Indium nitride is one of the very few semiconductors which is known to have a superconducting phase at temperatures of Tc > 1 K. Superconductivity occurs in a window of carrier densities of approximately  1018–1020 cm−3. This is a very low density when compared to other superconductors (i.e. metals, alloys, high Tc oxides) and thus raises interesting fundamental questions as well as technological possibilities. In this paper we address one key question about the dimensionality of the superconducting state of InN by using angle dependent critical field measurements. Our samples were grown by two different growth techniques (chemical vapour deposition and plasma-assisted molecular beam epitaxy) on c-oriented sapphire, with and without a GaN buffer layer. In both cases we find that for film thicknesses much larger than the coherence length d ≫ ξ, the angle dependence of the critical field (down to T < 280 mK) with respect to the c-axis continues to be clearly two-dimensional, demonstrating a characteristic cusp when the angle crosses 90° with respect to the c-axis. This indicates that the superconducting electrons are most likely confined to a layer much thinner than the thickness of the InN film. Further we find the magnitude of the gap to be 2Δ(0)/kBTc = 3.6, very close to the BCS prediction.

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Small changes in electrical conductance of quasi-2 dimensional samples often need to be measured at low temperatures, T∼1K and lower. Care needs to be taken to minimize self-heating due to the excitation current itself and the possibility of any unexpected source of variation of the electrochemical potential around the contacts need to be understood. It is not only the low resistance of the ohmic contacts but also their “noninvasive” character that must be ensured. While the importance of the “noninvasiveness” of the voltage probes is well appreciated for mesoscopic devices—it turns out that these considerations continue to remain important even in macroscopic samples that are a few millimeters in size. We have done low temperature measurements on different types of gallium nitride samples with contacts made of pure indium (popularly called indium dots), which have a superconducting transition and contacts made of Ti/Au, which remain nonsuperconducting. We show that there are qualitative differences in the measured four-terminal resistance in the two cases. Obviously, correct conclusions about phase relaxation times, localization lengths, etc., will require ensuring that there are no effects arising from the “invasiveness” of the probes.

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A scale for magnetic field resilience of a superconductor is set by the paramagnetic limit. Comparing the condensation energy of the Bardeen–Cooper–Schrieffer (BCS) singlet ground state with the paramagnetically polarized state suggests that for an applied field [Formula: see text] (in SI), singlet pairing is not energetically favorable. Materials exceeding or approaching this limit are interesting from fundamental and technological perspectives. This may be a potential indicator of triplet superconductivity, Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) pairing, and other mechanisms involving topological aspects of surface states and may also allow Cooper pair injection at high magnetic fields. We have analyzed the microscopic composition of such a material arising from an unexpected source. A microjet of an organo-metallic gas, [Formula: see text], can be decomposed by a gallium ion-beam, leaving behind a track of complex residue of gallium, tungsten, and carbon with remarkable superconducting properties, like an upper critical field, [Formula: see text], above its paramagnetic limit. We carried out atomic probe tomography to establish the formation of nano-crystalline tungsten carbide (WC) in the tracks and the absence of free tungsten. Supporting calculations show that for Ga distributed on the surface of WC, its s,p-orbitals enhance the density of states near the Fermi energy. The observed variation of [Formula: see text] does not show features typical of enhancement of critical field due to granularity. Our observations may be significant in the context of some recent theoretical calculation of the band structure of WC and experimental observation of superconductivity in a WC-metal interface.