Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                

Dynamical Cooper pairing in nonequilibrium electron-phonon systems

Michael Knap, Mehrtash Babadi, Gil Refael, Ivar Martin, and Eugene Demler
Phys. Rev. B 94, 214504 – Published 8 December 2016
PDFHTMLExport Citation
Abstract
Authors
Article Text
  • INTRODUCTION
  • ROLE OF THE PHONON NONLINEARITY
  • A MINIMAL ELECTRON-PHONON MODEL
  • EXPERIMENTAL IMPLICATIONS
  • SUMMARY AND OUTLOOK
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    We analyze Cooper pairing instabilities in strongly driven electron-phonon systems. The light-induced nonequilibrium state of phonons results in a simultaneous increase of the superconducting coupling constant and the electron scattering. We demonstrate that the competition between these effects leads to an enhanced superconducting transition temperature in a broad range of parameters. Our results may explain the observed transient enhancement of superconductivity in several classes of materials upon irradiation with high intensity pulses of terahertz light, and may pave new ways for engineering high-temperature light-induced superconducting states.

    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    • Received 20 July 2016
    • Revised 10 October 2016

    DOI:https://doi.org/10.1103/PhysRevB.94.214504

    ©2016 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Electron-phonon couplingFermionsNonequilibrium statistical mechanicsOptical transient phenomenaPhononsSuperconducting phase transitionSuperconductivity
    Statistical Physics & ThermodynamicsNonlinear DynamicsAtomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Michael Knap1, Mehrtash Babadi2, Gil Refael2, Ivar Martin3, and Eugene Demler4

    • 1Department of Physics, Walter Schottky Institute, and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany
    • 2Institute for Quantum Information and Matter, Caltech, Pasadena, California 91125, USA
    • 3Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
    • 4Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

    Article Text (Subscription Required)

    Click to Expand

    References (Subscription Required)

    Click to Expand
    Issue

    Vol. 94, Iss. 21 — 1 December 2016

    Reuse & Permissions
    Access Options
    CHORUS

    Article Available via CHORUS

    Download Accepted Manuscript
    Author publication services for translation and copyediting assistance advertisement

    Authorization Required

    Log In
    Other Options
    ×

    Images

    • Figure 1
      Figure 1

      Dynamical enhancement of the superconducting transition temperature. A schematic representation of the physical processes leading to light-induced superconductivity: (1) The pump pulse couples coherently to (2) an infrared-active phonon mode which in turn (3) via nonlinear interactions drives Raman phonons that are responsible for superconducting pairing. The nonequilibrium occupation of the Raman phonons (4) universally enhances the superconducting coupling strength γ, which is a product of the density of states at the Fermi level NF and the induced attractive interaction between the electrons U, and hence (5) increases the transition temperature Tc of the superconducting state. We calculate the relative enhancement of Tc compared to equilibrium (Tc−Tc,eq)/Tc,eq by taking into account the competition between dynamical Cooper pair-formation and Cooper pair breaking processes, as a function of the pump frequency Ω/ω¯ and the driving amplitude A. The data are evaluated for linearly dispersing phonons with mean frequency ω¯, relative spread Δω/ω¯=0.2, and negative quartic couplings of type II between the Raman and infrared-active modes (Table 1). Moreover, the electron-phonon interaction strength is chosen to give an equilibrium effective attractive interaction U/W=1/8 that is weak compared to the bare electronic bandwidth W. The static renormalization of Raman modes leads to the uniform increase of Tc with increasing driving amplitude A, the squeezed phonon state manifests in the strong enhancement near parametric resonance Ω∼ω¯, and the temporal proximity effect dominates near Ω/ω¯∼0.

      Reuse & Permissions
    • Figure 2
      Figure 2

      Dynamical Cooper instability. The dynamical Cooper instability evaluated within the Floquet BCS theory including nonequilibrium pair breaking processes, red solid line, is compared to the one without pair breaking, black dotted line, and the BCS solution for the equilibrium problem, blue dashed line. Data are evaluated for mean phonon frequency ω¯/W=1/8 and effective attractive interactions U/W=1/8 that are weak compared to the bare electronic bandwidth W, a phonon frequency spread of Δω=0.2ω¯, driving strength A=0.1, and driving frequency (a) Ω/ω¯=0.001 and (b) Ω/ω¯=0.8. The nonequilibrium Cooper pair-formation rate dominates over the pair breaking, hence, leading to an enhanced transition temperature.

      Reuse & Permissions
    • Figure 3
      Figure 3

      Phonon squeezing as a universal mechanism for the enhancement of Tc. The relative change of the superconducting transition temperature is shown for (a) quartic type-II phonon nonlinearities with positive Λk>0 and (b) cubic type-III phonon nonlinearities, taking into account the competition between Cooper pair formation and pair breaking. (a) Quartic phonon nonlinearities that couple to finite momentum Raman modes have two distinguished effects on the bandwidth renormalization: (i) the static displacement of the Raman modes and (ii) phonon squeezing. For positive nonlinearities, the static displacement hardens the frequency of the Raman phonons. This leads to the uniform suppression of Tc with increasing magnitude of the driving amplitude A. However, near parametric resonance Ω∼ω¯, the phonon squeezing dominates over the static displacement, leading to the universal enhancement of Tc. (b) Cubic nonlinearities exhibit only the squeezing mechanism, and hence irrespectively of the sign of the coupling lead to an enhanced transition temperature. Furthermore, the shape of the enhancement diagram is similar to the one for quartic interaction with the main difference that in the case of quartic nonlinearities the resonance condition is Ω∼ω¯ while in the cubic case it is Ω∼2ω¯. The data are evaluated for ω¯/W=1/8,U/W=1/8,Δω=0.2ω¯.

      Reuse & Permissions
    • Figure 4
      Figure 4

      Mathieu equation. Numerical solution of the Mathieu equation at parametric resonance (A=0.1,Ω=ω1−A), blue solid line, and off resonance (A=0.1,Ω=0.9ω1−A), red dashed line. On resonance the phonon squeezing |ξ| increases linearly in time, while off resonance it oscillates around a finite mean value.

      Reuse & Permissions
    • Figure 5
      Figure 5

      Relative strength of the oscillations in the microscopic parameters. We show the time dependence of U/J(t) relatively to the undriven system for ω¯=U=W/8,Δω=0.2ω¯,A=0.1, (a) off resonance Ω/ω¯=0.1 and (b) near the parametric resonance Ω/ω¯=0.9 (blue solid line). Initially oscillations at multiple frequencies appear; however, all oscillations except for the driving frequency are washed out in time because for a dispersive phonon the only common frequency of all modes is the driving frequency. Oscillations with Ω are indicated by the red dashed line which we choose to approximate the dynamics of the microscopic parameters. The time average of U/J(t), black dashed line, is enhanced near resonance and with increasing driving strength.

      Reuse & Permissions
    • Figure 6
      Figure 6

      Relative enhancement of the effective mass in the driven system compared to the undriven one and the amplitude of coherent oscillations. The data are shown for linearly dispersing phonons ω¯=U=W/8, and Δω=0.2ω¯. Near Ω/ω¯∼1 we find a strong enhancement of (a) the effective mass exp[ζ] and (b) the effective amplitude A due to the efficient phonon squeezing. Furthermore, a weaker enhancement is observed at the higher-order resonances where Ω/ω¯∼1/n with n being an integer. In addition to the enhancement of the effective mass near the parametric resonance, it generically increases with increasing driving amplitude A due to the softening of the phonon modes.

      Reuse & Permissions
    • Figure 7
      Figure 7

      Cooper pair breaking rate. The Cooper pair breaking rate due to phonon fluctuations and the modulation of the effective electron-electron interactions evaluated from Floquet Fermi's golden rule for ω¯=U=W/8.

      Reuse & Permissions
    ×

    Sign up to receive regular email alerts from Physical Review B

    Log In

    Cancel
    ×

    Search

    Article Lookup

    Paste a citation or DOI
    Enter a citation
    ×