We uncover a superconducting state with partial spin polarization induced by a magnetic field. This state, which we call “magnonic superconductor,” lacks a conventional pairing order parameter but is characterized instead by a composite order parameter that represents the binding of electron pairs and magnons. We rigorously demonstrate the existence of magnonic superconductivity with high transition temperature in one-dimensional and two-dimensional Hubbard models with repulsive interaction. We further show that magnonic Cooper pairs can attract to form higher-charge bound states, which can give rise to charge-6 e superconductivity.
We uncover a superconducting state with partial spin polarization induced by a magnetic field. This state, which we call “magnonic superconductor,” lacks a conventional pairing order parameter but is characterized instead by a composite order parameter that represents the binding of electron pairs and magnons. We rigorously demonstrate the existence of magnonic superconductivity with high transition temperature in one-dimensional and two-dimensional Hubbard models with repulsive interaction. We further show that magnonic Cooper pairs can attract to form higher-charge bound states, which can give rise to charge-6 e superconductivity.
Magnon-Mediated Superconductivity in the Infinite-U Triangular Lattice
We demonstrate that the infinite-U triangular-lattice Hubbard model supports a superconducting state built from tightly bound Cooper pairs composed of two holes and one magnon (2h1m). Building on the seminal prediction of repulsively bound 2h1m states, we show that next-nearest-neighbor hopping t2 coherently mixes symmetry-related configurations, stabilizing an s-wave bound state with substantial binding energy and a light effective mass. Large-scale DMRG calculations at finite doping identify a magnetization plateau corresponding to a gas of such bound states and quasi--long--range superconducting order with power-law 2h1m pair correlations. Our results establish a magnon-mediated superconducting mechanism driven by kinetic frustration, with immediate detectable signatures for moiré Hubbard materials and ultracold-atom simulators.
We propose a pairing mechanism between holes in the dilute limit of doped frustrated Mott insulators. Hole pairing arises from a hole-hole-magnon three-body bound state. This pairing mechanism has its roots on single-hole kinetic energy frustration, which favors antiferromagnetic (AFM) correlations around the hole. We demonstrate that the AFM polaron (hole-magnon bound state) produced by a single hole propagating on a field-induced polarized background is strong enough to bind a second hole. The effective interaction between these three-body bound states is repulsive, implying that this pairing mechanism is relevant for superconductivity.
We have rigorously shown that a strong Hubbard repulsion can cause superconductivity. The model, which has a particular set of local symmetries, manifests the phase diagram of many unconventional superconductors; anti-ferromagnetism paramagnetism, superconductivity, and even ferromagnetism are all observed. The key technique in the analysis is an exact non-linear fermion transformation, which preserves the correlated motion of electrons while removing the strong interactions. Using resolvent formalism, it is exactly shown that two holes at the Mott point bind to form a localised Cooper pair. As interactions are now weak, we then use BCS mean field theory to calculate the energy, excess pairing, and superconducting gap. These results are compared to exact diagonalisation of finite sized systems and show good agreement. At the Mott point the system is an anti-ferromagnet, and a superconducting phase quickly appears upon doping, and then vanishes.
A phase of matter in which fermion quartets form a superconducting condensate, rather than the paradigmatic Cooper pairs, is a recurrent subject of experimental and theoretical studies. However, a comprehensive microscopic understanding of charge-4e superconductivity as a quantum phase is lacking. Here, we study a two-orbital tight-binding model with attractive Hubbard-type interactions. Such a model naturally provides the Bose-Einstein condensate as a limit for electron quartets and supports charge-4e superconductivity, as we show by mapping it to a spin-1/2 chain in this perturbative limit. Using density matrix renormalization group calculations for the one-dimensional case, we further establish that the ground state is indeed a superfluid phase of 4e charge carriers and that this phase can be stabilized well beyond the perturbative regime. Importantly, we demonstrate that 4e condensation dominates over 2e condensation even for nearly decoupled orbitals, which is a more likely scenario in electronic materials. Our model paves the way for both experimental and theoretical exploration of 4e superconductivity and provides a natural starting point for future studies beyond one dimension or more intricate 4e states.
We study the thermodynamics of a superconductor with strongly bound Cooper pairs by solving the self-consistent T-matrix equations for the attractive Hubbard model within a local approximation. We determine the transition temperature as a function of the interaction strength at quarter filling, and compute the temperature dependence of the superconducting order parameter, the specific heat, the spin susceptibility, and the density of local pairs in the normal and superconducting phase. Pronounced deviations from BCS behavior are found already for moderate interactions, where superconductivity sets in at a critical temperature above the coherence temperature for Fermi liquid behavior.
The theoretical understanding of conventional superconductivity as the phonon-assisted formation and condensation of two-electron Cooper pairs is a significant triumph in condensed matter physics. Here, we propose many-electron characterizations of higher-charge superconductivity with Cooper pairs consisting of more than two electrons, by implementing translation symmetrization on parent pair-density-wave-ordered states. In particular, we demonstrate many-electron constructions with vanishing charge- 2 e sectors, but with sharp signatures in charge- 4 e or charge- 6 e expectation values instead. Such characterizations are consistent with previous phenomenology of vestigial order and Ginzburg-Landau theory. Furthermore, we demonstrate that at the microscopic level, momentum conservation alone may be vital and sufficient for the robust emergence of higher-charge superconductivity. Our study thus offers a general and microscopic route to understand and characterize higher-charge superconductivity, including nontrivial experimental signatures such as fractional magnetic flux and period in interferometry, as well as localized Cooper pairs at lattice topological defects.