Large variation in superconducting transition temperature in the ${\mathrm{Nb}}_x{\mathrm{Bi}}_{2-x}{\mathrm{Se}}_3$ system

Samples synthesized as Nb substituted onto Bi sites from the nominal composition of ${\mathrm{Nb}}_x{\mathrm{Bi}}_{2-x}{\mathrm{Se}}_3$ resulted in superconducting critical temperatures ( $T_c$ 's) in transport measurements reaching 5.6 K and 5.4 K, for $x$ = 0.2 and 0.25, respectively. All, significantly higher than reported in earlier studies of compositions aiming at Nb intercalation ${\mathrm{Nb}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$. Bulk susceptibility showed lower responses for powders with a large variety, including $T_c$ 's ranging from 1.8 K to 4.5 K. Magnetotransport experiments were conducted with angular dependence at the High Field Magnet Laboratory (HFML). Clear Shubnikov–de Haas oscillations were observed in all substituted samples, and a thorough study of the angular dependence of the Shubnikov–de Haas frequencies is presented together with estimates of the Fermi energy ($E_F$). All samples contain the phases of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ and the misfit compound $({\mathrm{BiSe})}_{1.1}{\mathrm{NbSe}}_2$. However, only some areas of the crystal boules contain the third phase of BiSe, and the calculated niobium contents from the nominal composition and the results from the phase analysis show large variations. The results obtained on these substituted samples are compared to the more studied Nb-doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ stoichiometry, thereby giving further insight into this system currently under high interest.

Figure 1

Resistivity as a function of temperature of (a) S3-B with high $T_c$ of 5.6 K, inset is the full range from 300 K to 4.2 K. (b) The three crystals from S2-C, S3-B, and S4-C. (c) Zoom-in on the transition in S2-C. (d) Lastly, the scan for the S5-B crystal.

Figure 1

Resistivity as a function of temperature of (a) S3-B with high $T_c$ of 5.6 K, inset is the full range from 300 K to 4.2 K. (b) The three crystals from S2-C, S3-B, and S4-C. (c) Zoom-in on the transition in S2-C. (d) Lastly, the scan for the S5-B crystal.

Figure 2

Differential Hall resistivity -$\mathrm{d}{\rho }_{yx}$/dB vs magnetic field B(T) for the three crystals, (a) S2-C, (b) S3-B, and (c) S4-D. (d) The FFT amplitude of the SdH oscillations at 1.4 K (B-field interval between 12 T and 30 T), with frequencies of crystals oscillations detected to be 153 T, 161 T, and 210 T, respectively. (e) Angular dependence of the differential longitudinal resistivity of S2-C at 1.4 K, with $\theta$ from zero to ${90}^{\circ }$.

Figure 2

Differential Hall resistivity -$\mathrm{d}{\rho }_{yx}$/dB vs magnetic field B(T) for the three crystals, (a) S2-C, (b) S3-B, and (c) S4-D. (d) The FFT amplitude of the SdH oscillations at 1.4 K (B-field interval between 12 T and 30 T), with frequencies of crystals oscillations detected to be 153 T, 161 T, and 210 T, respectively. (e) Angular dependence of the differential longitudinal resistivity of S2-C at 1.4 K, with $\theta$ from zero to ${90}^{\circ }$.

Figure 3

(a) Angular dependence of SdH frequencies at 1.4 K for S2-C, S3-B, and S4-C. [The same color scheme is used for all plots, but only shown in (a).] (b) The extraction of the Dingle temperature ($T_D$) from the SdH amplitudes, 1/B. (c) The effective mass ($m$*) for three samples was calculated from the normalized FFT (fast Fourier transform) amplitude as a function of temperature (in the range $B$ = 21–30 T).

Figure 3

(a) Angular dependence of SdH frequencies at 1.4 K for S2-C, S3-B, and S4-C. [The same color scheme is used for all plots, but only shown in (a).] (b) The extraction of the Dingle temperature ($T_D$) from the SdH amplitudes, 1/B. (c) The effective mass ($m$*) for three samples was calculated from the normalized FFT (fast Fourier transform) amplitude as a function of temperature (in the range $B$ = 21–30 T).

Figure 4

An estimate of the Fermi energy (assuming a spherical Fermi surface) using the Hall data and SdH frequencies for four samples.

Figure 5

Susceptibility measurements as ZFC with a magnetic field of 10 Oe on selected areas for the five samples (S1–S5). The inset shows zoom-in on the S1–S3 superconducting transitions.

Figure 6

(a) Pictures and illustrations of the crystal ingots of S2 and S5. (b) The powder x-ray diffraction pattern of the areas in S2 and S5. (c) Selected reflection peak positions for the three different phases known for this system, as indicated by their (hkl) indices. (d) The final results from the phase content analysis, with the amount of the different phases present in the sample areas, with ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ (gray), BiSe (red), and “misfit” indicating the misfit layer compound (${\mathrm{BiSe})}_{1.1}{\mathrm{NbSe}}_2$ (blue).

Figure 7

Final results from the phase content analysis, with the amount of the different phases present in the different sample areas, with ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ (gray), “misfit” indicating the misfit compound (${\mathrm{BiSe})}_{1.1}{\mathrm{NbSe}}_2$ (blue) and BiSe (red).

Figure 8

(a) Seebeck measurements on samples S2–S5 with potential Seebeck microprobe (PSM), with the crystals shown next to the resulting scan, the area indicated on each. On S5, there are indications of the “top” and “tip” regions of the crystal boule. (b) The histogram for each sample for comparison.