Quantitative theory of triplet pairing in the unconventional superconductor ${\mathrm{LaNiGa}}_2$

The exceptionally low-symmetry crystal structures of the time-reversal symmetry-breaking superconductors ${\mathrm{LaNiC}}_2$ and ${\mathrm{LaNiGa}}_2$ lead to an internally antisymmetric nonunitary triplet state as the only possibility compatible with experiments. We argue that this state has a distinct signature: a double-peak structure in the density of states (DOS) which resolves in the spin channel in a particular way. We construct a detailed model of ${\mathrm{LaNiGa}}_2$ capturing its electronic band structure and magnetic properties ab initio. The pairing mechanism is described via a single adjustable parameter. The latter is fixed by the critical temperature $T_c$ allowing parameter-free predictions. We compute the electronic specific heat and find excellent agreement with experiment. The size of the ordered moment in the superconducting state is compatible with zero-field muon spin relaxation experiments and the predicted spin-resolved DOS suggests the spin splitting is within the reach of present experimental technology.

Figure 1

Properties of quasiparticles in the INT state with $s=0.05, \delta =0.075, |{\mathrm{\Delta }}_0|=1$, and $\left|\mathit{q}\right|=\sqrt{2/3}$ in arbitrary units. (a) Quasiparticle spectrum for the $+$ and $-$ bands for $\uparrow$ and $\downarrow$ spins. (b) and (c) show the corresponding DOS calculated from this spectrum using the same parameters. The DOS features have been artificially broadened by convolution with a Gaussian of width $\sigma =0.07$ in (b) and $\sigma =0.025$ in (c).

Figure 2

Superconducting phase diagram of the toy model in Eq. (6). $T_c$ is the critical temperature where interorbital, equal-spin pairing sets in. Each curve shows the dependence of $T_c$ on the interaction strength $U$ for a different value of the band splitting $2s$, as indicated. The inset shows the temperature dependence of the pairing amplitude ${\mathrm{\Delta }}_0$ for the largest splitting $s/t=0.1$ and a few values of $U$ just above the critical value $U_c$ at which $T_c$ becomes finite.

Figure 3

Properties of the superconducting ground state corresponding to a phenomenological interorbital equal-spin pairing interaction between the ($d_{z^2}-d_{xy}$) orbitals in the $3d$ sector of the Ni atom in ${\mathrm{LaNiGa}}_2$. (a) Variation of the specific heat with temperature ($\gamma$ is the Sommerfeld coefficient). We note an excellent agreement between the theoretical result and the experimental data taken from Ref. [11]. (b) Variation of the spontaneous magnetic moment (${\mu }_s$) as a function of temperature. A clear increase in the magnetic moment below $T_c$ is an indication of the imbalance between two spin species due to migration of Cooper pairs. (c) Spin-resolved density of states (arbitrary units) of the Bogoliubov quasiparticles as a function of energy. We note that the two coherence peaks correspond to up and down species of Cooper pairs leading to two gaps in the quasiparticle spectrum.