Low-Energy Electrodynamics of Superconducting Diamond

Abstract

Boron-doped diamond films can become superconducting with critical temperatures Tc well above 4 K. Here we first measure the reflectivity of such a film down to 5 cm −1 , by also using Coherent Synchrotron Radiation. We thus determine the optical gap 2∆, the field penetration depth λ, the range of action of the Ferrell-Glover-Tinkham sum rule, and the electron-phonon spectral function α 2 F (ω). We conclude that diamond behaves as a "dirty" BCS superconductor.PACS numbers: 74.78. Db, Diamond, with its extraordinary mechanical properties, excellent thermal conductivity, and large gap between the valence and the conduction band, is potentially a semiconductor more attractive than silicon for many applications. Therefore the transport properties of diamond films, deposited by Chemical Vapor Deposition (CVD), and doped by acceptors or donors, are being extensively explored in view of a possible, future diamondbased electronics. In this framework it has been discovered recently that heavily boron-doped diamond can also become a superconductor [1] below critical temperatures T c well above the liquid helium temperature [2], if the doping level is 2.5%.Strongly covalent bonds, high concentration of impurities, and high phonon frequencies make B-doped diamond much different from the conventional metals where the Bardeen-Cooper-Schrieffer (BCS) [3] theory of superconductivity holds. Indeed, the metallic properties of heavily B-doped diamond are now the subject of an intense theoretical investigation. If many authors suggest that B-doped diamond in the doping regime above ∼ 0.5% should be a degenerate metal [4,5], with a conduction band strongly broadened by disorder, others point out that the deep 0.37 eV level of the isolated Bacceptor [6] may prevent the merging of the B-like bands with the C valence band, and propose unconventional models for the metallization of diamond [7]. One thus may wonder whether diamond is anyhow a BCS material, eventually with a high degree of disorder, or an exotic superconductor like most of those discovered in the last two decades. The study of the electron-phonon interaction in metallic diamond, a likely candidate for the Cooper pairing mechanism, has also attracted considerable attention, since the high phonon frequencies make the adiabatic limit questionable and the covalent bonds may produce a very strong coupling costant, like in MgB 2 [8, 9]. Here we approach both this problems by first measuring the reflectivity of a superconducting diamond film, in the sub-Terahertz region down to 5 cm −1 where the gaps of superconductors are observed, and in the infrared region, where the signatures of the electron-phonon coupling appear. The sub-Terahertz frequencies have been reached, with the required signal-to-noise ratio, by use of Coherent Synchrotron Radiation.A basic feature of the superconducting state is the opening, for T < T c , of a gap E g in the electronic density of states. Correspondingly, if the Cooper pairs are in a spherically symmetric s state, the reflectivity becomes R s (ω)...

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“…[14,15] The R(ω) curve at 10 K is almost flat below 150 cm −1 (18 meV), thus being very similar to the lineshape for a s-wave superconductor. However, above this frequency R(ω) develops a downward curvature, and its magnitude becomes slightly lower than unity, suggesting that week absorption already exists.…”

Superconducting group-IV semiconductors

“…On the other hand, SC calculations for diamond [45][46][47] lead to a spectral distribution of the electron-phonon coupling parameter with a major contribution from the dopant-related stretching mode. A Kramers-Kronig analysis of reflectivity measurements [60] supports a possible contribution of boron-related vibrational modes. However, the experimental identification is difficult as the B-C stretching modes frequencies lie in the continuum of bulk diamond modes.…”

Selected topics related to the transport and superconductivity in boron-doped diamond

“…The main stream is represented by various modifications of classical Bardeen-Cooper-Schrieffer (BCS) theory based on phonon-mediated pairing [22][23][24][25][26][27][28][29]. A review discussing this theory both for BDD and for other semiconductors can be found in [30].…”