Intrinsic granularity in nanocrystalline boron-doped diamond films measured by scanning tunneling microscopy

We report on low-temperature scanning tunneling microscopy/spectroscopy experiments performed on superconducting boron-doped nanocrystalline diamond (NCD) thin films prepared by chemical-vapor deposition methods. The most representative sample reveals the observed superconducting gap $\left(\Delta \right)$ highly modulated over a length scale on the order of $\sim 30\text{nm}$, which is much shorter than the typical diamond grain size. The sample local and macroscopic behavior favors for the $\Delta$ modulation as being an intrinsic property of the NCD granules. On the other hand, $\Delta$ shows its temperature dependence $\left[\Delta \left(T\right)\right]$ consistent with the results obtained by Fominov and Feigel’man [Phys. Rev. B 63, 094518 (2001)], who studied theoretically the behavior of the superconducting gap of a BCS superconductor in contact with a normal layer by solving the one-dimensional Usadel equations on the superconducting side of the superconducting to normal interface.

Figure 1

(Color online) (a) A typical resistance versus temperature dependence of a superconducting NCD sample. The broad superconducting transition is revealed by the splitting of the $R\left(T\right)$ curves measured under 0 and 12 T fields at temperatures above 8 K. A $T_C=2.35\text{K}$ has been obtained for this particular sample when taking the half value of its normal-state resistance. (b) The corresponding zero-field-cooling and field-cooling magnetic moment versus temperature dependence measured in a SQUID magnetometer. The onset of the increase in the sample’s diamagnetic signal occurs at 6.3 K when a small field of 20 mT is applied.

Figure 2

(Color online) (a) A $560\times 560{\text{nm}}^2$ STM scanned area and (b) the STS map constructed from the $I\text{−}V$ curves measured on $64\times 64$ equidistanced points on the region displayed in (a), at a temperature of 0.1 K. The brighter pixels in (b) indicate a larger ${\sigma }_{\text{N}}-\sigma \left(0\right)$ while the dark spots correspond to normal regions.

Figure 3

(Color online) The normalized conductance ${\sigma }_{norm}$, obtained by deriving the measured $I\left(V\right)$ characteristics at a fixed point and at different temperatures versus the bias voltage (units in millivolts).

Figure 4

(Color online) Fittings of the experimental data plotted in Fig. 3. (Inset) The fit performed on the 0.3 K experimental data (circles) by solving the Usadel (solid line) equations. As a comparison, the result obtained for the case in which the normal layer is absent is also shown (dashed line). This corresponds to the pure BCS situation.

Figure 5

(Color online) The (red) dots are the experimentally obtained $\Delta$ (with 20% error bars), corresponding to the voltage where $d\sigma /dV$ is maximum. The (green) squares and (blue) triangles are the calculated $\Delta$ by solving the Eq. (2) at $x=L_{\text{S}}$ and $x=0$, respectively. The solid (black) lines are the expected BCS dependence for $T_C=2.4\text{K}$, $T_C=2.78\text{K}$, and $T_C=3.8\text{K}$, respectively. A $T_C=2.78\text{K}$ was obtained from transport measurements by taking the half value of the maximum resistance criterion. $T_C=2.4\text{K}$ is the temperature above which ${\sigma }_{norm}\left(V\right)$ of Fig. 3 is constant. In addition, a dashed straight line is shown as a guide to the eyes.

Figure 6

(Color online) Correlation between the $H_{C2}$ obtained by applying the local $\Delta \left(T\right)$ to the Clogston’s formula (red circles) and the $H_{C2}$ obtained from magnetoresistance measurements under the criteria shown in the inset: criteria 1 (blue squares) and 2 (black triangles).