Research ArticleCONDENSED MATTER PHYSICS

Cavity quantum-electrodynamical polaritonically enhanced electron-phonon coupling and its influence on superconductivity

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Science Advances  30 Nov 2018:
Vol. 4, no. 11, eaau6969
DOI: 10.1126/sciadv.aau6969
  • Fig. 1 Setup of 2D material in optical cavity, phonon polariton frequency dispersions, and momentum-dependent electron-phonon coupling vertices for the polariton branches.

    (A) We consider a setup with a 2D material on a dielectric substrate inside a small optical cavity with mirrors as shown. (B) Schematic phonon, photon, and upper and lower polariton dispersions versus 2D in-plane momentum q. The coupling of the phononic dipole current to the photonic vector potential leads to a splitting determined by the plasma frequency ωP. In the cavity, ωP is controlled by the cavity volume. (C) Momentum-dependent squared electron-boson vertex g2(q). For forward scattering, the squared bare electron-phonon vertex Embedded Image is peaked near q = 0. In the polaritonic case (ωP > 0), the upper polariton branch inherits some of the electron-phonon coupling at small q.

  • Fig. 2 Temperature-dependent electron-phonon coupling for different coupling ranges and plasma frequencies.

    (A) Dimensionless electron-phonon coupling strength extracted from the normal self-energy at Embedded Image at the smallest Matsubara frequency, Embedded Image, as a function of temperature for a value of the coupling range in momentum space q0/kF = 0.105 representative of FeSe/SrTiO3, and different phononic plasma frequencies ωP as indicated. The case ωP = 0 represents the system without cavity. For increasing ωP, λ increases. Below the superconducting transition, which also shifts with ωP (see Fig. 3), λ decreases consistently for all values of ωP. (B) Temperature-dependent λ for smaller q0/kF = 0.053 and different ωP. As for the superconducting order parameter, the effects of the cavity coupling that is parameterized by ωP are more pronounced. (C) For even smaller q0/kF = 0.021, we obtain a strongly enhanced λ accompanied by the shift in the superconducting transition that shows up as a cusp in λ(T), which reaches a maximum at Tc.

  • Fig. 3 Temperature-dependent superconducting gap for different coupling ranges and plasma frequencies.

    (A) The superconducting gap at Embedded Image at the smallest Matsubara frequency, Embedded Image, as a function of temperature for a value of the coupling range in momentum space q0/kF = 0.105 representative of FeSe/SrTiO3, and different phononic plasma frequencies ωP (measured in electron volts for the FeSe example) as indicated. The case ωP = 0 represents the system without cavity. For the decreasing cavity volume, ωP increases, causing a decrease in Δ and the superconducting critical temperature Tc. (B) Temperature-dependent gap for smaller q0/kF = 0.053 and different ωP. The light-suppressed superconductivity is more pronounced. (C) For even smaller q0/kF = 0.021, strongly reduced Δ values are observed with increasing ωP.

  • Table 1 Parameters of the bare material system without the cavity used for the simulations discussed in the main text.
    Parameter setABC
    Phonon frequency Ω (eV)0.0920.0920.092
    Electron-phonon coupling g0 (eV)2.254.45511.1
    Coupling range q0/kF0.1050.0530.026
    Dimensionless coupling strength λ at 116.5 K0.1800.1800.180

Supplementary Materials

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Relevant photon modes in cavity
    • Section S2. Phonon-photon Hamiltonian
    • Section S3. Electron-polariton Hamiltonian
    • Section S4. Migdal-Eliashberg simulations

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