1. Dependence of the Superconducting Transition Temperature on the Doping Level in Single-Crystalline Diamond Films

   Homoepitaxial diamond layers doped with boron in the 1020–1021 cm-3 range are shown to be type II superconductors with sharp transitions (~ 0.2 K) at temperatures increasing from 0 to 2.1 K with boron contents. The critical concentration for the onset of superconductivity in those 001-oriented singlecrystalline films is about 5–7*1020 cm-3. The H - T phase diagram has been obtained from transport and ac-susceptibility measurements down to 300 mK.

Figure 1: Dependence of the superconducting transition temperature Tc on the boron concentration nB. The different Tc values were obtained from the onset of the diamagnetic signal (see inset for the real (solid symbols) and imaginary (open symbols) parts of the magnetic susceptibility.

E. Bustarret, J. Kačmarčík, C. Marcenat, E. Gheeraert, C. Cyetrmann, J. Marcus, T. Klein:
Dependence of the Superconducting Transition Temperature on the Doping Level in Single-Crystalline Diamond Films,
Phys. Rev. Lett. 93 (2004) 237005.

2. Tunneling spectroscopy and vortex imaging in boron-doped diamond

   Since heavily boron-doped diamond have been found to be superconductive at temperatures below 0.5 and up to 10 K, depending mainly on the boron concentration in the 0.3 to 5 at% range, relatively few experimental studies have tried to assign which pairing mechanism was involved. We report here on low temperature tunneling spectroscopy and vortex images of superconducting hole doped diamond films.
Tunneling spectroscopy performed at different locations revealed the surface to be superconducting with very little spatial inhomogeneity. In Figure 1 we show a representative differential conductance curve performed at 70 mK with a tunnel resistance of 20 MW. Most of the experimental spectra can be well reproduced by a theoretical BCS density of states as can be seen in Figure 1. The fit gives a superconducting order parameter D = 285 µeV and a thermal broadening with an effective temperature Teff = 235 mK. No additional parameters to describe pair breaking were needed. The temperature dependence of the order parameter D(T) is well described by the BCS theory with a critical temperature of 1.85 K very close to the superconducting transition temperature of 1.9 K obtained by ac susceptibility and transport measurements. This clearly demonstrates that boron-doped diamond is well described by s-wave BCS superconductivity with a measured ratio 2Δ/kTc ~ 3.48 characteristic of weak coupling, as expected from theoretical calculations.
In a magnetic field for a type II superconductor a mixed state forms where magnetic vortices each carrying one flux quantum penetrate the sample. A vortex represents a singularity with the superconducting order parameter  suppressed at its center. We have imaged the vortex arrangement by combining topography and spectroscopy measurements in a magnetic field applied perpendicular to the diamond film. Contrary to the perfect Abrikosov vortex lattice, the spatial distribution of vortices is strongly disordered even though a local hexagonal arrangement persists. In order to map the local density of states inside a vortex we acquired spectra every 0.7 nm along lines equally spaced by 2.2 nm. We obtained numerous localized resonances at nonzero energies inside the gap while crossing a vortex along different lines. More striking is the periodiclike spatial occurrence of these resonances. Such a spatial modulation appears in the theoretical clean limit, but our sample is in the dirty limit. Moreover, because of thermal smearing, quantum states would appear as a zero bias conductance peak. On the other hand, these puzzling resonances could be associated to low-lying vortex bound states shifted away from the Fermi level by the impurity potential. Then, the spatial position and the energy of these resonances would be specific to the local configuration of disorder.
In conclusion, we performed the first spectroscopic tunneling study and STM images of the vortex lattice in superconducting boron-doped diamond. Our results provide a local density of states in excellent agreement with the BCS s-wave theory with a ratio 2Δ/kTc ∼ 3.48 characteristic of a weak-coupling superconductor. Under magnetic field, vortices which are arranged in a strongly disordered triangular lattice present unexpected resonances inside the BCS gap at nonzero energies. Further investigations are needed in order to understand whether these magnetic field-induced resonances are a generic feature of any superconducting state neighboring a Anderson-Mott insulator.

Figure 2: Experimental normalized tunneling conductance measured at 70 mK (open circle). Solid lines correspond to BCS fits with Δ = 285 eV and Teff = 235 mK.

B. Sacépé, C. Chapelier, C. Marcenat, J. Kačmarčík, T. Klein and E. Bustarret:
Tunneling Spectroscopy and Vortex Imaging in Boron-Doped Diamond,
Phys. Rev. Lett. 96 (2006) 097006.

3. Metal-insulator transition and superconductivity in boron-doped diamond

   We report on a detailed analysis of the transport properties and superconducting critical temperatures of boron-doped diamond films grown along the {100} direction. The system presents a metal-insulator transition (MIT) for a boron concentration (nB) on the order of nc ∼ 4.5x1020 cm-3, in excellent agreement with numerical calculations. The temperature dependence of the conductivity and Hall effect can be well described by variable range hopping for nB <nc with a characteristic hopping temperature T0 strongly reduced due to the proximity of the MIT. All metallic samples (i.e., for nB >nc) present a superconducting transition at low temperature. The zero-temperature conductivity σ0 deduced from fits to the data above the critical temperature (T0) using a classical quantum interference formula scales as σ0≈ (nB/nc-1)ν with ν∼1. Large Tc values (> 0.4 K) have been obtained for boron concentration down to nB/nc ∼ 1.1 and Tc surprisingly mimics a (nB/nc-1)1/2 law. Those high Tc values can be explained by a slow decrease of the electron-phonon coupling parameter ? and a corresponding drop of the Coulomb pseudopotential μ* as nB→ nc.

Figure 2: (a) Conductivity extrapolated to zero temperature as a function of the boron content deduced from SIMS measurements (nB) in boron-doped diamond films. The solid line corresponds to the prediction of the scaling theory of the MIT taking ν ∼1 . (b) Critical temperature as a function of the boron content deduced from SIMS measurements (nB) in boron-doped diamond films. The solid line corresponds to Tc≈ (nB/nc-1)0.5.

T. Klein, P. Achatz, J. Kačmarčík, C. Marcenat, F. Gustafsson, J. Marcus, E. Bustarret, J. Pernot, F. Omnes, Bo E. Sernelius, C. Persson, A. Ferreira da Silva, and C. Cytermann:
Metal-insulator transition and superconductivity in boron-doped diamond,
Phys. Rev. B 75 (2007) 165313.