Molecular dynamics of pancake vortices with realistic interactions: Observing the vortex lattice melting transition

Goldschmidt, Yadin Y.

doi:10.1103/physrevb.72.064518

Cited by 6 publications

(6 citation statements)

References 36 publications

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“…In this paper we use the London-Langevin molecular dynamics simulation method. The details of the simulation method, for a system without columnar defects is given in our previous paper 31 . Here we summarize the main ingredients of the method.…”

Section: A Methodsmentioning

confidence: 99%

“…The details are explained in Ref. [31]. The final expression we used for the pair energy of two pancakes with fully implemented PBC is…”

Section: B Interactionsmentioning

confidence: 99%

“…The functions G 0 (R/λ, L 1 /λ) and G 0C (x/L 1 , y/L 2 ) represent the periodic screened and bare Greens functions for the Coulomb interactions in 2D and are given in the Appendix of Ref. [31]. The factor f m comes from the summation of the EM interaction between a pancake and another pancake in the same cell and all its images along the z-direction.…”

Section: B Interactionsmentioning

confidence: 99%

“…We have also implemented the Josephson interaction among adjacent pancakes belonging to the same FL 31 . The approximate formula we use is based on our recent paper that derives a numerical solution to the nonlinear sine Gordon equation in two dimensions 32 .…”

Section: B Interactionsmentioning

confidence: 99%

“…The problem of ergodicity is really not much of an issue for Langevin simulations since the thermal noise helps the system explore the configuration space and it can be shown by using the corresponding Fokker-Planck equation that equilibrium is reached in the long time limit. For flux-lines we have found a way to implement "permutations" in the MD simulations by flux cutting and recombining and this was explained in a recent publication 31 which reported on MD simulations of the melting transition in pure BSCCO without columnar or point defects. We were also able to implement periodic boundary conditions in all directions (including the z direction), and to include the in and out of plane electromagnetic interaction as well as the Josephson interaction using the new approximation we have recently obtained 32 .…”

Section: Introductionmentioning

confidence: 98%

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Langevin Dynamics of the vortex matter two-stage melting transition in Bi_2Sr_2CaCu_2O$_{8+δ}$ in the presence of straight and of tilted columnar defects

Goldschmidt,

Liu

2007

Preprint

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In this paper we use London Langevin molecular dynamics simulations to investigate the vortex matter melting transition in the highly anisotropic high-temperature superconductor material Bi2Sr2CaCu2O 8+δ in the presence of low concentration of columnar defects (CDs). We reproduce with further details our previous results obtained by using Multilevel Monte Carlo simulations that showed that the melting of the nanocrystalline vortex matter occurs in two stages: a first stage melting into nanoliquid vortex matter and a second stage delocalization transition into a homogeneous liquid. Furthermore, we report on new dynamical measurements in the presence of a current that identifies clearly the irreversibility line and the second stage delocalization transition. In addition to CDs aligned along the c-axis we also simulate the case of tilted CDs which are aligned at an angle with respect to the applied magnetic field. Results for CDs tilted by 45 • with respect to c-axis show that the locations of the melting and delocalization transitions are not affected by the tilt when the ratio of flux lines to CDs remains constant. On the other hand we argue that some dynamical properties and in particular the position of the irreversibility line should be affected.

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Section: A Methodsmentioning

confidence: 99%

“…The details are explained in Ref. [31]. The final expression we used for the pair energy of two pancakes with fully implemented PBC is…”

Section: B Interactionsmentioning

confidence: 99%

Section: B Interactionsmentioning

confidence: 99%

Section: B Interactionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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Langevin Dynamics of the vortex matter two-stage melting transition in Bi_2Sr_2CaCu_2O$_{8+δ}$ in the presence of straight and of tilted columnar defects

Goldschmidt,

Liu

2007

Preprint

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Roles of pinning strength and density in vortex melting

Kim¹,

Khawaja²,

Benkraouda³

2008

Supercond. Sci. Technol.

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We have investigated the role of pinning strength and density on the equilibrium vortex-lattice to vortex-liquid phase transition under several applied magnetic fields. This study was conducted using a series of molecular dynamic simulations on several samples with different strengths and densities of pinning sites which are arranged in periodic square arrays. We have found a single solid–liquid vortex transition when the vortex filling factor n>1. We have found that, for fixed pinning densities and strengths, the melting temperature, Tm, decreases almost linearly with increasing magnetic field. Our results provide direct numerical evidence for the significant role of both the strength and density of pinning centers on the position of the melting line. We have found that the vortex-lattice to vortex-liquid melting line shifts up as the pinning strength or the pinning density was increased. The effect on the melting line was found to be more pronounced at small values of strength and density of pinning sites.

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Langevin simulations of the out-of-equilibrium dynamics of vortex glasses in high-temperature superconductors

2007

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We study the relaxation dynamics of flux lines in dirty high-temperature superconductors using numerical simulations of a London-Langevin model of the interacting vortex lines. By analysing the equilibrium dynamics in the vortex liquid phase we find a dynamic crossover to a glassy non-equilibrium regime. We then focus on the out-of-equilibrium dynamics of the vortex glass phase using tools that are common in the study of other glassy systems. By monitoring the two-times roughness and dynamic wandering we identify and characterize finite-size effects that are similar, though more complex, than the ones found in the stationary roughness of clean interface dynamics. The two-times density-density correlation and mean-squared-displacement correlation age and their temporal scaling follows a multiplicative law similar to the one found at criticality. The linear responses also age and the comparison with their associated correlations shows that the equilibrium fluctuationdissipation relation is modified in a simple manner that allows for the identification of an effective temperature characterizing the dynamics of the slow modes. The effective temperature is closely related to the vortex liquidvortex glass crossover temperature. Interestingly enough, our study demonstrates that the glassy dynamics in the vortex glass is basically identical to the one of a single elastic line in a disordered environment (with the same type of scaling though with different parameters). Possible extensions and the experimental relevance of these results are also discussed.

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Molecular dynamics of pancake vortices with realistic interactions: Observing the vortex lattice melting transition

Cited by 6 publications

References 36 publications

Langevin Dynamics of the vortex matter two-stage melting transition in Bi_2Sr_2CaCu_2O$_{8+δ}$ in the presence of straight and of tilted columnar defects

Langevin Dynamics of the vortex matter two-stage melting transition in Bi_2Sr_2CaCu_2O$_{8+δ}$ in the presence of straight and of tilted columnar defects

Roles of pinning strength and density in vortex melting

Langevin simulations of the out-of-equilibrium dynamics of vortex glasses in high-temperature superconductors

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