Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1909.00627

Pairing in the Two-Dimensional Hubbard Model from Weak to Strong Coupling

Astrid T. Rømer·Thomas A. Maier·Andreas Kreisel·Ilya Eremin·P. J. Hirschfeld·Brian M. Andersen
View original source ↗Read source document ↗Export metadata ↓

Abstract

The Hubbard model is the simplest model that is believed to exhibit superconductivity arising from purely repulsive interactions, and has been extensively applied to explore a variety of unconventional superconducting systems. Here we study the evolution of the leading superconducting instabilities of the single-orbital Hubbard model on a two-dimensional square lattice as a function of onsite Coulomb repulsion $U$ and band filling by calculating the irreducible particle-particle scattering vertex obtained from dynamical cluster approximation (DCA) calculations, and compare the results to both perturbative Kohn-Luttinger (KL) theory as well as the widely used random phase approximation (RPA) spin-fluctuation pairing scheme. Near half-filling we find remarkable agreement of the hierarchy of the leading pairing states between these three methods, implying adiabatic continuity between weak- and strong-coupling pairing solutions of the Hubbard model. The $d_{x^2-y^2}$-wave instability is robust to increasing $U$ near half-filling as expected. Away from half filling, the predictions of KL and RPA at small $U$ for transitions to other pair states agree with DCA at intermediate $U$ as well as recent diagrammatic Monte Carlo calculations. RPA results fail only in the very dilute limit, where it yields a $d_{xy}$ ground state instead of a $p$-wave state established by diagrammatic Monte Carlo and low-order perturbative methods, as well as our DCA calculations. We discuss the origins of this discrepancy, highlighting the crucial role of the vertex corrections neglected in the RPA approach. Overall, comparison of the various methods over the entire phase diagram strongly suggests a smooth crossover of the superconducting interaction generated by local Hubbard interactions between weak and strong coupling.

Explore related subjects

cond-mat.supr-concond-mat.str-el

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Astrid T. Rømer, Thomas A. Maier, Andreas Kreisel, Ilya Eremin, P. J. Hirschfeld, Brian M. Andersen. 2019-09-02. Pairing in the Two-Dimensional Hubbard Model from Weak to Strong Coupling. https://doi.org/10.1103/physrevresearch.2.013108

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Growth of superconducting boron doped diamond on 4inch silicon wafers

Superconducting boron-doped diamond (BDD) films were grown on 4-inch silicon wafers by microwave plasma chemical vapour deposition using gas-phase B/C ratios ranging from 6536 to 36421 ppm. Surface morphology, boron incorporation and superconducting properties were investigated as a function of gas-phase boron concentration. No systematic variation in apparent lateral grain size was observed across the series. Superconductivity was observed in all films except that grown at a B/C ratio of 6536 ppm within the measured temperature range down to 2 K. The superconducting transition temperature initially increased with increasing B/C ratio, reaching a maximum T$_c$ of 4.03 K at 24691 ppm, before decreasing at higher gas-phase B/C ratios. The corresponding resistive upper critical field at 2 K reached 3.091 T. Raman spectroscopy showed an increase in boron incorporation with increasing gas-phase B/C ratio up to 30303 ppm, followed by a slight decrease at 36421 ppm. Spatial measurements across the film grown at 24691 ppm showed T$_c$ values of 4.02, 4.19 and 3.33 K at the centre, intermediate and edge positions, respectively, with Raman spectroscopy showing a corresponding spatial variation in boron concentration. Comparison with previous growth on 2-inch wafers showed that substantially higher gas-phase B/C ratios were required to obtain comparable boron concentrations and superconducting properties on 4-inch wafers, indicating reduced boron incorporation efficiency during large-area growth. These results demonstrate the feasibility of producing superconducting BDD over a substantial area of a 4-inch silicon wafer while identifying boron incorporation and radial uniformity as key parameters for further wafer-scale optimisation.

cond-mat.supr-con↗
arXiv2026

Multigap superconductivity in Ising superconductors: The case of (LaSe)1.14(NbSe2)m misfit layer compounds

Strong spin-orbit coupling and broken inversion symmetry in transition metal dichalcogenides give rise to Ising superconductivity, a spin-protected pairing state first identified in monolayer NbSe$_2$ through in-plane critical fields far exceeding the Pauli limit. More recently, Ising superconductivity has been proposed as a potential route to unconventional and even topological superconductivity in bulk misfit compounds. Here, we investigate the superconducting order parameter of layered misfit compounds composed of alternating transition metal dichalcogenide and rocksalt layers, which host extremely doped, electronically decoupled NbSe$_2$ sheets within a three-dimensional crystal. Using directional scanning tunneling spectroscopy on the misfit superconductors (LaSe)$_{1.14}$(NbSe$_2$) and (LaSe)$_{1.14}$(NbSe$_2$)$_2$, we uncover a strongly anisotropic multigap superconducting state: a fragile gap on the $Γ$-centered Fermi-surface pocket coexists with a robust, intrinsic gap on the K and K$'$ pockets. These features are in quantitative agreement with momentum-resolved gaps $Δ(\mathbf{k})$ obtained from anisotropic Migdal-Eliashberg calculations. The marked fragility of the $Γ$-centered gap, combined with the strong sensitivity of the critical temperature to non-magnetic disorder, points to pairing beyond conventional $s$-wave symmetry, potentially involving a topological order parameter. These results establish NbSe$_2$-based misfit compounds as a tunable bulk platform for multigap, unconventional superconductivity, with Ising protection offering a promising route toward topological pairing.

cond-mat.supr-con↗
arXiv2026

Thermal Hall effect in elemental niobium, a two-gap superconductor

Niobium holds a pivotal place in superconductivity history: it is not only the elemental superconductor with the highest critical temperature, but also a long-standing candidate for multiband pairing whose evidence has remained controversial. A two-gap scenario was proposed as early as 1959, yet experimental proof stayed elusive. Here, through thermal Hall effect measurements, we unambiguously demonstrate a crossover in transverse thermal transport below $T_{\rm c}$, where the dominant carrier switches from hole-like to electron-like upon cooling. This crossover is a clear hallmark of two distinct superconducting condensates. Fitting our data to a two-gap Bardeen-Rickayzen-Tewordt (BRT) model yields a second energy gap of approximately 0.22 $k_{\rm B}T_{\rm c}$, only 11\% of the dominant gap. This small gap size accounts for the difficulty in resolving the two-gap structure in earlier experiments. Crucially, the temperature at which the electron-like contribution to longitudinal thermal conductivity begins to dominate coincides with the onset of the sign reversal in the thermal Hall coefficient, confirming consistency between the two methods, and providing crucial information on the assignment of the superconducting gaps to their respective hole- or electron-like Fermi surface sheets. These findings not only resolve a longstanding controversy, but also establish that multigap superconductivity is far more common than previously assumed, and demonstrate the thermal Hall effect as a powerful probe for resolving gap multiplicities in superconductors.

cond-mat.supr-con↗