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arXiv:1702.02942 · Physical review. B./Physical review. B

Nonequilibrium steady states and transient dynamics of conventional superconductors under phonon driving

Yuta Murakami, Naoto Tsuji, Martin Eckstein, Philipp Werner

Published Jul 19, 2017• 154 citations
arXivHTMLPDF

Abstract

The optical manipulation of phonon degrees of freedom can change the effective interactions in solids and potentially enhance superconductivity. However, heating and nonthermal energy distributions need to be considered to understand the ultimate effects of such a driving on ordered states. Using nonequilibrium dynamical mean field theory in the Kadanoff-Baym and Floquet implementation, the authors systematically discuss the effects of parametric phonon driving on conventional superconductivity. Both the transient dynamics of isolated systems and the nonequilibrium steady states in driven-dissipative systems are considered. While the phonon-mediated attractive interaction can be enhanced in certain driving regimes because of Floquet phonon sidebands, the heating and nonthermal distribution effects dominate and generically result in a suppression of superconductivity.

DOI
10.1103/physrevb.96.045125

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The optical manipulation of phonon degrees of freedom can change the effective interactions in solids and potentially enhance superconductivity. However, heating and nonthermal energy distributions need to be considered to understand the ultimate effects of such a driving on ordered states. Using nonequilibrium dynamical mean field theory in the Kadanoff-Baym and Floquet implementation, the authors systematically discuss the effects of parametric phonon driving on conventional superconductivity. Both the transient dynamics of isolated systems and the nonequilibrium steady states in driven-dissipative systems are considered. While the phonon-mediated attractive interaction can be enhanced in certain driving regimes because of Floquet phonon sidebands, the heating and nonthermal distribution effects dominate and generically result in a suppression of superconductivity.
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Floquet engineering offers exhilarating opportunities for controlling the dynamics of quantum many body systems and realizing new nonequilibrium phases of matter. However, generic interacting Floquet systems tend to heat up due to energy absorption from the drive, washing away the desired behavior. In this work, the authors characterize the steady states of an interacting electronic system, coupled to a phonon heat bath. They determine the regimes where the system-bath coupling stabilizes Floquet-insulator-like states, an important prerequisite for realizing topological states through Floquet engineering.
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We investigate the nonequilibrium steady states of a microwave-driven BCS superconductor in the presence of nonmagnetic impurity scattering and energy relaxation. Using the Floquet-Nambu-Keldysh Green's function method together with the self-consistent Born approximation, we self-consistently determine the superconducting order parameter in the microwave-driven steady state. We find that the nonequilibrium phase diagram depends strongly on the impurity-scattering strength. When impurity scattering is absent or weak, the steady-state order parameter is single-valued at each temperature and drive frequency. At intermediate scattering strengths, we find bistability between microwave-enhanced and microwave-suppressed superconducting states. As the impurity-scattering strength increases further, we instead find bistability between the superconducting and normal states. This evolution reflects competition between two effects of microwave driving: Eliashberg-type enhancement through the redistribution of thermally excited quasiparticles and suppression through pair-breaking-induced quasiparticle generation. In contrast to the robustness of equilibrium sss-wave superconductivity against nonmagnetic impurity scattering, our results demonstrate that nonmagnetic impurity scattering plays a central role in determining the character of nonequilibrium superconducting phase transitions under microwave driving.
A deeper theoretical understanding of driven-dissipative interacting systems and their nonequilibrium phase transitions is essential both to advance our fundamental physics understanding and to harness technological opportunities arising from optically controlled quantum many-body states. This paper provides a numerical study of dynamical phases and the transitions between them in the nonequilibrium steady state of the prototypical two-dimensional Heisenberg antiferromagnet with drive and dissipation. We demonstrate a nonthermal transition that is characterized by a qualitative change in the magnon distribution from subthermal at low drive to a generalized Bose-Einstein form including a nonvanishing condensate fraction at high drive. A finite-size analysis reveals static and dynamical critical scaling at the transition, with a discontinuous slope of the magnon number versus driving field strength and critical slowing down at the transition point. Implications for experiments on quantum materials and polariton condensates are discussed.