[Paper Review] Metastability and Transient Effects in Vortex Matter Near a Disorder Driven Transition

C. J. Olson, C. Reichhardt+3 more|arXiv (Cornell University)|Jun 9, 2000

Theoretical and Computational Physics3 citations

TL;DR

This study presents the first numerical investigation of metastability and transient effects in vortex matter near a disorder-driven 3D-to-2D transition in layered superconductors. Using 3D simulations of magnetically interacting pancake vortices in quenched point disorder, it demonstrates supercooling, superheating, memory effects, and hysteresis in V(I) curves, linking them to microscopic dynamics: ordered channels grow in supercooled states, while homogeneous disordering occurs in superheated states, with critical current strongly dependent on preparation history and ramp rate.

ABSTRACT

We examine metastable and transient effects both above and below the first-order disorder driven decoupling line in a 3D simulation of magnetically interacting pancake vortices. We observe pronounced transient and history effects as well as supercooling and superheating between the ordered and disordered phases. In the disordered supercooled state as a function of DC driving, reordering occurs through the formation of growing moving channels of the ordered phase. We find that hysteresis in V(I) is strongly dependent on the proximity to the decoupling transition line.

Motivation & Objective

• To investigate metastable and transient states in vortex matter near a disorder-driven 3D-to-2D transition, which are observed experimentally but not yet simulated.
• To understand the microscopic dynamics underlying supercooling, superheating, and hysteresis in vortex transport, particularly the role of vortex channel formation and lattice reorganization.
• To quantify how the critical current depends on preparation protocol and current ramp rate in systems near the decoupling transition.
• To establish a link between experimentally observed voltage response transients and the underlying vortex dynamics in disordered superconductors.

Proposed method

• Simulates 3D overdamped dynamics of magnetically interacting pancake vortices in quenched point disorder using the equation of motion: $\mathbf{f}_i = -\sum_j \nabla_i \mathbf{U}(\rho_{ij}, z_{ij}) + \mathbf{f}^{vp}_i + \mathbf{f}_d = \mathbf{v}_i$.
• Models vortex-vortex interactions via magnetic interaction energy with interlayer coupling $s_m$, using expressions for $\mathbf{U}(\rho_{ij}, 0)$ and $\mathbf{U}(\rho_{ij}, z)$ involving logarithmic and exponential terms.
• Applies DC driving force $f_d$ with variable ramp rates $\delta f_d$ to probe transient voltage responses and hysteresis in $V(I)$ curves.
• Prepares systems in disordered or ordered states to simulate supercooled or superheated conditions, analyzing voltage evolution and vortex structure changes over time.
• Uses periodic boundary conditions in $x,y$ and open boundaries in $z$, with parameters $\lambda = 0.01$, $\xi = 0.01\lambda$, $d = 0.005\lambda$, $R = 22.6\lambda$.
• Analyzes memory effects by applying sequences of driving pulses and measures critical current $f_c$ under equilibrium and non-equilibrium conditions.

Experimental results

Research questions

• RQ1 How do transient voltage responses in vortex matter depend on the initial state (ordered or disordered) and driving protocol near the 3D-2D transition?
• RQ2 What microscopic vortex dynamics underlie the formation of ordered channels during supercooling, and how do they evolve over time?
• RQ3 Why does the critical current $f_c$ exhibit history dependence and ramp-rate dependence in non-equilibrium states?
• RQ4 How does the presence of metastable states affect the shape of $V(I)$ curves, particularly the appearance of N-shaped characteristics?
• RQ5 To what extent do simulated transient behaviors reproduce experimentally observed memory effects and hysteresis in low- and high-temperature superconductors?

Key findings

• In supercooled systems, voltage response increases over time due to the nucleation and growth of moving, ordered channels of vortices, which propagate and widen.
• In superheated systems, the ordered vortex lattice homogeneously disorders without channel formation, leading to a decay in voltage response.
• Hysteresis in $V(I)$ curves is strongly dependent on the proximity to the decoupling transition, with larger hysteresis observed near the transition line.
• The critical current $f_c$ is not a unique value but depends on the system's preparation: it is intermediate between equilibrium values when the system is prepared in a supercooled disordered state.
• For slow current ramps, $V(I)$ curves show negative $dV/dI$ characteristics (N-shaped), indicating a transient ordered state that decouples as vortices flow.
• Memory effects are observed: after a current pulse is shut off and re-applied, the voltage response depends on prior history, consistent with experimental observations.