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arXiv:2402.02120 · Physical review. B./Physical review. B

Theory of symmetry-resolved quench-drive spectroscopy: Nonlinear response of phase-fluctuating superconductors

Matteo Ballerini Puviani

Published Jun 24, 2024• 5 citations
arXivHTMLPDF

Abstract

Recent experiments on cuprates have shown the possibility of opening a gap above the superconducting critical temperature, in the so-called phase-fluctuating state, by enhancing the phase coherence of preformed Cooper pairs. Quench-drive spectroscopy, an implementation of 2D coherent spectroscopy, has emerged as a powerful tool for investigating out-of-equilibrium superconductors and their collective modes. In this paper, we enrich the quench-drive scheme by developing a systematic generalization to study the nonlinear response of d -wave incoherent Cooper pairs in a symmetry-resolved manner. In particular, we not only show that it is possible to obtain a third-harmonic signal from fully incoherent pairs with an equilibrium vanishing order parameter, but we also characterize the full flourishing 2D spectrum of the generated nonlinear response. The results provide a deeper theoretical insight on recent experimental results, opening the door to a symmetry-driven design of future experiments on unconventional and enhanced superconductors. Published by the American Physical Society 2024

DOI
10.1103/physrevb.109.214515

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Recent experiments on cuprates have shown the possibility of opening a gap above the superconducting critical temperature, in the so-called phase-fluctuating state, by enhancing the phase coherence of preformed Cooper pairs. Quench-drive spectroscopy, an implementation of 2D coherent spectroscopy, has emerged as a powerful tool for investigating out-of-equilibrium superconductors and their collective modes. In this paper, we enrich the quench-drive scheme by developing a systematic generalization to study the nonlinear response of d -wave incoherent Cooper pairs in a symmetry-resolved manner. In particular, we not only show that it is possible to obtain a third-harmonic signal from fully incoherent pairs with an equilibrium vanishing order parameter, but we also characterize the full flourishing 2D spectrum of the generated nonlinear response. The results provide a deeper theoretical insight on recent experimental results, opening the door to a symmetry-driven design of future experiments on unconventional and enhanced superconductors. Published by the American Physical Society 2024
Cuprates are d-wave superconductors which exhibit a rich phase diagram: they are characterized by superconducting fluctuations even above the critical temperature, and thermal disorder can reduce or suppress the phase coherence. However, photoexcitation can have the opposite effect: recent experiments have shown an increasing phase coherence in optimally doped BSCCO with mid-infrared driving. Time-resolved terahertz spectroscopies are powerful techniques to excite and probe the non-equilibrium states of superconductors, directly addressing collective modes, such as amplitude (Higgs) oscillations. In this work, we calculate the full time evolution of the current generated by a cuprate with a quench-drive spectroscopy setup. Analyzing the response in Fourier space with respect to both the real time and the quench-drive delay time, we look for the signature of a transient modulation of higher harmonics, as well as the Higgs mode, in order to characterize the ground state phase. In particular, this approach can provide a smoking gun for induced or increased phase coherence when applied to the pseudogap phase. These results can pave the way for future experimental schemes to characterize and study superconductors alongside incoherent phases and phase transitions, including induced and transient superconductivity.
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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Recent experimental progress in the fields of cold quantum gases and ultrafast optical spectroscopy of quantum materials allows us to controllably induce and probe nonadiabatic dynamics of superconductors and superfluids. The time evolution of the gap function before relaxation with the lattice is determined by the superposition of coherently evolving individual Cooper pairs within the manifold of the Bardeen-Cooper-Schrieffer (BCS) wave function. While dynamics following an abrupt quench of the pairing interaction strength in the single-band BCS model has been exactly solved due to the integrability of the model, the dynamics of postquench multiband superconductors remain under scrutiny. Here, we develop a generalization of the Volkov-Kogan Laplace-space perturbative method that allows us to determine the nonadiabatic gap dynamics of two-band fully gapped superconductors for a wide range of quench amplitudes. Our approach expands the long-time dynamics around the steady-state asymptotic value of the gap, which is self-consistently determined, rather than around the equilibrium value of the gap. We explicitly demonstrate that this method recovers the exact solution of the long-time gap dynamics in the single-band case and perfectly agrees with a numerical solution of the two-band model. We discover that dephasing of Cooper pairs from different bands leads to faster collisionless relaxation of the gap oscillation with a power law of ${t}^{\ensuremath{-}3/2}$ instead of the well-known ${t}^{\ensuremath{-}1/2}$ behavior found in the single-band case. Furthermore, the gap oscillations display beating patterns arising from the existence of two different asymptotic gap values. Our results have important implications to a variety of two-band superconductors driven out of equilibrium, such as iron-based superconductors, MgB2{\mathrm{MgB}}_{2}MgB2​, and SrTiO3{\mathrm{SrTiO}}_{3}SrTiO3​.
The pseudogap state of cuprate high-temperature superconductors has been often viewed as either a yet unknown competing order or a precursor state to superconductivity. While awaiting the resolution of the pseudogap problem in cuprates, we demonstrate that local pairing fluctuations, vortex liquid dynamics, and other precursor phenomena can emerge quite generally whenever fermionic excitations remain gapped across the superconducting transition, regardless of the gap origin. Our choice of a tractable model is a lattice band insulator with short-range attractive interactions between fermions in the sss-wave channel. An effective crossover between Bardeen-Cooper-Schrieffer (BCS) and Bose-Einstein condensate (BEC) regimes can be identified in any band insulator above two dimensions, while in two dimensions only the BEC regime exists. The superconducting transition is ``unconventional'' (non-pair-breaking) in the BEC regime, identified by either the bosonic mean field or XY\mathit{XY}XY universality class. The insulator adjacent to the superconductor in the BEC regime is a bosonic Mott insulator of Cooper pairs, which may be susceptible to charge density wave ordering. We construct a function of the many-body excitation spectrum whose nonanalytic changes define a sharp distinction between band and Mott insulators. The corresponding ``second-order transition'' can be observed out of equilibrium by driving a Cooper pair laser in the Mott insulator. We explicitly show that the gap for charged bosonic excitations lies below the threshold for Cooper pair breakup in any BEC regime, despite quantum fluctuations. Our discussion ends with a view of possible consequences for cuprates, where antinodal pair dynamics has certain features in common with our simple sss-wave picture.
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