Decoupled two-dimensional superconductivity and continuous melting transitions in layered superconductors immersed in a parallel magnetic field

Possible phases and the $B-T$ phase diagram of interlayer Josephson vortices induced by a magnetic field parallel to the superconducting layers are investigated by Monte Carlo simulations based on the anisotropic, frustrated $XY$ model. While for low magnetic fields and small anisotropy parameters a single first-order transition is observed similarly to the melting of an Abrikosov (or pancake) vortex lattice, an intermediate phase, characterized by decoupled, two-dimensional $\left(2\mathrm{D}\right)$ quasi-long-range crystalline order (QLRCO) and superconductivity, is found at high magnetic fields and large anisotropy parameters. Combining the simulation results with a symmetry argument, it is revealed that this intermediate phase is of Kosterlitz-Thouless (KT) type, and the melting of $2\mathrm{D}$ quasi lattices of Josephson vortices and suppression of superconductivity is a KT transition. Evolution of the intermediate phase to the low-temperature phase of $3\mathrm{D}$ LRCO is second order and belongs to the $3\mathrm{D}$ $XY$ universality class. The three phase boundaries merge at a multicritical point at the magnetic field of order $B_{\mathrm{mc}}={\varphi }_0∕2\sqrt{3}\gamma d^2$ in the $B-T$ phase diagram. It is revealed that decoupling of the $3\mathrm{D}$ Josephson vortex lattice into the $2\mathrm{D}$ phase is triggered by hops of Josephson flux lines across superconducting layers activated by thermal fluctuations. The equilibrium phase diagram with the KT phase at high magnetic fields and large anisotropy parameters is consistent with the peculiar Lorentz-force-independent dissipation observed in the highly anisotropic high-$T_c$ superconductor ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+y}$ by Iye et al. [Physica C, 159 433 (1989)].

Figure 1

Structure factors $S(k_x,k_c)$ for $\gamma =8$ at several typical temperatures. Top-left: $T=0.1J∕k_B$; top-right: $T=0.96J∕k_B$; bottom-left: $T=0.98J∕k_B$; and bottom-right: $T=1.5J∕k_B$. The panels are for wave numbers within $k_x∊[-25\pi ∕192d,25\pi ∕192d]$ (horizontal) and $k_c∊[-2\pi ∕d,2\pi ∕d]$ (vertical). The spots at $(k_x,k_c)=(0,\pm 2\pi ∕d)$ are quivalent to $(0,0)$ in the present system.

Figure 2

$k_x$ (left) and $k_c$ (right) profiles of Bragg peaks in the top-right panel of Fig. 1 for $\gamma =8$ at $T=0.96J∕k_B$.

Figure 3

Structure factors $S(k_x,k_c)$ for $\gamma =20$ at several typical temperatures. Top-left: $T=0.65J∕k_B$; top-right: $T=0.7J∕k_B$; bottom-left: $T=0.95J∕k_B$; and bottom-right: $T=0.97J∕k_B$. The panels are for wave numbers within $k_x∊[-25\pi ∕192d,25\pi ∕192d]$ (horizontal) and $k_c∊[-2\pi ∕d,2\pi ∕d]$ (vertical). The spots at $(k_x,k_c)=(0,\pm 2\pi ∕d)$ are quivalent to $(0,0)$ in the present system.

Figure 4

$k_x$ (left) and $k_c$ (right) profiles of Bragg peaks in the top-left panel of Fig. 3 for $\gamma =20$ at $T=0.65J∕k_B$.

Figure 5

$k_x$ (left) and $k_c$ (right) profiles of Bragg peaks in the top-right panel of Fig. 3 for $\gamma =20$ at $T=0.7J∕k_B$.

Figure 6

$k_x$ profiles of structure factors $S(k_x,k_c)$ around the Bragg spots for $\gamma =20$ in the intermediate phase. The solid curves are results of the least-squares fittings to the power-law function as described in text.

Figure 7

Temperature dependence of the intensity of Bragg peaks for $\gamma =8$ and 20.

Figure 8

Profiles of the structure factor $S(k_x,k_y)$ around the Bragg spot $(k_x,k_y)=(\pi ∕16d,0)$ for $\gamma =20$ at $T=0.8J∕k_B$.

Figure 9

Temperature dependence of ratios of Josephson flux lines which contain segments hopping into neighboring block layers, of those which either hop or collide with neighbors in the same block layers, of populations of thermally excited, closed loops of Josephson vortices (normalized by $40\times 240$), and of those containing also pancake vortices (normalized by 240).

Figure 10

Temperature dependence of in-plane helicity moduli for $\gamma =8$ and 20. The solid line is for the theoretical prediction of the universal jump at KT transitions. For a pure $2\mathrm{D}$ unfrustrated $XY$ model corresponding to $\gamma =\infty$ in Hamiltonian (1) $T_{\mathrm{KT}}^{\mathrm{bare}}\simeq 0.89J∕k_B$.

Figure 11

A typical configuration of phase variables on an $ab$ plane at $T=0.1J∕k_B$ for $\gamma =8$. Shown is a region of dimensions $l_x\times l_y=64d\times 64d$.

Figure 12

Supercurrents between two sites neighboring to each other in the $x$ direction. Shown is the region of the same origin of Fig. 11 but of larger dimensions $l_x\times l_y=128d\times 128d$.

Figure 13

A typical configuration of phase variables on an $ac$ section at low temperatures for $\gamma =8$. Shown is a region of dimensions $l_x\times l_z=64d\times 20d$.

Figure 14

$B–T$ phase diagram for interlayer Josephson vortices with a multicritical point at $B_{\mathrm{mc}}={\varphi }_0∕2\sqrt{3}\gamma d^2$. The phase boundaries $T_m\left(B\right),$ $T_{\mathrm{KT}}\left(B\right)$, and $T_{\times }\left(B\right)$ are associated with first-order, KT and $3\mathrm{D}$ $XY$ phase transitions as discussed in text. Possible crossovers are included by dashed lines.