Entanglement of Solid Vortex Matter: A Boomerang-Shaped Reduction Forced by Disorder in Interlayer Phase Coherence in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+y}$

We present evidence for entangled solid vortex matter in a glassy state in a layered superconductor ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+y}$ containing randomly splayed linear defects. The interlayer phase coherence—probed by the Josephson plasma resonance—is enhanced at high temperatures, reflecting the recoupling of vortex liquid by the defects. At low temperatures in the vortex solid state, the interlayer coherence follows a boomerang-shaped reentrant temperature path with an unusual low-field decrease in coherence, indicative of meandering vortices. We uncover a distinct temperature scaling between in-plane and out-of-plane critical currents with opposing dependencies on field and time, consistent with the theoretically proposed “splayed-glass” state.

Figure 1

Microwave dissipation $1/Q$ (left) and frequency shift (right) of the 28-GHz Cu cavity including the BSCCO crystal with splayed CDs ($B_{\Phi }\approx 1\mathrm{T}$) as a function of $H$ applied parallel to the $c$ axis. Each curve is vertically shifted for clarity. Arrows mark the second resonance.

Figure 2

(a) Resonance field $H_p$ normalized by ${\omega }^{-2}$ as a function of $T/T_c$ for $B_{\Phi }\approx 1$ (solid circles) and 0.5 T (solid squares) compared with those of pristine (open triangles) and heavy-ion irradiated BSCCO with $B_{\Phi }=1\mathrm{T}$ (open diamonds) [18]. (b) Angle dependence of $H_p$ for the high-field state at 49 K (squares) and for the low-field state at 70 K (circles). ${\theta }_H$ is the angle between the applied field and the $c$ axis. (c) $c$-axis component of $H_p$ vs ${\theta }_H$. The solid line is a fit to Eq. (2) with $\gamma =400$ and $A=0.47°$.

Figure 3

(a) Contour map of the creep rate $S$ in $H-T$ plane. (b) Temperature dependence of $H_p$ normalized by $B_{\Phi }$ [27]. The dashed lines are the contours of in-plane $J_c^{ab}$ for the $B_{\Phi }\approx 1\mathrm{T}$ sample. Bottom inset: A sketch of splayed defects and entangled vortices. (c) Temperature dependence of $H_p$ together with $J_c^{ab}$ contours for the $B_{\Phi }\approx 0.5\mathrm{T}$ sample.

Figure 4

(a) In-plane $J_c^{ab}$ as a function of field at different times for $B_{\Phi }\approx 1\mathrm{T}$ (squares) and pristine samples (circles). (b) The field dependence of $c$-axis $J_c^c$ for $B_{\Phi }\approx 1\mathrm{T}$ (squares) with different field-sweep rates shows a sharp contrast to the monotonic $J_c^c(H)$ in a pristine crystal [13] with smaller interlayer coupling (circles). Our measurement frequency corresponds to $J_c^c\approx 7\mathrm{A}/{\mathrm{cm}}^2$. The lines are guides for the eyes. The JPR fields change with the sweep rate at 26 K (c) but stay constant at 34 K (d). The two resonances for each rate in (c) correspond to the two points in (b) in the same color [27]. In (c) and (d), data are shifted vertically.