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arXiv:2512.20689

Controlled pairing symmetries in a Fermi-Hubbard ladder with band flattening

J. P. Mendonça, S. Biswas, M. Dziurawiec, U. Bhattacharya, K. Jachymski, M. Aidelsburger, M. Lewenstein, M. M. Maśka, T. Grass

cond-mat.str-elquant-phSubmitted Dec 22, 2025• Announced Dec 24, 2025• 0 citations
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Abstract

Band flattening has been identified as key ingredient to correlation phenomena in Moiré materials and beyond. Here, we examine strongly repulsive fermions on a ladder -- a minimal platform for unconventional $d$-wave pairing -- and show that flattening of the lower band through an additional diagonal hopping term produces non-Fermi liquid behavior, evidenced by the violation of Luttinger's theorem, as well as axial $d$-wave pairing correlations. Alternatively, plaquette ring exchange can also generate pairing, albeit with a distinct diagonal $d$-wave pairing symmetry. Hence, our finding showcases a competition of different unconventional pairing channels, and demonstrates via a simple model how band geometry can induce fermionic pairing. This offers broadly relevant insights for correlated flat-band systems, ranging from ultracold atoms to strongly interacting electrons in solids.

Journal reference
Phys. Rev. B 113, L241119 (2026)

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Band flattening has been identified as key ingredient to correlation phenomena in Moiré materials and beyond. Here, we examine strongly repulsive fermions on a ladder -- a minimal platform for unconventional ddd-wave pairing -- and show that flattening of the lower band through an additional diagonal hopping term produces non-Fermi liquid behavior, evidenced by the violation of Luttinger's theorem, as well as axial ddd-wave pairing correlations. Alternatively, plaquette ring exchange can also generate pairing, albeit with a distinct diagonal ddd-wave pairing symmetry. Hence, our finding showcases a competition of different unconventional pairing channels, and demonstrates via a simple model how band geometry can induce fermionic pairing. This offers broadly relevant insights for correlated flat-band systems, ranging from ultracold atoms to strongly interacting electrons in solids.
Motivated by recent research works on the flat-band correlated electron systems, we construct a plaquette-Lieb lattice, which exhibits nearly flat bands close to the Fermi level around half-filling, when the inter-plaquette hopping integral is much smaller than the intra-plaquette one. A detailed comparison study with the well-known checkerboard lattice indicates that there exist significant differences for the pairing property between the two lattices, and the nearly flat bands on the plaquette-Lieb lattice strongly enhance the [Formula: see text]-wave pairing correlation for repulsive on-site Hubbard interaction and [Formula: see text]-wave pairing correlation for attractive on-site Hubbard interaction. Our study not only provides a new lattice with nearly flat bands, but also deepens the understanding of electronic structure on superconductivity.
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Unconventional strongly correlated phases of the repulsive Fermi–Hubbard model, which could be emulated by ultracold vapors loaded in optical lattices, are investigated by means of energy minimizations with quantum number projection before variation and without any assumed order parameter. Using a tube-like geometry of optical plaquettes to realize the four-leg ladder Hubbard Hamiltonian, we highlight the intertwining of spin-, charge-, and pair-density waves embedded in a uniform d -wave superfluid background. As the lattice filling increases, this phase emerges from homogenous states exhibiting spiral magnetism and evolves towards a doped antiferromagnet. A concomitant enhancement of long-ranged d -wave pairing correlations is also found. Numerical tests of the approach for two-dimensional clusters are carried out, too.
Moiré materials have emerged as a rich platform for exploring strong correlation effects in low dimensions, with twisted bilayer graphene (TBG) as a paradigmatic example. To distill the essential ingredients driving moiré-induced phases, a simplified one-dimensional analog -- a two-leg ladder with spatially modulated interleg hopping and a uniform magnetic flux -- was recently introduced. This model, which we refer to as the moiré ladder, features a nearly flat lowest-energy band in a suitable parameter regime, capturing the band-flattening mechanism of TBG. We investigate the ground-state phase diagram of the moiré ladder using a combination of bosonization and density matrix renormalization group (DMRG) techniques, and systematically disentangle the respective roles of the flux and the hopping modulation. At half filling, previous numerical work identified a metal-insulator transition at finite interaction strength and an unexpected ferromagnetic ground state. Revisiting this, we show that the metal-insulator transition can be understood perturbatively within bosonization, governed by the number of Fermi points. In contrast, the ferromagnetic correlations are nonperturbative and require both flux and spatial modulation -- neither alone is sufficient. We extend our analysis to other fillings: one-quarter, three-quarters, slightly above half filling (half filling plus two electrons), and slightly below half filling (half filling minus two electrons). At moderate interactions, we observe ferromagnetism below half filling and antiferromagnetism above; at stronger interactions, ferromagnetism dominates across all studied fillings. Crucially, the analysis demonstrates that periodic interleg hopping alone does not engender new correlated phases; the magnetic flux is essential for the observed unconventional behavior.
Interaction-induced charge orders with electronic origin occur as states of spontaneously broken symmetry in several materials platforms. An electronic mechanism for charge order requires an attractive component in the effective charge vertex. We put forward such a mechanism for the formation of unconventional charge density waves in a metal. These states result from the condensation of particle-hole pairs with finite wave vector and nonzero angular momentum and correspond to bond or loop current order on a lattice. The mechanism we describe can be viewed as Kohn Luttinger analysis in the particle-hole channel with finite transferred momentum. It incorporates one-loop spin and pairing corrections, which are then used as an input for a summation in the charge channel triggering an instability. We extend our analysis to a spin-fluctuation approach, where the effective charge interaction is dressed by the particle-hole ladder with exchanged momentum. We argue that this mechanism works for weakly interacting metals with a nested Fermi surface and a large number of fermion flavors. We apply the Kohn-Luttinger-like approach to square–PLXINSERT-, and triangular-lattice Hubbard models with SU ( N f ) flavour symmetry and show that it leads to different types of p -wave charge density waves. We also study effects beyond weak coupling at and away from Van Hove filling in terms of a phenomenological model with additional exchange interaction. In the vicinity of Van Hove filling, we obtain d -wave charge density waves with wave vectors determined by nesting as leading instabilities. In addition, we find another charge density wave with wave vector K / 4 on the triangular lattice on both sides of the Van Hove filling. We demonstrate that this K / 4 instability can win the competition against pairing for N f = 4 via an unbiased functional renormalization group calculation.
We study the Kohn-Luttinger effect in a two-dimensional (2D) nested fermion liquid with a repulsive interaction via the renormalization group method and identify the resulting order parameter symmetry. Using the band structure of the 2D Hubbard model close to half-filling as a prototype, we construct an effective low-energy theory. We use multidimensional bosonization to incorporate the zero-sound channel and find marginal Fermi liquid behavior in the absence of any instability. We show an analog of the Landau theorem in nested fermion liquids, which serves as the criterion of the BCS instability. Including repulsive or antiferromagnetic exchange interactions in the low-energy theory, we show that the ${\mathrm{d}}_{{\mathrm{x}}^{2}\mathrm{\ensuremath{-}}{\mathrm{y}}^{2}}$-wave BCS channel is renormalized to be the most attractive. Below half-filling, when the nesting is not perfect, there is competition between the spin-density-wave (SDW) and the BCS channels; when the SDW coupling is small enough, there occurs a ${\mathrm{d}}_{{\mathrm{x}}^{2}\mathrm{\ensuremath{-}}{\mathrm{y}}^{2}}$-wave superconducting instability at sufficiently low temperatures.