Magnetic field and temperature dependence of complex conductance of ultrathin La${}_{1.65}$Sr${}_{0.45}$CuO${}_4$/La${}_2$CuO${}_4$ films

We used atomic-layer molecular beam epitaxy to synthesize bilayers of a cuprate metal (La${}_{1.55}$Sr${}_{0.45}$CuO${}_4$) and a cuprate insulator (La${}_2$CuO${}_4$) film, in which each layer is just one unit cell thick. We have studied the magnetic field and temperature dependences of the complex sheet conductance, σ(ω), of these films. Experiments have been carried out at frequencies between 2 and 20 MHz using the single-spiral coil technique. We found that (i) the inductive response, $L_k^{-1}$($T$), starts at 1.7 K lower temperatures than Reσ($T$), which in turn is characterized by a peak close to the transition, (ii) this shift is almost constant with magnetic field up to 8 T; (iii) the vortex diffusion constant $D$($T$) is not linear with $T$ at low temperature, as in the case of free vortices, but rather is exponential due to pinning of vortex cores, and (iv) the Berezinski-Kosterlitz-Thouless (BKT) transition temperature occurs at the point where $Y$ = ($l_{\omega }$/${\xi }_{+}$)${}^2$ = 1. Our experimental results can be described well by the extended dynamic theory of the BKT transition and the dynamics of bound vortex-antivortex pairs with short separation lengths.

Figure 1

Re$M$($T$) and Im$M$($T$) of a bilayer LSCO/LCO film at different magnitudes of the magnetic field perpendicular to the film surface: $B=0$, 0.0014, 0.0023, 0.003, 0.006, 0.013, 0.019, 0.036, 0.1, 0.2, 0.4, 0.6, 1.0, 1.5, 2.0, 3.4, 4.6, 5.2, 6.0, and 7.0 T. The long oblique arrow shows the direction of increasing magnetic field. The short vertical arrows indicate the temperatures at which Re$M$($T$) and Im$M$($T$), respectively, drop to zero.

Figure 2

Temperature dependence of $L_k^{-1}$($T$) and ωReσ($T$) for bilayer film at 8 MHz and different magnetic fields perpendicular to the film face: $B$ = 0, 0.0014, 0.0023, 0.003, 0.006, 0.013, 0.019, 0.036, 0.1, 0.2, 0.4, 0.6, 1.0, 1.5, 2.0, 3.4, 4.6, 5.2, 6.0, and 7.0 T. The solid lines are quadratic fits to $L_k^{-1}$($T$) below $T_{\mathrm{BKT}}$ at different magnetic fields. Also shown is the theoretical BKT function (dashed line).

Figure 3

The real part of the high-frequency conductivity, ωReσ($T$), at the same magnetic fields as in Fig. 2.

Figure 4

$H_{c2}\left(T\right)$ determined as the onsets of $L_k^{-1}$($T$) (black points) and Reσ($T$) (red points) field dependences. Right-hand-side curves present the same data on the log scale. The solid lines indicate the temperature dependences according to the WHH model. The solid lines for the right-hand-side curves are a guide to the eye.

Figure 5

Plot of Re$M$($T$) and Im$M$($T$) of 50-nm-thick Nb film on SiO${}_2$.

Figure 6

Temperature dependence of $Y$ = ($l_{\omega }$/${\xi }^{+}$)${}^2$ at different magnetic fields perpendicular to the film face: $B$ = 0, 0.0014, 0.0023, 0.003, 0.006, 0.013, 0.019, 0.036, 0.1, 0.2, 0.4, 0.6, 1.0, 1.5, 2.0, 3.4, 4.6, 5.2, 6.0, and 7.0 T.