Phonon softening in superconducting diamond

We observe strong softening of optical-phonon modes in superconducting $(T_c=4.2\mathrm{K})$ boron-doped diamond near the Brillouin-zone center using inelastic x-ray scattering from a chemical vapor deposition grown highly oriented sample. The magnitude of the softening, and our observation that it becomes stronger approaching zone center, supports theoretical models suggesting a phonon-mediated pairing mechanism via coupling of optical-phonon modes to Fermi surfaces around the zone center. The electron-phonon coupling parameter is determined as approximately $\lambda =0.33$.

Figure 1

(Color online) (a) Schematic view of the $\sim 100\text{−}\mu \mathrm{m}$-thick B-doped sample B. (b) Temperature-dependent resistance curve. Above $T_c$ the resistance is almost flat with a room-temperature resistivity of $\sim 15\Omega \mathrm{cm}$. (c) X-ray rocking curves of the (004) reflection of sample B (엯) and undoped sample N (▵).

Figure 2

(Color online) IXS spectra from undoped sample N (▿) and sample B (엯) for momentum transfer along the [001] direction $\Gamma \text{−}X$ [(a) and (b)] and the [111] direction $\Gamma \text{−}L$ [(c) and (d)] in a geometry where only longitudinal phonons contribute, as well as at $Q=\left(0.51.50.5\right)$ (e) where mostly transverse phonons contribute. The total momentum transfer $Q$ is indicated for each pair of spectra in relative lattice units. The peak position and width at half height is indicated.

Figure 3

(Color online) (a) Dispersion of the optical phonons in samples N (▿) and B (엯) as determined by the peak positions as shown in Fig. 2. On the left-hand side the $\Gamma \text{−}L$ and on the right-hand side the $\Gamma \text{−}X$ direction is shown. Most data are from the LO phonons, but on the left-hand side at $L$ the TO phonons are also indicated. (b) Softening curve: peak shift for sample B with respect to sample N as a function of momentum. (c) Momentum-dependent EPC parameter $\lambda \left(q\right)$ as determined by Eq. (1).