Phase Diagram of the Electron-Doped ${\mathrm{La}}_{2-x}{\mathrm{Ce}}_x{\mathrm{CuO}}_4$ Cuprate Superconductor from Andreev Bound States at Grain Boundary Junctions

We use quasiparticle tunneling across ${\mathrm{La}}_{2-x}{\mathrm{Ce}}_x{\mathrm{CuO}}_4$ grain boundary junctions to probe the superconducting state and its disappearance with increasing temperature and magnetic field. A zero bias conductance peak due to zero energy surface Andreev bound states is a clear signature of the phase coherence of the superconducting state. Hence, such a peak must disappear at or below the upper critical field $B_{c2}(T)$. For ${\mathrm{La}}_{2-x}{\mathrm{Ce}}_x{\mathrm{CuO}}_4$ this approach sets a lower bound for $B_{c2}(0)\approx 25\mathrm{T}$ which is substantially higher than reported previously. The method of probing the superconducting state via Andreev bound states should also be applicable to other cuprate superconductors.

Figure 1

$\rho (T)$ of a LCCO thin film for $0\mathrm{T}\le B\le 10\mathrm{T}$ (in steps of 1 T). Dashed lines and full circles on the 6 T curve indicate determination of temperatures where the resistance has dropped to, respectively, 10%, 50%, and 90% of its normal state value (gray line). These values define the critical fields $B_{10}$, $B_{50}$, and $B_{90}$. The inset shows $\rho (T)$ at $B=0$ up to 200 K with a parabolic fit (gray line).

Figure 2

Quasiparticle conductance spectra of a 24° GBJ at $T=5\mathrm{K}$ for $0\mathrm{T}\le B\le 16\mathrm{T}$ in steps of 2 T. Graph (a) shows conductance as measured. In (b) the voltage across the leads appearing above 6 T has been subtracted. The inset in (a) shows an enlargement of the low bias region at 16 T. The upper inset in (b) shows the zero field conductance on a larger voltage scale at $T=5\mathrm{K}$ (black line) and at $T=32\mathrm{K}$ (gray line), where the ZBCP has disappeared. The lower left inset shows the integral over the conductance curves taken for voltages between $\pm 15\mathrm{mV}$. The lower right inset in (b) illustrates the geometry of the bicrystal GBJ. Vortices are indicated by circles, screening currents by arrows.

Figure 3

Quasiparticle conductance, corrected for the voltage across the leads, of a 24° GBJ near zero bias showing the disappearance of the ZBCP (a) at constant field $B=16\mathrm{T}$ for different $T$ and (b) at constant temperature $T=13\mathrm{K}$ for different $B$. Thin lines are parabolic fits to the quasiparticle conductance outside the ZBCP.

Figure 4

Magnetic field vs temperature phase diagram showing the fields $B_{10}$ (open squares), $B_{50}$ (open diamonds), and $B_{90}$ (open triangles), as determined from $\rho (T)$ curves of Fig. 1, together with the field $B_{\mathrm{ZBCP}}$ where the ZBCP in the quasiparticle tunnel spectrum disappears. Black (gray) circles: 24° GBJ, measured (extrapolated) values; full squares: 30° GBJ. The black and the gray lines correspond to $B_{c2}(T)$, calculated for a 2D Fermi cylinder and a 3D Fermi sphere, respectively. The inset shows the ZBCP area vs $B$ for different temperatures. Lines are linear fits, which, by extrapolation to zero ZBCP area, define values of $B_{\mathrm{ZBCP}}$ for $B>16\mathrm{T}$.