Temperature-Dependent Localized Excitations of Doped Carriers in Superconducting Diamond

Laser-excited photoemission spectroscopy is used to show that the doped carriers in metallic or superconducting diamond couple strongly to the lattice via high-energy ($\sim 150\mathrm{meV}$) optical phonons, with direct observations of localized Franck-Condon multiphonon sidebands appearing as Fermi-edge replicas. It exhibits a temperature-dependent spectral weight transfer from higher to lower energy sidebands and zero-phonon Fermi-edge states. The quantified coupling strength shows a systematic increase on lowering temperature, implicating its relation to the normal state transport and superconductivity.

Figure 1

(a) is a schematic of adiabatic potential curves with quantized phonon levels, for the initial and final (ionized) states. The PES spectral intensity from this model shows characteristic sidebands obeying the Franck-Condon factor, i.e., Poisson distribution [17], shown by blue (black) bars in (b). Here, $b$ is the $e\mathrm{\text{−}}\mathrm{ph}$ coupling parameter, corresponding to the number of phonons that can compensate the relaxation energy, $b{\omega }_0$. The “0-0” peak (zero-phonon line) at $E_k=E_0$ corresponds to a transition between the equilibrium states of the initial (e.g., ${\mathrm{H}}_2$) and of the final (e.g., ${\mathrm{H}}_2^{+}$) state system, where as the sidebands at $E_k=E_0-n{\omega }_0$ reflect the transitions to vibrationally excited states. A light blue (gray) shaded area shows the envelope of the Poisson distribution.

Figure 2

The PES results showing the doping dependence of electronic structure for BDD1-4. Near-$E_F$ region for BDD1-BDD3 is magnified in the upper part. The inset shows the intensity at $E_F$ of PES normalized at 0.6 eV, as a function of $n_B$. I, M, and SC stand for insulator, metal, and superconducting phases as the ground state, respectively.

Figure 3

The raw PES is shown in (a), while (b) shows the $E_B$ derivative of PES. The solid (broken) curves in (b) indicate the fitting function (background) for respective $T$. The bars in (a) indicate the sideband intensities $S_n$, obtained by the analysis on the $E_B$-derivative curves in (b).

Figure 4

(a) $T$ dependence of sideband intensities $S_n$ obtained by the analysis on BDD4. The broken curves are guides for eyes to show the envelope of the Poisson distribution. (b) shows the $T$ dependence of the $e\mathrm{\text{−}}\mathrm{ph}$ coupling factor $b$.