Dynamic Coupling-decoupling Crossover in the Current-driven Vortex State in Tl<inf>2</inf>Ba<inf>2</inf>CaCu<inf>2</inf>O<inf>8</inf> Probed by the Josephson Plasma Resonance

Abstract

Employing terahertz time-domain spectroscopy, we have measured the Josephson plasma resonance in Tl 2 Ba 2 CaCu 2 O 8 high-T c thin films, and studied the current-driven coupling-decoupling crossover in the driven vortex lattice.The properties of driven periodic structures subject to quenched disorder, including charge-density waves, Wigner crystals and vortex lattices, have become one of the central issues in the phenomenology of nonequilibrium statistical mechanics [1,2]. In the context of the vortex lattice, Koshelev and Vinokur [2] predicted the driven system to undergo a dynamic phase transition at some threshold current between the fluidlike and crystal-like moving states. In other words, an applied current puts forth a scenario where a pinned vortex lattice flows plastically at first as some vortices are depinned, and then becomes more ordered at higher applied currents as more vortices are depinned, possible forming a moving ordered vortex lattice. Thus, beyond some critical value a dynamic phase transition may occur to a more ordered state, characterized by a change from incoherent to coherent vortex motion. C. J. Olson et al.[3] studied both the in-plane and the longitudinal ordering of pancakes in a current-driven anisotropic superconductor by numerical simulations as a function of temperature and pinning disorder. The authors concluded that a dynamic coupling-decoupling crossover does indeed take place at higher currents and temperatures.For a highly anisotropic superconductor, the vortices are stacks of two-dimensional "pancake" vortices in the CuO 2 layers weakly coupled by Josephson and magnetic interactions [4]. At low temperatures and low magnetic fields the vortex lattice is composed of aligned stacks of pancakes (vortex lines). However, the interactions between pancakes in adjacent layers are very weak and vortex lines are easily destroyed by either thermal fluctuations at high temperatures, or by random pinning. The c-axis correlations (longitudinal ordering) are directly related to the interlayer phase coherence, cos[ϕ n,n+1 (r, B)] . ϕ n,n+1 (r, B) is the phase difference between layer n and n + 1, r is the in-plane coordinate, and B is the magnetic field along the c-axis. When the pancake vortices form straight lines perpendicular to the layers, cos[ϕ n,n+1 (r, B)] = 1. However, when the pancake vortices are misaligned perpendicular to the layers, a nonzero phase difference is induced which results in the reduction of cos[ϕ n,n+1 (r, B)] from unity. The Josephson plasma resonance (JPR) is a Cooper pair charge oscillation mode perpendicular to the CuO 2 planes, and directly proportional to the longitudinal ordering. In the presence of a c-axis magnetic field B, the JPR can be written as [5]Here we investigate the current-driven vortex state in the high-T c superconductor, Tl 2 Ba 2 CaCu 2 O 8 (Tl-2212), measuring the Josephson plasma resonance employing terahertz time-domain spectroscopy in transmission [6]. The growth process of Tl-2212, and the experimental setup are discussed in Ref. [7]....