Superconductor-insulator transition driven by pressure-tuned intergrain coupling in nanodiamond films

We report on the pressure-driven superconductor-insulator transition in heavily boron-doped nanodiamond films. By systematically increasing the pressure, we suppress the Josephson coupling between the superconducting nanodiamond grains. The diminished intergrain coupling gives rise to an overall insulating state in the films, which is interpreted in the framework of a parallel-series circuit model to be the result of bosonic insulators with preserved localized intragrain superconducting order parameters. Our investigation opens up perspectives for the application of high pressure in research on quantum confinement and coherence. Our data unveil the percolative nature of the electrical transport in nanodiamond films, and highlight the essential role of grain boundaries in determining the electronic properties of this material.

Figure 1

Structural analysis of the heavily boron-doped nanodiamond films. (a) SEM image of the upper surface of the nanodiamond film, and (b) ADF-STEM image of its cross section. To protect the nanodiamond surface from ion milling damage during TEM sample preparation, a thin layer of Pt was deposited onto the boron-doped nanodiamond (BDD) surface. The substrate (Subs) is still present in these samples for ease of handling. (c) STEM-EELS imaging of boron (in green) and carbon (in red) distributions in the white dashed window in (b). The superposition of green and red pixels results in the yellow/orange color of the film. (d) Characteristic EELS spectra recorded from the intragrain and intergrain regions. The boron $K$-edge fine structures (subpeaks of A, B, and C) indicate the tetrahedral coordination of boron in nanodiamond, while the features of the boron $K$ edge and carbon $K$ edge are indicative of an amorphous boron/carbon mixture in the intergrain regions.

Figure 2

Thermoresistivity of the heavily boron-doped nanodiamond films. (a) The dirty metallic (or weakly insulating) normal state and the superconducting transition of the nanodiamond film at zero magnetic field. Inset: magnification of the resistive superconducting transition. (b) Magnetic field dependence of the resistive superconducting transition. When increasing the applied magnetic field, the superconductivity is suppressed, and the ρ($T$) maximum is shifted towards zero temperature. Inset: quadratic fit to the ${\mu }_{0}H\text{−}T$ phase boundary for the determination of the Ginzburg-Landau coherence length.

Figure 3

Characteristic differential conductance spectra demonstrating the local density of states of the nanodiamond films. (a) Normalized tunneling conductance $G_{\mathrm{norm}}$ as a function of bias voltage $V_{\mathrm{b}}$ at different temperatures. The temperature-induced evolution of the $G_{\mathrm{norm}}\left(V_{\mathrm{b}}\right)$ spectra shows the emergence of in-gap states, the decrease of the gap size, the U-V transformation of the superconducting gap, and the decline of the coherence peaks. The last two phenomena suggest the localization of remaining Cooper pairs. (b) Temperature-induced evolution of the half-width of the superconducting gap. The BCS-like fit to Δ($T$) indicates the local onset critical temperature ${T_{\mathrm{c}}}^{\mathrm{onset}}\left(\mathrm{local}\right)=7\mathrm{K}$ and the zero-temperature superconducting gap $2{\mathrm{\Delta }}_0=2.96\mathrm{meV}$.

Figure 4

Pressure-driven superconductor-insulator transition in the nanodiamond films. (a) Thermoresistivity under different pressures. The enhancement of the applied pressure results in an increase of the normal-state resistivity and a suppression of the superconducting state (curves from up to bottom: 19.2, 18.0, 16.0, 12.2, 11.2, 9.2, 2.4, and 0 GPa). (b) Exponential fits (red curves) to the thermoresistivity at high temperatures. The deviations of ρ($T$) from the exponential fits are indicative of the emergence of insulating states at low temperatures. (c) The influence of the applied pressure on the resistive superconducting transition. Inset: linear fit to the pressure $P$ dependence of ${T_{\mathrm{c}}}^{\mathrm{onset}}$ suggests the complete suppression of the bulk superconductivity at about 32 GPa.

Figure 5

Modeling of the pressure-driven superconductor-insulator transition with a series-parallel circuit. (a) Representation of the nanodiamond thin films as a resistor network. Under pressure, the nanodiamond grains (blue) are interconnected by tunable resistors (red). (b) The two-channel model, i.e., a fermionic channel (${\rho }_{\mathrm{F}}$) connected in parallel with a bosonic channel (${\rho }_{\mathrm{B}}$). The intragrain resistivity (${\rho }_{\mathrm{intra}}$) and the intergrain resistivity (${\rho }_{\mathrm{inter}}$) are connected in series to describe the fermionic channel. Accordingly, the resistor network is simplified into a parallel-series circuit. (c) Magnification of the resistive superconducting transition and the insulating state fitted by the parallel-series circuit model (red curves) (curves from top to bottom: 19.2, 16.0, 12.2, 11.2, 9.2, 2.4, and 0 GPa). Inset: the fitting covers the entire temperature range of the superconducting transition.