We propose doping
SU(3)-symmetric spin liquids as a route toward charge-
6e superconductivity. This generalizes the idea of constructing charge-
4e superconductivity from doped
SU(4)-symmetric phases. As a concrete platform, we study a bilayer triangular-lattice Hubbard model with
SU(3) spin symmetry and interlayer antiferromagnetic exchange. Using complementary parton constructions, we analyze doped
Z3 quantum spin liquid and
SU(3)-related chiral spin liquids. Doping a
Z3 quantum spin liquid can produce an orthogonal metal with a gauge invariant fermi surface of charge-
3e fermionic trions. Pairing these trions gives a time-reversal-symmetric charge-
6e superconductor. Doping Abelian
SU(3)1 and
SU(6)1 chiral spin liquids yields chiral charge-
6e superconductors with and without residual Abelian topological order, respectively. Doping a non-Abelian
SU(3)2 chiral spin liquid leads to a non-Abelian chiral charge-
6e superconductor intertwined with
SO(3)−3 topological order and supporting non-Abelian
h/(6e) superconducting vortices. We also identify several other phases, including
Z3 orthogonal metal, quantum anomalous Hall (crystal) phases enriched by
Z3 or
Z2 topological order,
SU(3)-breaking charge-
2e superconductors, composite fermi liquid coupled to non-Abelian gauge field, and descendant chiral spin liquids. Our results identify doped
SU(3) spin liquids as a natural setting where symmetry, fractionalization, and topology cooperate to produce charge-
6e superconductivity.
We study the phase diagram of an effective three-orbital model of the cuprates using variational Monte Carlo calculations on asymptotically large lattices and exact diagonalization on a 24-site cluster. States with ordered orbital current loops (LC), itinerant antiferromagnetism, d-wave superconductivity, and the Fermi liquid are investigated using appropriate Slater determinants refined by Jastrow functions for on-site and intersite correlations. We find an LC state stable in the thermodynamic limit for a range of parameters compatible with the Fermi surface of a typical hole doped superconductor provided the transfer integrals between the oxygen atoms have signs determined by the effects of indirect transfer through the Cu-4s orbitals as suggested by Andersen. The results of the calculations are that the LC phase gives way at lower dopings to an antiferromagnetism phase, and at larger dopings to superconductivity and Fermi liquid phases.
The emergence of superconductivity from doping strongly correlated chiral topological phases in purely repulsive two-dimensional fermionic systems is a problem of broad and fundamental interest. However, existing numerical evidence has been limited to finite-size studies, and direct thermodynamic-limit evidence for superconducting long-range order has remained lacking. Here we provide such evidence for chiral superconductivity in the triangular Hofstadter-Hubbard model by advancing a simplex tensor-network approach that simultaneously captures superconducting long-range order and chiral topological order in the presence of intrinsic charge fluctuations, a capability that has remained challenging for previous two-dimensional approaches. We show that a broad intermediate-
U chiral spin liquid is separated from the weak-
U Chern insulator by a Mott transition, together forming undoped parent chiral topological states. Upon hole doping, we identify a uniform chiral superconducting state in the infinite system, characterized by a finite complex pairing order parameter. The pairing field exhibits an almost universal phase winding over a broad interaction-doping regime, with a distinct pocket of opposite winding near the Mott criticality. In addition, the entanglement spectrum retains the chiral structure of the parent topological phases while developing additional low-energy branches upon doping. These results establish that chiral superconductivity emerges robustly from doped chiral topological phases.
A spin-charge binding mechanism is analyzed using the Schwinger boson representation of the two-dimensional $t\ensuremath{-}J$ model. In the normal state spinons are paired into singlets which evolve out of the antiferromagnetic phase at half-filling. The singlets induce, via the hopping term, a pairing of holons and bind with the latter. The ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ symmetry of the order parameter and the shape of the
Tc vs doping curve, observed in cuprate superconductors, emerge naturally as a consequence of the symmetry of the spinon pairs, thus connecting superconductivity with quantum spin fluctuations in the insulator.
Demonstrating superconductivity in purely repulsive Hubbard models is a compelling goal which underscores the counter-intuitive ability of Coulomb interactions to mediate superconductivity. Here, we present numerical evidence for robust superconductivity in a triangular Hubbard-Hofstadter model at
π/2 flux per plaquette. Employing infinite density matrix renormalization group calculations on infinite cylinders of finite circumference, we observe superconducting ground states for a wide range of dopings, whose pair-correlations strengthen as the 2D limit is approached. At a density of one electron per site, Hubbard interactions have been reported to drive the insulating parent state of the superconductor from an integer quantum Hall (IQH) state to a chiral spin liquid (CSL). Our findings give credence to a recent proposal that proximity to the IQH-CSL transition serves to make chiral superconductivity energetically favorable on doping, and also correctly predicts the nature of the edge modes in the superconductor. On the CSL side, this suggests the superconductor can be thought of as arising from Laughlin's `anyon superconductivity' mechanism. Thus the Hubbard-Hofstadter model studied here offers a clean and experimentally accessible setup, potentially realizable in moiré heterostructures, for exploring the properties of anyonic matter at finite density and the interplay of topological order, quantum criticality and superconductivity.
The influence of chiral molecular potentials on phase-coherent transport in superconducting Josephson junctions is investigated. Within a Bogoliubov--de Gennes tight-binding framework, a superconducting--normal--superconducting (SNS) junction functionalized by adsorbed chiral molecules is modeled, where electrostatic gradients generated by the molecules induce spin--orbit coupling in the normal region. The equilibrium charge current--phase relation is found to remain largely insensitive to molecular chirality in symmetric, zero-field configurations. In contrast, the spin-polarized equilibrium current exhibits a pronounced chirality-dependent response, with opposite enantiomers producing distinct and anisotropic spin-polarized Josephson currents. The resulting handedness contrast can be enhanced through control parameters such as molecular orientation and the strength of the induced spin--orbit coupling. The temperature dependence of these currents further shows that the chirality-dependent signatures persist across a range of temperatures well below the superconducting critical temperature. These results identify Josephson interferometry as a phase-sensitive setting for probing chirality-dependent spin structure and highlight spin-polarized superconducting transport as a controlled route toward integrating chiral molecular functionality into superconducting spintronic devices.