Spin-Depairing-Induced Exceptional Fermionic Superfluidity

Abstract

We investigate the non-Hermitian (NH) attractive Hubbard model with spin depairing, which is a spin-resolved asymmetric hopping that nonreciprocally operates spins in the opposite direction. We find that spin depairing stabilizes a superfluid state unique to the NH system. This phase is characterized not only by a finite order parameter, but also by the emergence of exceptional points (EPs) in the momentum space - a feature that starkly contrasts with previously discussed NH fermionic superfluidity, where EPs are absent within the superfluid state and emerge only at the onset of the superfluid breakdown. We uncover the rich mechanism underlying this ``exceptional fermionic superfluidity'' by analyzing the interplay between EPs and the effective density of states of the complex energy dispersion. Furthermore, we reveal that the exceptional superfluid state breaks down induced by strong spin depairing on the cubic lattice, while it remains robust on the square lattice.

Figures (8)

• Figure 1: Phase diagrams of the attractive Hubbard model with spin depairing on (a) cubic and (b) square lattices. $\gamma$ and $U$ stand for the rate of spin depairing and the strength of attraction, respectively. Spin depairing induces a stable exceptional superfluid state, which is not realized in the Hubbard model with two-body dissipation discussed in previous studies yamamoto19. The corresponding phase diagrams for the model with two-body dissipation $\gamma_2$ on the cubic and square lattices are shown in (c) and (d), respectively footnote.
• Figure 2: Spin-resolved asymmetric hopping (spin depairing) given in Eq. \ref{['sdBCS_effNHHamiltonian_eq']}. The hopping amplitude of the fermion with an up spin along the positive (negative) $x,y,z$ directions is described by $-t(1+\gamma)$ [$-t(1-\gamma)$]. In contrast, the hopping amplitude for down-spin fermions is the opposite of that for the up-spin fermions.
• Figure 3: (a) [(c)] Contour plot of the effective DOS \ref{['sdBCS_eff_DOS_def_eq']} on the cubic (square) lattice for $\gamma=1$. Blue region indicates the effective DOS being zero. (b)[(d)] Cross section of the effective DOS.
• Figure 4: (a) Normalized order parameter and (b) condensation energy for the NH system with the constant effective DOS. Exceptional SF is realized in the green shaded area.
• Figure 5: Numerical results for the NH system on the cubic lattice with $\gamma=0.5$. (a) Order parameter $\Delta_{0}$ as a function of the attraction $U$. Exceptional SF is realized in the green shaded area, where EPs appear at $\epsilon=\pm i\Delta_0$. (b) Contour plot of the effective DOS \ref{['sdBCS_eff_DOS_def_eq']} and (c) its cross section at $\mathrm{Re}\epsilon=0$. The marks in (b) and (c) stand for the points $\mathrm{Im}\epsilon=i\Delta_0$ at $\mathrm{Re}\epsilon=0$ by using the corresponding value of $\Delta_0$ shown in (a). (d) Exceptional lines in the momentum space when $U=5.57$ and $7.02$.