Observation of Time-Reversal Symmetry Breaking in the Type-I Superconductor YbSb$_2$

Abstract

The spontaneous breaking of time-reversal symmetry is a hallmark of unconventional superconductivity, typically observed in type-II superconductors. Here, we report evidence of time-reversal symmetry breaking in the type-I superconductor YbSb$_2$. Zero-field $μ$SR measurements reveal spontaneous internal magnetic fields emerging just below the superconducting transition, while transverse-field $μ$SR confirms a fully gapped type-I superconducting state. Our first-principles calculations identify YbSb$_2$ as a ${\mathbb Z}_2$ topological metal hosting a Dirac nodal line near the Fermi level. Symmetry analysis within the Ginzburg Landau framework indicates an internally antisymmetric nonunitary triplet (INT) state as the most probable superconducting ground state. Calculations based on an effective low-energy model further demonstrate that this INT state hosts gapless Majorana surface modes, establishing YbSb$_2$ as a topological superconductor. Our results highlight YbSb$_2$ as a unique material platform where type-I superconductivity coexists with triplet-pairing and nontrivial topology.

Figures (3)

• Figure 1: Sample characterization and electronic band structure of YbSb$_2$: (a) Schematic of a unit cell of YbSb$_2$. (b) XRD spectrum for the single crystals. The inset shows the as-grown single crystal (left) and the Laue pattern (right). (c) Temperature-dependent specific heat data indicating $T_c$ and the normal state data fitting. Inset: Zero drop in the resistivity data showing $T_c$ at the midpoint. (d) The first Brillouin zone, including the $(1\bar{1}0)$ surface-Brillouin zone and the high symmetry directions. (e) Fermi surfaces with SOC composed of one conduction, and two valence bands. (f) Nodal line along the Z-T path of the bulk BZ representing four-fold degeneracy due to doubly-degenerate top two valence bands VB1 and VB2 near the Fermi level. (g) Electronic band structure with SOC, where SOC introduces an overall direct band gap between the conduction (red) and valence (blue) bands. (h) Bulk and surface spectral functions calculated for the $(1\bar{1}0)$ surface.
• Figure 2: Time reversal symmetry breaking and type-I superconductivity in YbSb$_2$: (a) Zero-field asymmetry spectra of YbSb$_2$, above (1.5 K) and below (0.1 K) the $T_c$, with longitudinal-field spectra at 100 G, 0.1 K, where the solid line indicates the corresponding fits. (b) Electronic relaxation rate ($\Lambda$) versus temperature indicates a significant increase below the superconducting transition temperature. Inset: The nuclear relaxation rate ($\Delta$) is almost constant with temperature. (c) The variation of 1st and 2nd principal component scores with temperature. Inset shows covariance percentage captured by different principal components. The shaded bands and dashed lines are guides to the eye. Transverse-field asymmetry spectra at 0.1 K for different applied magnetic fields (d) 20 G, (e) 40 G, and (f) 100 G. The probability distribution of the magnetic field for the respective spectra is shown in the corresponding inset, indicating different states.
• Figure 3: Nontrivial topology of the internally antisymmetric nonunitary triplet superconducting state: Surface spectral function for the internally antisymmetric nonunitary triplet state of a $\mathbb{Z}_2$ topological metal for two different values of the chemical potential (a) $\mu=0.90$ and (b) $\mu=1.2$, with $\Delta_0=0.1$ and $\mathbf{\eta}=(1/\sqrt{2})(1, e^{i\pi/4},0)$. The parameters chosen in the Hamiltonian in Eq. (\ref{['eqn:dirac_eq']}) are $b=0.5$, $v=1.0$ and $m=-0.7$. The surface states display a pronounced twisting dispersion, featuring an additional crossing away from the $\Gamma$-point that becomes more prominent with increasing $\mu$.