Bipolaronic superconductivity out of a Coulomb gas

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Letter

Bipolaronic superconductivity out of a Coulomb gas

J. Sous, C. Zhang, M. Berciu, D. R. Reichman, B. V. Svistunov, N. V. Prokof'ev, and A. J. Millis

Phys. Rev. B 108, L220502 – Published 13 December 2023

Abstract

Employing an unbiased sign-problem-free quantum Monte Carlo approach, we investigate the effects of long-range Coulomb forces on Bose-Einstein condensation of bipolarons using a model of bond phonon-modulated electron hopping. In the absence of long-range repulsion, this model was recently shown to give rise to small-size light-mass bipolarons that undergo a superfluid transition at high values of the critical transition temperature $T_{c}$ . We find that $T_{c}$ in our model, even with the long-range Coulomb repulsion, remains much larger than that of Holstein bipolarons and can be on the order of or greater than the typical upper bounds on phonon-mediated $T_{c}$ based on the Migdal-Eliashberg and McMillan approximations. Our work points to a physically simple mechanism for superconductivity in the low-density regime that may be relevant to current experiments on dilute superconductors.

Received 4 December 2022
Revised 2 July 2023
Accepted 6 November 2023

DOI:https://doi.org/10.1103/PhysRevB.108.L220502

Physics Subject Headings (PhySH)

BEC-BCS crossover Electron-phonon coupling Superconducting phase transition

High-temperature superconductors Two-dimensional electron gas

Quantum Monte Carlo

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

J. Sous ^1,2,*,†, C. Zhang ^3,*,‡, M. Berciu^4,5, D. R. Reichman⁶, B. V. Svistunov ^7,8, N. V. Prokof'ev ⁷, and A. J. Millis^9,10,§

¹Department of Physics, Stanford University, Stanford, California 93405, USA
²Stanford Institute for Theoretical Physics, Department of Physics, Stanford University, Stanford, California 93405, USA
³Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and Hefei National Laboratory, University of Science and Technology of China, Hefei, Anhui 230088, China
⁴Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
⁵Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z4
⁶Department of Chemistry, Columbia University, New York, New York 10027, USA
⁷Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
⁸Wilczek Quantum Center, School of Physics and Astronomy and T. D. Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China
⁹Department of Physics, Columbia University, New York, New York 10027, USA
¹⁰Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA

^*These authors contributed equally to this work.
^†Present address: Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, California 92093, USA.
^‡Author to whom correspondence should be addressed: zhangchao1986sdu@gmail.com
^§Author to whom correspondence should be addressed: ajm2010@columbia.edu

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Issue

Vol. 108, Iss. 22 — 1 December 2023

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Images

Figure 1
Estimates of $T_{c}$ of the bond-Peierls (bP) bipolaronic superconductor (closed squares, blue lines) for different $t / Ω$ at $U = 8 t$ and $V_{r > 0} = V / r$ , with $V = U / 10$ , as a function of $λ$ computed according to Eq. (3) from QMC simulations of the bipolaron effective mass $m_{BP}^{★}$ and its mean-square radius $R_{BP}^{2}$ , contrasted with superconductivity of Holstein (H) bipolarons (open circles, orange line) at $t / Ω = 2$ for the same values of $U / t$ and $V$ . Here we define $λ = α^{2} / 3 Ω t$ for bond-Peierls bipolarons and $λ = 0.85 α^{2} / 6 Ω t$ for Holstein bipolarons. The doubly wavy symbol indicates the absence of bipolarons in the Holstein model for $λ ≲ 0.91$ where a crossover from BEC to the BCS regime may occur.
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Figure 2
Estimates of $T_{c}$ of the bond-Peierls bipolaronic superconductor for $t / Ω = 2$ as a function of $λ = α^{2} / 3 Ω t$ for (a) different strengths of the Coulomb repulsion $V$ at fixed on-site $U / t = 8$ and (b) different strengths of the on-site $U$ at fixed long-range repulsion $V = U / 10$ , computed according to Eq. (3) from QMC simulations of the bipolaron effective mass $m_{BP}^{★}$ and mean-square radius $R_{BP}^{2}$ .
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Figure 3
Bipolaron properties in the model (1) at $t / Ω = 2$ as a function of $λ = α^{2} / 3 Ω t$ for different $V$ at fixed $U / t = 8$ : (a) bipolaron binding energy $T_{p}$ , (b) bipolaron effective mass $m_{BP}^{★}$ in units of the mass of two free electrons $m_{0} = 2 m_{e} = 1 / t$ , and (c) bipolaron square radius $R_{BP}^{2}$ and, in the inset, its radial size probability density distribution $P_{BP} (R)$ (probability distribution of finding the two electrons within a bound bipolaron at a distance $R$ from their center-of-mass position) at large coupling for $V = U / 10$ . Error bars in $P_{BP} (R)$ correspond to statistical errors smaller than the symbol size and therefore are not shown.
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Figure 4
Phase diagram in the $T / Ω − λ$ space of the bond-Peierls model in the adiabatic limit $t / Ω = 2$ with strong on-site $U / t = 8$ and Coulomb $V = U / 10$ interactions. A BEC superconductor forms at $T \leq T_{c}$ (dark blue region). There is a large region at temperatures $T_{c} < T \leq T_{p}$ characterized by nonsuperconducting correlations and phase fluctuations in a normal gas of bipolarons (light blue region). Above $T_{p}$ , the bipolarons unbind into a polaron gas (gray region).
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Figure 5
The heavy black line shows the superfluid transition temperature $T_{c}$ of the bipolaronic gas normalized to the BEC temperature $T_{BEC}$ of a gas of bosons of density $n$ and mass $2 m_{p}$ as a function of the inverse density $n^{- 1}$ normalized to the effective bipolaron density $3 / 2 π R_{BP}^{3}$ . The black dashed line shows the proposed extrapolation of $T_{c}$ beyond the density at which the bipolarons overlap (black dot) and the BEC picture breaks down. As the density enters the $n > 3 / 2 π R_{BP}^{3}$ BCS regime we expect, based on comparison to the unitary Fermi gas (blue dashed line), that the decrease in mass associated with unbinding of bipolarons into Fermi-liquid quasiparticles may drive a further increase in $T_{c}$ .
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