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

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

Phys. Rev. Lett. 125, 247001 – Published 7 December 2020

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.

Received 10 August 2020
Accepted 22 October 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.247001

Physics Subject Headings (PhySH)

Superconductivity

Strongly correlated systems

Extended Hubbard model Quantum Monte Carlo

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Morten H. Christensen ^1,‡, Xiaoyu Wang ^2,‡, Yoni Schattner^3,†, Erez Berg⁴, and Rafael M. Fernandes^1,*

¹School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
²National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA
³Department of Physics, Stanford University, Stanford, California 94305, USA
⁴Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel

^*Corresponding author. rfernand@umn.edu
^†Also at Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, California 94025, USA.
^‡M. H. C. and X. W. contributed equally to this work.

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Vol. 125, Iss. 24 — 11 December 2020

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Images

Figure 1
Phase diagram obtained from thermodynamic observables. In the vicinity of $U / t \sim 1$ , the phase diagram shows a variety of electronic phases, including AFM, SC, and a transition between metallic and insulating behaviors. No other ordered phases were observed for $0 \leq U \leq 4 t$ . The dark red full circles mark the magnetic transitions determined from a scaling analysis. Near $U / t \approx 0.75$ for $T / t < 0.1$ , we find that the transition becomes first order (see Supplemental Material [34]), which is indicated by empty squares and a dashed red line. The color scale is logarithmic and corresponds to the compressibility $χ_{c}$ [see Fig. 2], while the black dashed line marks the contour $χ_{c} = 0.01$ . We interpret this near complete suppression of the compressibility as a sign of insulating behavior. The green triangles mark the superconducting critical temperatures obtained from the Berezinskii–Kosterlitz–Thouless criterion for the system size $L = 12$ ; the green dashed line is an interpolation. The inset shows the simulated band structure, exhibiting one electron pocket centered at (0,0) and one hole pocket centered at $(π, π)$ .
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Figure 2
Thermodynamic observables in the vicinity of $U / t \sim 1$ . (a) AFM spin, (b) pair, and (c) charge susceptibilities (denoted by $χ_{s}$ , $χ_{p}$ , and $χ_{c}$ , respectively) for different temperatures as a function of $U / t$ . The pair susceptibility peaks in the immediate vicinity of the AFM transition. At low temperatures, within our resolution, we cannot separate the transition to the AFM phase from the crossover to the insulating phase.
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Figure 3
Evolution of the quasiparticle spectral weight proxy, ${\tilde{Z}}_{k}$ , with interaction strength. In the upper right half (lower left half) of the panels, we plot ${\tilde{Z}}_{k}$ for $T / t = 0.05$ in a color scale (gray scale) from 0 to ${\tilde{Z}}_{\max}$ (0 to 1). Note that the two halves are identical; we use two different color schemes only to highlight the loss of spectral weight across the magnetic transition. Here (a) and (b) correspond to the region prior to the AFM transition, while (c) and (d) are after. For small values of the interaction, the quasiparticle spectral weight matches the noninteracting Fermi surface shown in Fig. 1. For larger values, the Fermi surface shrinks and, beyond $U / t = 0.75$ , is reconstructed, signaling the onset of AFM order with wave vector $Q = (π, π)$ . To produce these figures, we combined simulations from 16 different twisted boundary conditions.
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Figure 4
Inverse dynamical spin susceptibility $χ_{s}^{- 1} (Ω_{n})$ in the metallic and insulating paramagnetic regions. (a) In the regime $U / t \leq 0.7$ (i.e., to the left of the AFM dome), where the system is metallic, the dependence on $Ω_{n}$ is roughly linear, $χ^{- 1} (Ω_{n}) \propto Ω_{n}$ , indicating that the magnetic fluctuations are overdamped. (b) In the regime $U / t \geq 1.5$ (i.e., to the right of the AFM dome), where the system is insulating, the magnetic fluctuations propagate ballistically, $χ^{- 1} (Ω_{n}) \propto Ω_{n}^{2}$ .
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