Altermagnetism-driven FFLO superconductivity in finite-filling 2D lattices

TL;DR

Altermagnetism can induce finite-momentum FFLO superconductivity in a finite-filling 2D square lattice with on-site attraction $U<0$. The authors combine a non-self-consistent $T$-matrix (Thouless) analysis in the normal state with Bogoliubov–de Gennes mean-field theory to map out the FFLO regions for two distinct $d$-wave altermagnetic orders, including next-nearest-neighbor hopping to shift the Van Hove singularity. They find that $d_{xy}$-wave altermagnetism stabilizes FFLO over a broad low-filling range, while $d_{x^2-y^2}$-wave altermagnetism produces FFLO only at high filling within a narrow window; Van Hove singularities tend to suppress FFLO in both cases. The results highlight how band structure and the symmetry of altermagnetic spin splitting jointly control finite-momentum pairing and offer guidance for experimental search in real materials with complex electronic structures.

Abstract

We systematically investigate the emergence of finite-momentum Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductivity in a square lattice Hubbard model with finite filling, driven by either $d_{xy}$-wave or $d_{x^{2}-y^{2}}$-wave altermagnetic order in the presence of on-site $s$-wave attractive interactions. Our study combines mean-field calculation in the superconducting phase with pairing instability analysis of the normal state, incorporating the next-nearest-neighbor hopping in the single-particle dispersion relation. We demonstrate that the two types of altermagnetism have markedly different impacts on the stabilization of FFLO states. Specifically, $d_{xy}$-wave altermagnetism supports FFLO superconductivity over a broad parameter regime at low fillings, whereas $d_{x^{2}-y^{2}}$-wave altermagnetism only induces FFLO pairing in a narrow range at high fillings. Furthermore, we find that the presence of a Van Hove singularity in the density of states tends to suppress FFLO superconductivity. These findings may provide guidance for experimental exploration of altermagnetism-induced FFLO states in real materials with more complex electronic structures.

Figures (11)

• Figure 1: Diagrammatic representation of the two-particle vertex function $\Gamma(\mathbf{k},\mathbf{k}';\mathbf{q},\omega)$, within the ladder approximation.
• Figure 2: (a) The inverse vertex function at zero frequency $\Gamma^{-1}(\mathbf{q},\omega=0)$, in units of $t^{-1}$, in the $q_{x}$-$q_{y}$ plane at the altermagnetic coupling $\lambda=2t$. The inverse vertex function reaches maximum at $(q_{x},q_{y})=(\pm q,0)$ or $(0,\pm q)$, where $q=\left|\mathbf{q}\right|$. (b) $\Gamma^{-1}(q_{x},q_{y}=0;\omega=0)$ at different altermagnetic couplings $\lambda$ as indicated. Here, we consider the $d_{xy}$-wave altermagnetism and take an attraction strength $U=-3t$ at the filling factor $\nu=1.0$. We have taken a negligible temperature $T=0.01t$ to smooth the sharp Fermi surface and to increase numerical accuracy.
• Figure 3: The contour plots of the thermodynamic potential $(\Omega-\Omega_{0})/(\nu t)$, as functions of the pairing amplitude $\Delta$ and the FFLO momentum $q_{x}$, at three altermagnetic coupling strengths: $\lambda=0.8t$ (a), $\lambda=1.0t$ (b) and $\lambda=1.2t$ (c). The chemical potential in each plot is, $\mu=2.05t$ (a), $\mu=1.98t$ (b) and $\mu=1.91t$ (c). The green dots indicate the stable or unstable BCS states, while the orange dots highlight the FFLO state. Here, we consider the $d_{xy}$-wave altermagnetism and take an attraction strength $U=-3t$ at the filling factor $\nu=1.0$.
• Figure 4: (a) The second derivative $\partial^{2}\Omega/\partial q_{x}^{2}$ of the BCS state as a function of $\lambda$. It becomes negative at $\lambda_{\textrm{FFLO}}\simeq0.87t$, where the FFLO state starts to emerge. (b) The pairing gaps of the BCS state (solid line) and of the FFLO state (colored dots) as a function of the altermagnetic coupling strength $\lambda$. The color of the dots shows the values of the FF momentum $q_{x}$, following the color map. Here, we consider the $d_{xy}$-wave altermagnetism and take an attraction strength $U=-3t$ at the filling factor $\nu=1.0$.
• Figure 5: The phase diagram under the $d_{xy}$-wave altermagnetism, as functions of the filling factor $\nu$ and the altermagnetic coupling strength $\lambda$. The transition from the BCS state to the FFLO state is shown by the red dashed line, while the transition from the FFLO state to the normal state is shown by the black solid line. The three phases meet at a quantum Lifshitz point, as highlighted by an orange dot. Here, we take an attraction strength $U=-3t$.