Dynamic Coupling-Decoupling Crossover in the Current-Driven Vortex State in ${\mathrm{Tl}}_2{\mathrm{Ba}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_8$ Probed by the Josephson Plasma Resonance

We have used terahertz spectroscopy to measure the Josephson plasma resonance in the superconductor ${\mathrm{Tl}}_2{\mathrm{Ba}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$. This allows us to probe the longitudinal ordering of pancake vortices as a function of applied $ab$-plane current in a 2.5 kG $c$-axis magnetic field. With increasing current in the low temperature vortex solid phase, we observe a decrease in the interlayer phase coherence consistent with a progressive misalignment of the pancake vortices in neighboring layers. In the high temperature vortex liquid phase, an increase in the longitudinal ordering occurs above a certain threshold current. Our results show evidence of a current-driven coupling-decoupling crossover in the pinned liquid phase.

Figure 1

Electric field $E(t)$ of THz pulse in the time-domain transmitted through MgO substrate as reference (a), and Tl-2212 thin film plus MgO substrate as sample (b) in 2.5 kG $c$-axis magnetic field at 10 K. (c) and (d) show the amplitude spectrum of $E(t)$ at 10 and 60 K, respectively, with and without an applied current in the $ab$-plane.

Figure 2

Interlayer phase coherence factor $W_c=⟨\cos {\varphi }_{n,n+1}⟩$ versus applied $ab$-plane current density in Tl-2212 in 2.5 kG $c$-axis magnetic field at 10, 60, 80, and 90 K. The solid lines are guides for the eye and show $W_c$ for increasing applied currents. The arrows at 0 mA indicate the value of $W_c$ for each temperature after the current has been switched off.

Figure 3

(a) $I\mathrm{\text{−}}V$ characteristics at various temperatures (see arrows) in 2.5 kG $c$-axis magnetic field. (b) Resistivity versus $c$-axis magnetic field in the low current regime ($J=7\mathrm{A}/{\mathrm{cm}}^2$).

Figure 4

FFT transmission amplitude at 90 K at increasing applied $ab$-plane current density in Tl-2212 in 2.5 kG $c$-axis magnetic field. The dotted lines are fits using two Lorentzian functions for the two JPR’s (One Lorentzian Function at 0, $489\mathrm{A}/{\mathrm{cm}}^2$ for one JPR). The plots are displaced vertically for clarity with decreasing current densities. The inset shows the dominance of the lower to the higher JPR (see text).