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Inducing superconductivity in bilayer graphene by alleviation of the Stoner blockade

Gal Shavit and Yuval Oreg
Phys. Rev. B 108, 024510 – Published 25 July 2023
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  • INTRODUCTION
  • STONER BLOCKADE
  • SUPERCONDUCTIVITY
  • REFINEMENTS
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    External magnetic fields conventionally suppress superconductivity, both by orbital and paramagnetic effects. A recent experiment has shown that, in a Bernal stacked bilayer graphene system, the opposite occurs—a finite critical magnetic field is necessary to observe superconducting features occurring in the vicinity of a magnetic phase transition. We propose an extraordinary electronic-correlation-driven mechanism by which this anomalous superconductivity manifests. Specifically, the electrons tend to avoid band occupations near high density of states regions due to their mutual repulsion. Considering the nature of spontaneous symmetry breaking involved, we dub this avoidance Stoner blockade. We show how a magnetic field softens this blockade, allowing weak superconductivity to take place, consistent with experimental findings. Our principle prediction is that a small reduction of the Coulomb repulsion would result in sizable superconductivity gains, both in achieving higher critical temperatures and expanding the superconducting regime. Within the theory we present, magnetic field and spin-orbit coupling of the Ising type have a similar effect on the Bernal stacked bilayer graphene system, elucidating the emergence of superconductivity when the system is proximitized to a WSe2 substrate. We further demonstrate in this paper the sensitivity of superconductivity to disorder in the proposed scenario. We find that a disorder that does not violate Anderson's theorem may still induce a reduction of Tc through its effect on the density of states, establishing the delicate nature of the Bernal bilayer graphene superconductor.

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    • Received 20 March 2023
    • Revised 28 June 2023
    • Accepted 10 July 2023

    DOI:https://doi.org/10.1103/PhysRevB.108.024510

    ©2023 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Superconductivity
    1. Physical Systems
    Bilayer grapheneStrongly correlated systems
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Gal Shavit and Yuval Oreg

    • Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel

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    Vol. 108, Iss. 2 — 1 July 2023

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    Images

    • Figure 1
      Figure 1

      (a) Density of states per flavor of the valence band, computed from the Hamiltonian H0 [Eq. (2)]. The gray rectangle demarcates the blockaded region in panel (b). (b) Flavor resolved densities νi as a function of total electron filling, calculated by the variational Hartree-Fock method. Spontaneous spin polarization develops in the system approaching the van Hove filling from either side. The gray rectangle emphasizes the forbidden range of flavor density due to the strong electronic interactions. Here, UC=1.8eVnm2 and J=0.25eVnm2. (c) Extent of the Stoner blockade with varying interaction strength UC. The van Hove filling is marked by a dashed blue line. Throughout this figure we use U=60meV.

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    • Figure 2
      Figure 2

      (a) Magnitude of the discontinuous magnetization jump at the phase transition points, as a function of Zeeman coupling [Eq. (10)]. As expected from a first-order magnetization transition, the jump softens with an increase in the magnetic field. Here, the magnetization is defined m≡∑τ,sσzssντs. (b) Flavor resolved densities νi as a function of total electron filling, with VZ=0.05meV. The gray rectangle marks the forbidden range of flavor density when VZ=0 [see Fig. 1]. Notice that, in the vicinity of the transition, some flavors occupy a previously forbidden region. Other than VZ≠0, the parameters used in this figure are identical to the ones in Fig. 1.

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    • Figure 3
      Figure 3

      Superconductivity near the ferromagnetic phase transition boundary. Left panels: the DOS at the Fermi level in the superconducting sector as a function of density and in-plane magnetic field. Right panels: the corresponding superconducting transition temperature, calculated by the methods of Sec. 3. Both features follow closely the phase transition line, as one would expect within the Stoner blockade mechanism. (a) Calculations with Coulomb repulsion parameter UC=1.8eVnm2. (b) Same as (a), with UC reduced by 10%. Notice the color scales are identical for panels (a) and (b), emphasizing the immense potential impact of slight modifications of the Coulomb interaction strength. For example, the maximal Tc increased by a factor of ∼2.5 (66 mK to 158 mK) after the the 10% reduction in UC. Other parameters used: U=60meV,J=0.25eVnm2,Λ0=25meV,ωc=0.6meV, and g=0.63eVnm2 (the last three parameters are defined in Sec. 3a).

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    • Figure 4
      Figure 4

      (a) Flavor resolved densities νi (calculated by the variational Hartree-Fock method) in the presence of strong ISOC, λISOC=0.7meV, consistent with Ref. [15]. Here, UC=1.8eVnm2 and J=−0.1eVnm2. (b) Zoom-in on one of the blockaded regions close to the van Hove filling. The blockaded region, where the intra-spin-valley sector spontaneously polarizes, thus suppressing intervalley pairing, is demarcated by a gray rectangle. Notice the y-axis scale is the same as Fig. 1, showing the blockaded region is significantly smaller due to the large ISOC.

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    • Figure 5
      Figure 5

      Main panel: superconducting Tc as a function of charge inhomogeneity δn induced by time-reversal symmetric disorder. The calculation was done for U=60meV and μ¯=−57.85meV, with parameters Λ0=25meV,ωc=0.6meV,J=0.25eVnm2, and g=0.65eVnm2. Inset: comparison of the pristine DOS to the broadened DOS for several values of δn (indicated by legend).

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    • Figure 6
      Figure 6

      Relating the magnetization jump Δm to the width of the Stoner blockaded region Δνb. The density n(x axis) controls the first-order magnetic transition and occurs at the critical densities n1c and n2c. For simplicity, we assume that the transition is symmetric around the vHS filling nvHS. Below n1c and above n2c the four flavors are equally occupied, νi=n/4 (purple line). At the transition points spontaneous magnetization of magnitude Δm develops, so that opposite spin electrons have different densities (red and blue lines). We assume the spin splitting is symmetric for simplicity. By examining the region of flavor-resolved densities, which is excluded by the spontaneous symmetry breaking, we arrive at the relation Eq. (B1).

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    • Figure 7
      Figure 7

      Comparing the two ferromagnetic phase transition boundaries. Left: the DOS at the Fermi level in the superconducting sector as a function of density and in-plane magnetic field. Right: the corresponding superconducting transition temperature, calculated by the methods of Sec. 3. The calculations were performed with the same parameters as in Fig. 3.

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