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Bulletin of the American Physical Society

Transient Dynamics of d-wave Superconductors after a Sudden Excitation

Marco Schirò, Francesco Peronaci, Massimo Capone

Published Mar 16, 2016• 3 citations
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Transient Dynamics of d -Wave Superconductors after a Sudden Excitation

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Motivated by recent ultrafast pump-probe experiments on high-temperature superconductors, we discuss the transient dynamics of a d-wave BCS model after a quantum quench of the interaction parameter. We find that the existence of gap nodes, with the associated nodal quasiparticles, introduces a decay channel which makes the dynamics much faster than in the conventional s-wave model. For every value of the quench parameter, the superconducting gap rapidly converges to a stationary value smaller than the one at equilibrium. Using a sudden approximation for the gap dynamics, we find an analytical expression for the reduction of spectral weight close to the nodes, which is in qualitative agreement with recent experiments.

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Transient dynamics of unconventional superconductors: d-wave symmetry and strong correlations

Francesco Peronaci

This thesis is about unconventional superconductors out of equilibrium. More precisely, it summarizes our theoretical efforts in addressing a few questions related to the real-time evolution in models displaying unconventional superconductivity. Apart from the purely theoretical interest, the motivation for these studies comes from the recent achievement in the field of ultrafast time-resolved spectroscopy on correlated materials, such as the high-temperature copper-oxide superconductors. The task of describing such systems in nonequilibrium is a very difficult one. In this thesis we attack the problem from two different points of view: • the anisotropic unconventional d-wave symmetry, • the strong electron-electron correlations. The thesis is organized as follows: The first part introduces the basic concepts which lay at the foundation of the work presented in the other two parts. In Chapter 1, the concept of unconventional superconductivity is briefly introduced. This mainly includes the high-temperature copper-oxide superconductors and their phenomenology: d-wave symmetry of the super- conducting gap and strong electron-electron interaction. Chapter 2 is devoted to a review of the recent experimental advances in the field of ultrafast spectroscopy of high temperature superconductors and correlated materials, with a particular focus on time- and angle- resolved photoemission spectroscopy. Finally, Chapter 3 is a short review of some works in the field of cold-atom Fermi gases. In the second part we address the physics of the d-wave superconductor after a sudden excitation. First, in Chapter 4 we introduce in some detail a model of mean-field superconductor with a d-wave symmetry. The principal feature of this model is the anisotropy of the gap and the nodal lines along which the gap vanishes. The results concerning the dynamics of the gap after a “quantum quench” are exposed in Chapter 5 where we compare our model to the s-wave superconductor. This comparison allows to identify the consequences of the unconventional symmetry. In Chapter 6 we discuss the spectral features of the transient nonequilibrium state of the d-wave superconductor. This is particularly important to move a first step towards photoemission experiments. In the third part we concentrate on the attractive Hubbard model as a prototype of strongly correlated superconductor. In Chapter 8 we discuss the superconducting state at equilibrium with the use of dynamical mean-field theory. In Chapter 9 we discuss the extension of this technique to systems out of equilibrium. In particular it is described the implementation in the superconducting phase. At the end of the thesis two appendices give some details of the calculations.

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Crossover from adiabatic to sudden interaction quenches in the Hubbard model: prethermalization and non-equilibrium dynamics

Michael Moeckel, Stefan K. Kehrein

The recent experimental implementation of condensed matter models in optical lattices has motivated research on their non-equilibrium behavior. Predictions about the dynamics of superconductors following a sudden quench of the pairing interaction have been made based on the effective Bardeen–Cooper–Schrieffer (BCS) Hamiltonian; however, their experimental verification requires the preparation of a suitable excited state of the Hubbard model along a twofold constraint: (i) a sufficiently non-adiabatic ramping scheme is essential to excite the non-equilibrium dynamics and (ii) overheating beyond the critical temperature of superconductivity must be avoided. For commonly discussed interaction ramps, there is no clear separation of the corresponding energy scales. Here we show that the matching of both conditions is simplified by the intrinsic relaxation behavior of ultracold fermionic systems: for the particular example of a linear ramp we examine the transient regime of prethermalization (Moeckel and Kehrein 2008 Phys. Rev. Lett. 100 175702) under the crossover from sudden to adiabatic switching using Keldysh perturbation theory. A real-time analysis of the momentum distribution exhibits a temporal separation of an early energy relaxation and its later thermalization by scattering events. For long but finite ramping times this separation can be large. In the prethermalization regime, the momentum distribution resembles a zero-temperature Fermi liquid as the energy inserted by the ramp remains located in high-energy modes. Thus ultracold fermions prove to be robust to heating, which simplifies the observation of non-equilibrium BCS dynamics in optical lattices.

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Quantum Phase Transitions and Collective Modes in d-Wave Superconductors

Matthias Vojta C, Subir Sachdev A

arXiv:cond-mat/0104176•Springer eBooks•Oct 12, 2007•2 citations
Motivated by recent ultrafast pump-probe experiments on high-temperature superconductors, we discuss the transient dynamics of a d-wave BCS model after a quantum quench of the interaction parameter. We find that the existence of gap nodes, with the associated nodal quasiparticles, introduces a decay channel which makes the dynamics much faster than in the conventional s-wave model. For every value of the quench parameter, the superconducting gap rapidly converges to a stationary value smaller than the one at equilibrium. Using a sudden approximation for the gap dynamics, we find an analytical expression for the reduction of spectral weight close to the nodes, which is in qualitative agreement with recent experiments.
This thesis is about unconventional superconductors out of equilibrium. More precisely, it summarizes our theoretical efforts in addressing a few questions related to the real-time evolution in models displaying unconventional superconductivity. Apart from the purely theoretical interest, the motivation for these studies comes from the recent achievement in the field of ultrafast time-resolved spectroscopy on correlated materials, such as the high-temperature copper-oxide superconductors. The task of describing such systems in nonequilibrium is a very difficult one. In this thesis we attack the problem from two different points of view: • the anisotropic unconventional d-wave symmetry, • the strong electron-electron correlations. The thesis is organized as follows: The first part introduces the basic concepts which lay at the foundation of the work presented in the other two parts. In Chapter 1, the concept of unconventional superconductivity is briefly introduced. This mainly includes the high-temperature copper-oxide superconductors and their phenomenology: d-wave symmetry of the super- conducting gap and strong electron-electron interaction. Chapter 2 is devoted to a review of the recent experimental advances in the field of ultrafast spectroscopy of high temperature superconductors and correlated materials, with a particular focus on time- and angle- resolved photoemission spectroscopy. Finally, Chapter 3 is a short review of some works in the field of cold-atom Fermi gases. In the second part we address the physics of the d-wave superconductor after a sudden excitation. First, in Chapter 4 we introduce in some detail a model of mean-field superconductor with a d-wave symmetry. The principal feature of this model is the anisotropy of the gap and the nodal lines along which the gap vanishes. The results concerning the dynamics of the gap after a “quantum quench” are exposed in Chapter 5 where we compare our model to the s-wave superconductor. This comparison allows to identify the consequences of the unconventional symmetry. In Chapter 6 we discuss the spectral features of the transient nonequilibrium state of the d-wave superconductor. This is particularly important to move a first step towards photoemission experiments. In the third part we concentrate on the attractive Hubbard model as a prototype of strongly correlated superconductor. In Chapter 8 we discuss the superconducting state at equilibrium with the use of dynamical mean-field theory. In Chapter 9 we discuss the extension of this technique to systems out of equilibrium. In particular it is described the implementation in the superconducting phase. At the end of the thesis two appendices give some details of the calculations.
The recent experimental implementation of condensed matter models in optical lattices has motivated research on their non-equilibrium behavior. Predictions about the dynamics of superconductors following a sudden quench of the pairing interaction have been made based on the effective Bardeen–Cooper–Schrieffer (BCS) Hamiltonian; however, their experimental verification requires the preparation of a suitable excited state of the Hubbard model along a twofold constraint: (i) a sufficiently non-adiabatic ramping scheme is essential to excite the non-equilibrium dynamics and (ii) overheating beyond the critical temperature of superconductivity must be avoided. For commonly discussed interaction ramps, there is no clear separation of the corresponding energy scales. Here we show that the matching of both conditions is simplified by the intrinsic relaxation behavior of ultracold fermionic systems: for the particular example of a linear ramp we examine the transient regime of prethermalization (Moeckel and Kehrein 2008 Phys. Rev. Lett. 100 175702) under the crossover from sudden to adiabatic switching using Keldysh perturbation theory. A real-time analysis of the momentum distribution exhibits a temporal separation of an early energy relaxation and its later thermalization by scattering events. For long but finite ramping times this separation can be large. In the prethermalization regime, the momentum distribution resembles a zero-temperature Fermi liquid as the energy inserted by the ramp remains located in high-energy modes. Thus ultracold fermions prove to be robust to heating, which simplifies the observation of non-equilibrium BCS dynamics in optical lattices.