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arXiv:2006.11203 · Physical Review Letters

Modeling Unconventional Superconductivity at the Crossover between Strong and Weak Electronic Interactions

Morten H. Christensen, Xiaoyu Wang, Yoni Schattner, Erez Berg, Rafael M. Fernandes

Published Dec 7, 2020• 7 citations
arXivHTMLPDF

Abstract

High-temperature superconductivity emerges in many different quantum materials, often in regions of the phase diagram where the electronic kinetic energy is comparable to the electron-electron repulsion. Describing such intermediate-coupling regimes has proven challenging as standard perturbative approaches are inapplicable. Here, we employ quantum Monte Carlo methods to solve a multiband Hubbard model that does not suffer from the sign problem and in which only repulsive interband interactions are present. In contrast to previous sign-problem-free studies, we treat magnetic, superconducting, and charge degrees of freedom on an equal footing. We find an antiferromagnetic dome accompanied by a metal-to-insulator crossover line in the intermediate-coupling regime, with a smaller superconducting dome appearing in the metallic region. Across the antiferromagnetic dome, the magnetic fluctuations change from overdamped in the metallic region to propagating in the insulating region. Our findings shed new light on the intertwining between superconductivity, magnetism, and charge correlations in quantum materials.

DOI
10.1103/physrevlett.125.247001

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High-temperature superconductivity emerges in many different quantum materials, often in regions of the phase diagram where the electronic kinetic energy is comparable to the electron-electron repulsion. Describing such intermediate-coupling regimes has proven challenging as standard perturbative approaches are inapplicable. Here, we employ quantum Monte Carlo methods to solve a multiband Hubbard model that does not suffer from the sign problem and in which only repulsive interband interactions are present. In contrast to previous sign-problem-free studies, we treat magnetic, superconducting, and charge degrees of freedom on an equal footing. We find an antiferromagnetic dome accompanied by a metal-to-insulator crossover line in the intermediate-coupling regime, with a smaller superconducting dome appearing in the metallic region. Across the antiferromagnetic dome, the magnetic fluctuations change from overdamped in the metallic region to propagating in the insulating region. Our findings shed new light on the intertwining between superconductivity, magnetism, and charge correlations in quantum materials.
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One of the most challenging problems in computational condensed matter physics is the simulation of many-electron systems by unbiased numerical techniques. Quantum Monte Carlo approaches – typically the method of choice for quantum many-body systems with bosonic or spin degrees of freedom – are oftentimes limited to handle many-electron systems due to the infamous fermion-sign problem that severely limits the computational efficiency of this otherwise very potent class of algorithms. Here we report on an elegant approach to overcome the fermion-sign problem in the study of competing quantum magnetism and superconductivity in metals. This approach allows us to study the onset of spin-density wave order in such itinerant electron systems via two-dimensional lattice models amenable to numerically exact, sign-problem-free determinantal quantum Monte Carlo simulations. The finite-temperature phase diagram of these models reveal a dome-shaped d-wave superconducting phase near the magnetic quantum phase transition. The striking similarity of these numerical results to the experimentally observed phenomenology of many unconventional superconductors points a way to a microscopic understanding of such strongly coupled systems in a controlled manner.
We compute transport and thermodynamic properties of a two-band spin-fermion model describing itinerant fermions in two dimensions interacting via Z2{Z}_{2}Z2​ antiferromagnetic quantum critical fluctuations by means of a sign-problem-free quantum Monte Carlo approach. We show that the phase diagram of this model indeed contains a ddd-wave superconducting phase at low enough temperatures. However, a crucial question that arises is whether a non-Fermi-liquid metallic regime exists above Tc{T}_{c}Tc​, exhibiting hallmark strange-metal transport phenomenology. Interestingly, we find that this version of the model describes a non-Fermi-liquid metallic regime that displays an approximately TTT-linear resistivity above Tc{T}_{c}Tc​ for a strong fermion-boson interaction. Using the Nernst-Einstein relation, our QMC results also show that this strange metal phase exhibits a crossover from being characterized by a charge compressibility given approximately by ${\ensuremath{\chi}}_{c}\ensuremath{\sim}1/T$ at high temperatures to being described by a charge diffusivity consistent with the scaling ${D}_{c}\ensuremath{\sim}1/T$ at low temperatures. Therefore, our paper adds support to the view that the Z2{Z}_{2}Z2​ antiferromagnetic spin-fermion model at strong coupling can be considered a minimal model that describes both unconventional superconductivity and strange metallicity, which are fundamentally interconnected in many important strongly correlated quantum materials.
We study the onset of spin-density wave order in itinerant electron systems via a two-dimensional lattice model amenable to numerically exact, sign-problem-free determinantal quantum Monte Carlo simulations. The finite-temperature phase diagram of the model reveals a dome-shaped d-wave superconducting phase near the magnetic quantum phase transition. Above the critical superconducting temperature, an extended fluctuation regime manifests itself in the opening of a gap in the electronic density of states and an enhanced diamagnetic response. While charge density wave fluctuations are moderately enhanced in the proximity of the magnetic quantum phase transition, they remain short ranged. The striking similarity of our results to the phenomenology of many unconventional superconductors points a way to a microscopic understanding of such strongly coupled systems in a controlled manner.
While superconductors are conventionally established by attractive interactions, higher-temperature mechanisms for emergent electronic pairing from strong repulsive electron-electron interactions remain under considerable scrutiny. Here, we establish a strong-coupling mechanism for intertwined superconductivity and magnetic order from purely repulsive interactions in a Kondo-like bilayer system, composed of a two-dimensional Mott insulator coupled to a layer of weakly-interacting itinerant electrons. Combining large scale DMRG and Monte Carlo simulations, we find that superconductivity persists and coexists with magnetism over a wide range of interlayer couplings. We classify the resulting rich phase diagram and find 2-rung antiferromagnetic and 4-rung antiferromagnetic order in one-dimensional systems along with a phase separation regime, while finding that superconductivity coexists with either antiferromagnetic or ferromagnetic order in two dimensions. Remarkably, the model permits a rigorous strong-coupling analysis via localized spins coupled to charge-2e bosons through Kugel-Khomskii interactions, capturing the pairing mechanism in the presence of magnetism due to emergent attractive interactions. Our numerical analysis reveals that pairing remains robust well beyond the strong-coupling regime, establishing a new mechanism for superconductivity in coupled weakly- and strongly-interacting electron systems, relevant for infinite-layer nickelates and superconductivity in moire multilayer heterostructures.
The ground state of the two-dimensional (2D) Hubbard model is investigated by adopting improved wave functions that take into account intersite electron correlation beyond the Gutzwiller ansatz. The ground-state energy is lowered considerably, giving the best estimate of the ground-state energy for the 2D Hubbard model. There is a crossover from weakly to strongly correlated regions as the on-site Coulomb interaction UUU increases. The antiferromagnetic correlation induced by UUU is reduced for hole doping when UUU is large, being greater than the bandwidth, thus increasing the kinetic energy gain. The spin and charge fluctuations are induced in the strongly correlated region. These antiferromagnetic and kinetic charge fluctuations induce electron pairings, which would result in high-temperature superconductivity.