Superconducting ground state of the topological superconducting candidates ${\mathrm{Ti}}_{3}X$ ($X=\mathrm{Ir},\mathrm{Sb}$)

The topologically nontrivial band structure of A15 compounds has drawn a significant amount of attention owing to the possible realization of topological superconductivity. The superconducting ground state of the A15 alloys ${\mathrm{Ti}}_{3}X$ ($X=\mathrm{Ir},\mathrm{Sb}$), by muon spectroscopy, has been investigated. Zero-field muon spin relaxation measurements have shown that time-reversal symmetry is preserved in these materials. Furthermore, specific-heat and transverse-field muon rotation measurements rule out any possibility of a nodal or anisotropic superconducting gap but reveal a conventional isotropic $s$-wave gap structure. This supports the idea that these A15 superconductors are time-reversal-symmetry-preserved topological superconducting candidate compounds.

Figure 1

Powder XRD pattern for (a) ${\mathrm{Ti}}_3\mathrm{Ir}$ and (b) ${\mathrm{Ti}}_3\mathrm{Sb}$. The greenish circles and the solid black lines correspond to the experimental data (obs) and the calculated pattern (calc), respectively. The red vertical bars give the Bragg positions, whereas the blue lines at the bottom of the plots display the difference between the observed and calculated patterns.

Figure 2

The temperature dependence of the magnetic susceptibility at 10-mT applied field showing the superconducting transition temperature for (a) ${\mathrm{Ti}}_3\mathrm{Ir}$ and (b) ${\mathrm{Ti}}_3\mathrm{Sb}$. ZFCW, zero-field-cooled warming.

Figure 3

(a) Variation of magnetization with the external field at different temperatures. (b) Temperature dependence of the lower critical field $H_{C1}$; the curves are fits to the data using the Ginzburg-Landau relation.

Figure 4

The temperature dependence of $H_{C2}$ for (a) ${\mathrm{Ti}}_3\mathrm{Ir}$ and (b) ${\mathrm{Ti}}_3\mathrm{Sb}$. The curves are fits to the data using the GL formula. The insets show the magnetization as a function of temperature for various applied magnetic fields. Here, mag and sp, magnetization and specific-heat measurements, respectively.

Figure 5

The variation of $C/T$ with $T^2$ in zero field, where the pronounced jump in the data indicates the superconducting transition. The dashed lines are the fits to the normal-state data (i.e., $T>T_C$).

Figure 6

(a) The specific-heat data in the superconducting region fitted for a single-gap $s$-wave model. (b) The field dependence of the Sommerfeld constant $\gamma$ is plotted after normalizing by ${\gamma }_n$ and $H_{C2}$(0), and the data are clearly best described by straight lines.

Figure 7

TF-$\mu \mathrm{SR}$ spectra above and below $T_C$ at 30 mT for (a) ${\mathrm{Ti}}_3\mathrm{Ir}$ and (b) ${\mathrm{Ti}}_3\mathrm{Sb}$. The spectra below $T_C$ decays faster for both samples indicating vortex formation. (c) and (d) Temperature dependence of the variation of depolarization across the flux-line lattice. The solid curves are the fits to the $s$-wave model in the dirty limit.

Figure 8

ZF-$\mu \mathrm{SR}$ spectra above and below $T_C$ for (a) ${\mathrm{Ti}}_3\mathrm{Ir}$ and (b) ${\mathrm{Ti}}_3\mathrm{Sb}$. The solid red curves are the fits to the static Kubo-Toyabe function times exponential decay for above the transition temperature. The insets show no significant change in fit parameters.

Figure 9

Uemura plot placing ${\mathrm{Ti}}_{3}X$ ($X=\mathrm{Ir}$, Sb) along with some other unconventional superconducting alloys and compounds. HTSC, high-temperature superconductor.