Absence of superconductivity in micrometer-sized $\varepsilon$-NbN single crystals

It is important to study the properties of high quality single crystal in order to resolve the issue of an interesting material in which certain debatable fundamental properties exist. However, it is unfortunate that a sizable single crystal for experimental measurements is not always available. NbN is one of the examples; it has attracted scientific and engineering interest due to its diverse physical properties and a variety of structural phases. Until now superconductivity is only observed in cubic $\delta$- and tetragonal $\gamma$-NbN but not in hexagonal $\varepsilon$-NbN. Recently, Zou et al. reported the observation of superconductivity with $T_c\sim 11.6\mathrm{K}$ in a hexagonal $\varepsilon$-NbN based on the measurement on a multiphase powder specimen. In order to resolve the issue, the work used the electron backscattering diffraction technique to characterize phases of micron-size NbN crystals from commercial powders and measure their transport properties. Our results unambiguously confirm that the hexagonal $\varepsilon$-NbN phase is not superconducting.

Figure 1

Powder x-ray diffraction patterns and Rietveld refinement. (a) A pure cubic $\delta$-NbN powder (from Alfa Aesar, after postannealing) (ICSD no. 98-008-9860). (b) A main phase of $\varepsilon$-NbN powder with wt % of various phases (from Goodfellow); impurity phases are represented by symbols * and •.

Figure 2

The zero-field cooling (ZFC) magnetic susceptibility for the cubic $\delta$-NbN and the major hexagonal $\varepsilon$-NbN powder at a constant field 10 Oe.

Figure 3

(a) Temperature dependence of specific heat for cubic $\delta$-NbN at different magnetic fields. Inset: $C/T$ versus $T^2$ fit. (b) Temperature dependence of electronic specific heat in superconducting state, $C_{es}$. The red dashed line is fitting of BCS theory.

Figure 4

(a) Temperature dependence of specific data of the major phase $\varepsilon$-NbN powder at 0 and 8 T, plotted as $C/T$ versus $T^2$. (b) The specific heat of superconducting state is fitted to the 12% tetragonal $\gamma$-NbN with $T_c$ of 6.8 K and 7% cubic $\delta$-NbN with $T_c$ of 13.7 K.

Figure 5

(a) The SEM image of the whole specimen for the cubic $\delta$-NbN crystal. The part enclosed by the yellow frame was taken for RT measurements. (b) EBSD phase mapping of the whole specimen. Pink color represents the $\delta$-NbN phase; although the orange color is assigned to represent tetragonal $\gamma$-NbN, it is believed to be misjudged by the roughness near sample edge since EBSD result is very sensitive to the surface flatness. The yellow color represents ${\delta }^{\prime }$-NbN and the red color represents $\varepsilon$-NbN; both of them are less than 2% which is in the range of measurement resolution. Panels (c) and (d) represent the measurement of crystal orientation by exam of pole figures, while (c) presents inverse pole figure mapping of the scanning plane close to the lattice plane (101) and (d) the reproduced pole figures for lattice plane {100}, {110}, and {111}. (e), (f) The in situ SEM EDX mapping for N-$K_{\alpha }$ and Nb-$L_{\alpha }$ lines of the crystal. (g) The overlapping of Kikuchi pattern and EBSD pattern of the crystal.

Figure 6

(a) The image of the cubic $\delta$-NbN crystal loaded on an electrical measurement platform. (b) A drawing of parallel electrodes at the center of the platform. (c) Temperature dependence of electrical resistance for the cubic $\delta$-NbN crystal with $50\times 30\mu \mathrm{m}$ in size. The black and red curves represent different measurements using different pairs of electrodes for voltage measurement; one has 8 μm and the other has 18 μm in separation. A minor phase of cubic NbN with even higher nitrogen deficiency was revealed in a second drop at $T\sim 10\mathrm{K}$ for measurements with two different set of electrodes. Due to the interference of first drop the real $T_c$ of the second drop is estimated to be $>10\mathrm{K}$.

Figure 7

(a) Temperature dependence of electrical resistivity of the cubic $\delta$-NbN crystal under magnetic fields 0, 1, 2, 3, 5, 7, and 9 T. (b) Upper critical field as a function of temperature. The $T_c$ is determined from the resistivity at 90% drop from the normal state value.

Figure 8

(a) The SEM image of the hexagonal $\varepsilon$-NbN crystal. (b) EBSD phase mapping of the specimen. Red color area represents $\varepsilon$-NbN phase; a tiny pink area is believed the unevenness near sample edge. (c) Inverse pole figure mapping of the lattice plane (001). Inverse pole figure mapping for crystal structural orientation. The red color indicates the sample surface is close to (001) plane as shown in the bottom color map. (d) The reproduced pole figures for lattice plane {0001} and {10-10}. Panels (e) and (f) are the in situ SEM EDX mapping for N-$K_{\alpha }$ and Nb-$L_{\alpha }$ lines respectively of the crystal. (g) The overlapping of Kikuchi pattern and EBSD pattern of the hexagonal $\varepsilon$-NbN phase.

Figure 9

(a) The SEM image of the $\varepsilon$-NbN crystal with four electrodes for electrical resistance measurements. (b) Temperature dependence of electrical resistance of the $\varepsilon$-NbN crystal; no superconductivity was discovered. (c) Temperature dependence of electrical resistance of the $\varepsilon$-NbN crystal in 0 and 1 T at low temperatures.