A path to superconductivity via strong short-range repulsion in a spin-polarized band

We predict that the spin-polarized electrons in a two-dimensional triangular lattice with strong electron-electron repulsion gives rise to f-wave pairing. The key point is that the first-order interaction, which is usually pair-breaking, vanishes or nearly vanishes in certain f-wave channels due to symmetry constraints. As a result, these f-wave pairing channels are governed by the subleading-order processes which enable pairing when the perturbation theory is controlled. We illustrate this using the Hubbard model on the triangular lattice with on-site and nearest-neighbor repulsion, where we find a $T_c\sim 1% $ of electron’s bandwidth. For a general screened interaction, the same idea works asymptotically, but a third-order calculation is needed to fully determine the strength of f-wave pairing.

💡 Research Summary

The authors address a long‑standing question: can a purely repulsive, short‑range electron–electron interaction give rise to superconductivity in a controlled, quantitative way? They focus on a spin‑polarized two‑dimensional electron system on a triangular lattice, where the Pauli principle eliminates any on‑site interaction and the dominant interaction is a nearest‑neighbor (NN) repulsion U₁.

A key observation is that the first‑order (direct + exchange) pairing kernel Γ^(1)(k,k′) is forced by the lattice point‑group symmetry (C₆ᵥ or C₃ᵥ) to vanish in certain odd‑parity (f‑wave) channels. In momentum space the NN interaction yields Γ^(1)∝∑_j sin(k·a_j) sin(k′·a_j). The three sine factors transform as a three‑dimensional representation that decomposes into p‑wave irreps (B₁, E₁) but not into the f‑wave irrep (B₂ in C₆ᵥ, A₁ in C₃ᵥ). Consequently, the overlap of Γ^(1) with an f‑wave gap function is exactly zero, i.e. the first‑order contribution is pair‑breaking for all channels except the f‑wave one, where it is absent.

Because the leading repulsive term is missing, the pairing problem is governed by higher‑order processes. The authors perform a second‑order perturbative calculation in the dimensionless coupling g₁ = 6 U₁ A_uc ν₀ (A_uc is the unit‑cell area, ν₀ the density of states at the Fermi level). They find that the effective f‑wave coupling g_p scales as g₁² and can reach values of order 0.2 for realistic fillings (≈0.4 electrons per site). Translating this to an electronic bandwidth of ~1 eV yields an estimated transition temperature Tc ≈ 100 K, i.e. about 1 % of the bandwidth. In the dilute limit (very small Fermi momentum) the leading f‑wave interaction scales as k_F⁶, making the second‑order contribution subdominant; a third‑order calculation would then be required for reliable estimates.

The paper also treats a more generic screened Coulomb interaction V(q) = V₀ − α(qd)² + …, where d is the distance to a metallic screening plane. Two regimes are distinguished: (i) weak screening (d ≫ a, a the lattice constant) where umklapp processes are negligible, and (ii) strong screening (d ≪ a) where umklapp must be retained. In the weak‑screening case the effective interaction is proportional to k·k′, again suppressing the first‑order term in f‑wave channels. However, the f‑wave attraction itself is O(k_F⁶), so the third‑order diagrams (∝ g_eff³) dominate over the second‑order ones (∝ g_eff² η). In the strong‑screening case the contact part V₀ cancels exactly for spin‑polarized electrons, leaving only the q²‑dependent piece. The small expansion parameter η is the sum of a non‑umklapp contribution η₀ ∼ k_F²d² and an umklapp contribution η₁ that depends on the decay of the form factors Λ_G with reciprocal‑lattice vector G. Using a Gaussian orbital model the authors estimate η₁ ∼ d²/r₀² (r₀ is the orbital radius), showing that the relative size of k_F and r₀ determines which term dominates.

Overall, the work demonstrates a concrete route to f‑wave superconductivity driven solely by strong short‑range repulsion in a spin‑polarized band. The mechanism relies on symmetry‑enforced cancellation of the first‑order repulsion, allowing controlled perturbative treatment of higher‑order attractive processes. While the second‑order calculation already predicts sizable Tc in the extended Hubbard model, a fully quantitative prediction for realistic screened Coulomb interactions requires a third‑order analysis.

The authors acknowledge several practical considerations: (1) the small parameter η must be sufficiently tiny for the perturbation series to converge; (2) longer‑range Coulomb tails, residual spin‑orbit coupling, and lattice distortions could re‑introduce first‑order pair‑breaking terms; (3) disorder and fluctuations beyond mean‑field may suppress the transition temperature. Nonetheless, the paper provides a compelling theoretical framework that extends the classic Kohn‑Luttinger idea to a regime where strong repulsion, rather than weak perturbations, can be harnessed to achieve relatively high‑temperature superconductivity.