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arXiv:1611.07089 · Physical review. B./Physical review. B

Twisting Anderson pseudospins with light: Quench dynamics in terahertz-pumped BCS superconductors

Yang-Zhi Chou, Yunxiang Liao, Matthew S. Foster

Published Mar 8, 2017• 55 citations
arXivHTMLPDF

Abstract

An exciting recent development is the ability to drive a quantum material into a highly excited, but still phase coherent state, using intense laser sources. Although such a state can be extremely short-lived, it can be long enough for detection using ultrafast spectroscopy. The authors here show how intense laser pulses can generate a new type of nonequilibrium superconducting phase. The authors demonstrate theoretically that the pump induces a ``twisted'' BCS state that subsequently evolves coherently after the cessation of the pulse. They show how the nonlinear coupling of the pump pulse light can induce coherent dynamics of $\mathrm{\ensuremath{\Delta}}(t)$, consistent with the experiment [R. Matsunaga et al. Phys. Rev. Lett. 111, 057002 (2013)]. Moreover, the authors show that more intense pump pulses can create a far-from-equilibrium phase of gapless superconductivity, originally predicted in the context of ultracold atomic gases. The terahertz pump is found to be much more efficient than the interaction quench at producing this gapless phase. These results open the door to engineering and observing new dynamical phases and phase transitions in quantum materials.

DOI
10.1103/physrevb.95.104507

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Ultrafast laser probing has revolutionized the study of quantum materials. Quantum magnets realize some of the most complex and entangled many-body states in condensed matter. Here, the authors unify ultrafast physics and quantum magnetism by pump-probe experiments on the frustrated magnet SrCu2{}_{2}2​(BO3{}_{3}3​)2{}_{2}2​, using terahertz light pulses to create coherent driving of the lattice phonons, which in turn creates a special singlet spin excitation. Their phonon-based method introduces a universal mechanism for controlling nonequilibrium quantum many-body physics on ultrafast timescales.
Using a nonequilibrium implementation of the Lanczos-based exact diagonalisation technique we study the possibility of the light-induced superconducting phase coherence in a solid state system after an ultrafast optical excitation. In particular, we investigate the buildup of superconducting correlations by calculating an exact time-dependent wave function reflecting the properties of the system in non-equilibrium and the corresponding transient response functions. Within our picture we identify a possible transient Meissner effect after dynamical quenching of the non-superconducting wavefunction and extract a characteristic superfluid density that we compare to experimental data. Finally, we find that the stability of the induced superconducting state depends crucially on the nature of the excitation quench: namely, a pure interaction quench induces a long-lived superconducting state, whereas a phase quench leads to a short-lived transient superconductor.
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.
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.