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arXiv:2002.05904 · Physical review. B./Physical review. B

Momentum-resolved analysis of condensate dynamic and Higgs oscillations in quenched superconductors with time-resolved ARPES

Lukas Schwarz, Benedikt Fauseweh, Dirk Manske

Published Jun 18, 2020• 12 citations
arXivHTMLPDF

Abstract

Higgs oscillations in nonequilibrium superconductors provide a unique tool to obtain information about the underlying order parameter. Several properties like the absolute value, existence of multiple gaps, and the symmetry of the order parameter can be encoded in the Higgs oscillation spectrum. Studying Higgs oscillations with time-resolved angle-resolved photoemission spectroscopy (ARPES) has the advantage over optical measurements that a momentum-resolved analysis of the condensate dynamic is possible. In this paper, we investigate the time-resolved spectral function measured in ARPES for different quench protocols. We find that analyzing amplitude oscillations of the ARPES intensity in the whole Brillouin zone allows to understand how the condensate dynamic contributes to the emerging of collective Higgs oscillations. Furthermore, by evaluating the phase of these oscillations, the symmetry deformation dynamic of the condensate can be revealed, which gives insight about the ground state symmetry of the system. With such an analysis, time-resolved ARPES experiments might be used in the future as a powerful tool in the field of Higgs spectroscopy.

DOI
10.1103/physrevb.101.224510

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Higgs oscillations in nonequilibrium superconductors provide a unique tool to obtain information about the underlying order parameter. Several properties like the absolute value, existence of multiple gaps, and the symmetry of the order parameter can be encoded in the Higgs oscillation spectrum. Studying Higgs oscillations with time-resolved angle-resolved photoemission spectroscopy (ARPES) has the advantage over optical measurements that a momentum-resolved analysis of the condensate dynamic is possible. In this paper, we investigate the time-resolved spectral function measured in ARPES for different quench protocols. We find that analyzing amplitude oscillations of the ARPES intensity in the whole Brillouin zone allows to understand how the condensate dynamic contributes to the emerging of collective Higgs oscillations. Furthermore, by evaluating the phase of these oscillations, the symmetry deformation dynamic of the condensate can be revealed, which gives insight about the ground state symmetry of the system. With such an analysis, time-resolved ARPES experiments might be used in the future as a powerful tool in the field of Higgs spectroscopy.
We study how time- and angle-resolved photoemission (tr-ARPES) reveals the dynamics of BCS-type, sss-wave superconducting systems with time-varying order parameters. Approximate methods are discussed, based on previous approaches to either optical conductivity or quantum dot transport, to enable computationally efficient prediction of photoemission spectra. One use of such predictions is to enable extraction of the underlying order parameter dynamics from experimental data, which is topical given the rapidly growing use of tr-ARPES in studying unconventional superconductivity. The methods considered model the two-time lesser Green's functions with an approximated lesser self-energy that describes relaxation by coupling of the system to two types of baths. The approach primarily used here also takes into consideration the relaxation of the excited states into equilibrium by explicitly including the level-broadening of the retarded and advanced Green's functions. We present equilibrium and nonequilibrium calculations of tr-ARPES spectrum from our model and discuss the signatures of different types of superconducting dynamics.
Quantum gas microscopes are a promising tool to study interacting quantum many-body systems and bridge the gap between theoretical models and real materials. One of the most powerful experimental methods in solids is angle-resolved photoemission spectroscopy (ARPES), which measures the single-particle spectral function. The authors propose a measurement scheme to experimentally access the momentum- and energy-resolved spectral function in a quantum gas microscope. As an example for possible applications, the spectrum of a single hole excitation in one-dimensional ttt-JJJ models is calculated and analyzed. A sharp asymmetry in the distribution of spectral weight, reminiscent of the Fermi arcs observed in the pseudogap phase of cuprates, appears in the case of an isotropic Heisenberg spin chain.
Symmetry-breaking phase transitions are central to our understanding of states of matter. When a continuous symmetry is spontaneously broken, new excitations appear that are tied to fluctuations of the order parameter. In superconductors and fermionic superfluids, the phase and amplitude can fluctuate independently, giving rise to two distinct collective branches. However, amplitude fluctuations are difficult to both generate and measure, as they do not couple directly to the density of fermions and have only been observed indirectly to date. Here, we excite amplitude oscillations in an atomic Fermi gas with resonant interactions by an interaction quench. Exploiting the sensitivity of Bragg spectroscopy to the amplitude of the order parameter, we measure the time-resolved response of the atom cloud, directly revealing amplitude oscillations at twice the frequency of the gap. The magnitude of the oscillatory response shows a strong temperature dependence, and the oscillations appear to decay faster than predicted by time-dependent Bardeen-Cooper-Schrieffer theory applied to our experimental setup.
This thesis reports on theoretical investigations of the ultrafast nonequilibrium dynamics in superconductors. In particular, two nonequilibrium scenarios are modeled by combining several analytical and numerical methods: transient superconducting phase transition and collective excitations of a superconducting condensate. In the first part of the thesis the possibility to induce singlet superconducting correlations far from equilibrium is explored by applying time-dependent Lanczos algorithm to the one-dimensional extended Hubbard model. Here, the system is driven into a nonequilibrium state by (i) interaction quench and (ii) quench by pulse. In both cases the buildup of the superconducting correlations is studied in view of several correlation functions. Moreover, a transient Meissner effect, which reflects fingerprints of the induced superconductivity, is observed in calculations of the important for experiments time-dependent optical conductivity. In addition, the differences between nonequilibrium dynamics of the extended Hubbard model initiated by interaction quench and by pulse quench are discussed in detail. The second part is devoted to the excitation of collective modes in a superconductor out of equilibrium. First of all, focus is given to the properties of collective modes close to equilibrium conditions, where a linearized response can be expected. Within the framework of the (Nambu-) matrix kinetic theory in the clean limit a comprehensive gauge-invariant description of the collective modes associated with phase fluctuations of the order parameter is analytically formulated for the generalized case of two- band superconducting systems. Particular emphasis is on the application to the recently discovered noncentrosymmetric superconductors. A detailed analysis of the collective modes includes specification of the gauge mode (common to all superconductors) and the Leggett mode (collective fluctuations of the interband phase difference), and investigation of their subtle interplay in view of validity of the charge conservation law and the participation in the Anderson-Higgs mechanism. Further, the nonequilibrium excitation of the superconducting gaps for the case of two-band superconductors with singlet pairing correlations is investigated in a view of optical pump-probe experiments. For this purpose a semi-numerical method based on the density- matrix theory is formulated. In this case additional amplitude (Higgs) modes were identified, which allow to directly detect the properties of the superconducting condensates as a function of time. Moreover, a new interplay between the phase (Leggett) and amplitude (Higgs) modes is studied in detail. In particular it was found that the nonadiabatic excitation process leads to strong coupling between both modes. Finally, based on calculations of the time-dependent optical conductivity the prediction is made that the coupled Higgs and Leggett modes can be clearly visible in the pump-probe absorption spectra.
Motivated by the recent development of terahertz pump-probe experiments, we investigate the short-time dynamics in superconductors with multiple attractive pairing channels. Studying a single-band square lattice model with a spin-spin interaction as an example, we find the signatures of collective excitations of the pairing symmetries (known as Bardasis-Schrieffer modes) as well as the order parameter amplitude (Higgs mode) in the short-time dynamics of the spectral gap and quasiparticle distribution after an excitation by a pump pulse. We show that the polarization and intensity of the pulse can be used to control the symmetry of the nonequilibrium state as well as frequencies and relative intensities of the contributions of different collective modes. We find particularly strong signatures of the Bardasis-Schrieffer mode in the dynamics of the quasiparticle distribution function. Our work shows the potential of modern ultrafast experiments to address the collective excitations in unconventional superconductors and highlights the importance of subdominant interactions for the nonequilibrium dynamics in these systems.
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