Absence of time-reversal symmetry breaking in the noncentrosymmetric superconductor ${\mathrm{Mo}}_3{\mathrm{Al}}_2\mathrm{C}$

Zero-field muon spin rotation and relaxation $\left(\mu \mathrm{SR}\right)$ studies carried out on the strongly coupled, noncentrosymmetric superconductor ${\mathrm{Mo}}_3{\mathrm{Al}}_2\mathrm{C},T_c=9$ K, did not reveal hints of time-reversal symmetry breaking as was found for a number of other noncentrosymmetric systems. Transverse field measurements performed above and below the superconducting transition temperature defined the temperature dependent London penetration depth, which in turn served to derive from a microscopic point of view a simple $s$-wave superconducting state in ${\mathrm{Mo}}_3{\mathrm{Al}}_2\mathrm{C}$. The present investigations also provide fairly solid grounds to conclude that time-reversal symmetry breaking is not an immanent feature of noncentrosymmetric superconductors.

Figure 1

Low temperature behavior of the heat capacity $C_p$ of ${\mathrm{Mo}}_3{\mathrm{Al}}_2\mathrm{C}$ plotted as $C_p/T$ vs $T$ (referring to the left axis) and of the magnetic susceptibility $\chi$ (zero-field cooling, right axis). The solid line comprises the heat capacity of an $s$-wave superconductor in the weak coupling regime. The dashed line is a fit as explained in the text.

Figure 2

$\mu \mathrm{SR}$ zero field spectra of ${\mathrm{Mo}}_3{\mathrm{Al}}_2\mathrm{C}$ measured at $T=1.7$ and 15 K, respectively. The solid lines are least squares fits according to the static Kubo-Toyabe formula, Eq. (1).

Figure 3

Zero-field muon depolarization rate ${\sigma }_{KT}$ of ${\mathrm{Mo}}_3{\mathrm{Al}}_2\mathrm{C}$.

Figure 4

$\mu \mathrm{SR}$ transverse field spectra of ${\mathrm{Mo}}_3{\mathrm{Al}}_2\mathrm{C}$ at external magnetic fields ${\mu }_{0}H=150$ Oe for temperatures below (a) and above (b) the superconducting phase transition $T_c=9$ K. The solid lines are least squares fits according to Eq. (2).

Figure 5

Temperature dependent muon spin relaxation rate $\sigma$ of ${\mathrm{Mo}}_3{\mathrm{Al}}_2\mathrm{C}$.

Figure 6

Temperature dependent penetration depth $\lambda$ of ${\mathrm{Mo}}_3{\mathrm{Al}}_2\mathrm{C}$ plotted as ${\lambda }^{-2}$ vs $T$. The solid line is a least-squares fit according to an $s$-wave BCS model.