10.1103/physrevlett.73.3580	journal	December 1994
Flux Flow Noise and Dynamical Transitions in a Flux Line Lattice Marley, A. C.; Higgins, M. J.; Bhattacharya, S. Physical Review Letters, Vol. 74, Issue 15 https://doi.org/10.1103/physrevlett.74.3029	journal	April 1995
Lateral Separation of Macromolecules and Polyelectrolytes in Microlithographic Arrays Ertaş, Deniz Physical Review Letters, Vol. 80, Issue 7 https://doi.org/10.1103/physrevlett.80.1548	journal	February 1998
Microfabricated Sieve for the Continuous Sorting of Macromolecules Duke, T. A. J.; Austin, R. H. Physical Review Letters, Vol. 80, Issue 7 https://doi.org/10.1103/physrevlett.80.1552	journal	February 1998
Fractal Networks, Braiding Channels, and Voltage Noise in Intermittently Flowing Rivers of Quantized Magnetic Flux Olson, C. J.; Reichhardt, C.; Nori, Franco Physical Review Letters, Vol. 80, Issue 10 https://doi.org/10.1103/physrevlett.80.2197	journal	March 1998
Nonequilibrium Dynamic Phase Diagram for Vortex Lattices Olson, C. J.; Reichhardt, C.; Nori, Franco Physical Review Letters, Vol. 81, Issue 17 https://doi.org/10.1103/physrevlett.81.3757	journal	October 1998
Hall Noise and Transverse Freezing in Driven Vortex Lattices Kolton, Alejandro B.; Domínguez, Daniel; Grønbech-Jensen, Niels Physical Review Letters, Vol. 83, Issue 15 https://doi.org/10.1103/physrevlett.83.3061	journal	October 1999
Superconducting Fluxon Pumps and Lenses Wambaugh, J. F.; Reichhardt, C.; Olson, C. J. Physical Review Letters, Vol. 83, Issue 24 https://doi.org/10.1103/physrevlett.83.5106	journal	December 1999
Collective Interaction-Driven Ratchet for Transporting Flux Quanta Olson, C. J.; Reichhardt, C.; Jankó, B. Physical Review Letters, Vol. 87, Issue 17 https://doi.org/10.1103/physrevlett.87.177002	journal	October 2001
Effective Temperature in Driven Vortex Lattices with Random Pinning Kolton, Alejandro B.; Exartier, Raphaël; Cugliandolo, Leticia F. Physical Review Letters, Vol. 89, Issue 22 https://doi.org/10.1103/physrevlett.89.227001	journal	November 2002
Vortex-Rectification Effects in Films with Periodic Asymmetric Pinning Van de Vondel, J.; de Souza Silva, C. C.; Zhu, B. Y. Physical Review Letters, Vol. 94, Issue 5 https://doi.org/10.1103/physrevlett.94.057003	journal	February 2005
Rocking Ratchets in Two-Dimensional Josephson Networks: Collective Effects and Current Reversal Marconi, Verónica I. Physical Review Letters, Vol. 98, Issue 4 https://doi.org/10.1103/physrevlett.98.047006	journal	January 2007
Origin of Reversed Vortex Ratchet Motion Gillijns, W.; Silhanek, A. V.; Moshchalkov, V. V. Physical Review Letters, Vol. 99, Issue 24 https://doi.org/10.1103/physrevlett.99.247002	journal	December 2007
Artificial Brownian motors: Controlling transport on the nanoscale Hänggi, Peter; Marchesoni, Fabio Reviews of Modern Physics, Vol. 81, Issue 1 https://doi.org/10.1103/revmodphys.81.387	journal	March 2009
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Influence of ultrashort laser drilling on magnetic and transport characteristics of HTS tapes Pokrovskii, S. V.; Mavritskii, O. B.; Egorov, A. N. Superconductor Science and Technology, Vol. 32, Issue 7 https://doi.org/10.1088/1361-6668/ab14a3	journal	June 2019
Transverse vortex commensurability effect and sign change of the Hall voltage in superconducting YBa 2 Cu 3 O 7 − δ thin films with a nanoscale periodic pinning landscape Zechner, G.; Lang, W.; Dosmailov, M. Physical Review B, Vol. 98, Issue 10 https://doi.org/10.1103/physrevb.98.104508	journal	September 2018
Superconductivity and hall effect of polycrystalline Pb82Bi18 thin films, a universal test platform for flux pinning by hybrid nanostructures Bang, Wonbae; Woo, Sung Oh; Morrison, T. D. International Journal of Modern Physics B, Vol. 33, Issue 25 https://doi.org/10.1142/s0217979219502886	journal	October 2019

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