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arXiv:1904.05820 · Physical review. B./Physical review. B

Nature of the superconducting fluctuations in photoexcited systems

Ryuta Iwazaki, Naoto Tsuji, Shintaro Hoshino

Published Sep 20, 2019• 5 citations
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Abstract

The photoexcited state associated with superconducting fluctuations above the superconducting critical temperature ${T}_{c}$ is studied based on the time-dependent Ginzburg-Landau approach. The excited state is created by an electric-field pulse and is probed by a weak secondary external field, which is treated by the linear response theory mimicking pump-probe spectroscopy experiments. The behavior is basically controlled by two relaxation rates: one is ${\ensuremath{\gamma}}_{1}$ proportional to the temperature measured from the critical point $T\ensuremath{-}{T}_{c}$, and the other is ${\ensuremath{\gamma}}_{2}$ proportional to the excitation intensity of the pump pulse. The excited state approaches the equilibrium state exponentially in a long time $t\ensuremath{\gg}{\ensuremath{\gamma}}_{1}^{\ensuremath{-}1}$, while in the intermediate-time domain we find a power-law or logarithmic decay with different exponents for $t\ensuremath{\ll}{\ensuremath{\gamma}}_{2}^{\ensuremath{-}1}$ and ${\ensuremath{\gamma}}_{2}^{\ensuremath{-}1}\ensuremath{\ll}t\ensuremath{\ll}{\ensuremath{\gamma}}_{1}^{\ensuremath{-}1}$, even though the system is located away from the critical point. This is interpreted as the critical point in equilibrium being extended to a finite region in the excited situation. The parameter dependences on both the pump and probe currents are also systematically studied in all dimensions.

DOI
10.1103/physrevb.100.104521

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The photoexcited state associated with superconducting fluctuations above the superconducting critical temperature Tc{T}_{c}Tc​ is studied based on the time-dependent Ginzburg-Landau approach. The excited state is created by an electric-field pulse and is probed by a weak secondary external field, which is treated by the linear response theory mimicking pump-probe spectroscopy experiments. The behavior is basically controlled by two relaxation rates: one is \ensuremathγ1{\ensuremath{\gamma}}_{1}\ensuremathγ1​ proportional to the temperature measured from the critical point T\ensuremath−TcT\ensuremath{-}{T}_{c}T\ensuremath−Tc​, and the other is \ensuremathγ2{\ensuremath{\gamma}}_{2}\ensuremathγ2​ proportional to the excitation intensity of the pump pulse. The excited state approaches the equilibrium state exponentially in a long time t\ensuremath≫\ensuremathγ1\ensuremath−1t\ensuremath{\gg}{\ensuremath{\gamma}}_{1}^{\ensuremath{-}1}t\ensuremath≫\ensuremathγ1\ensuremath−1​, while in the intermediate-time domain we find a power-law or logarithmic decay with different exponents for t\ensuremath≪\ensuremathγ2\ensuremath−1t\ensuremath{\ll}{\ensuremath{\gamma}}_{2}^{\ensuremath{-}1}t\ensuremath≪\ensuremathγ2\ensuremath−1​ and \ensuremathγ2\ensuremath−1\ensuremath≪t\ensuremath≪\ensuremathγ1\ensuremath−1{\ensuremath{\gamma}}_{2}^{\ensuremath{-}1}\ensuremath{\ll}t\ensuremath{\ll}{\ensuremath{\gamma}}_{1}^{\ensuremath{-}1}\ensuremathγ2\ensuremath−1​\ensuremath≪t\ensuremath≪\ensuremathγ1\ensuremath−1​, even though the system is located away from the critical point. This is interpreted as the critical point in equilibrium being extended to a finite region in the excited situation. The parameter dependences on both the pump and probe currents are also systematically studied in all dimensions.
Despite extensive work on high-temperature superconductors, the critical behavior of an incipient condensate has so far been studied exclusively under equilibrium conditions. Here, we excite Bi(2)Sr(2)CaCu(2)O(8+δ) with a femtosecond laser pulse and monitor the subsequent nonequilibrium dynamics of the midinfrared conductivity. Our data allow us to discriminate temperature regimes where superconductivity is either coherent, fluctuating or vanishingly small. Above the transition temperature T(c), we make the striking observation that the relaxation to equilibrium exhibits power-law dynamics and scaling behavior, both for optimally and underdoped superconductors. Our findings can in part be modeled using time-dependent Ginzburg-Landau theory, and they provide strong indication of universality in systems far from equilibrium.
Despite extensive work on high-temperature superconductors, the critical behavior of an incipient condensate has so far been studied exclusively under equilibrium conditions. Here, we excite Bi2Sr2CaCu2O8+d with a femtosecond laser pulse and monitor the subsequent nonequilibrium dynamics of the mid-infrared conductivity. Our data allow us to discriminate temperature regimes where superconductivity is either coherent, fluctuating or vanishingly small. Above the transition temperature Tc, we make the striking observation that the relaxation to equilibrium exhibits power-law dynamics and scaling behavior, both for optimally and underdoped superconductors. Our findings can in part be modeled using time-dependent Ginzburg-Landau theory and provide strong indication of universality in systems far from equilibrium.
Using a state-of-the-art numerical scheme, we show that the Higgs mode under excitation exhibits chirped oscillations and exponential decay when fluctuations are included. This is in stark contrast to conventional BCS collisionless dynamics which predict power-law decay and the absence of chirping. The chirped amplitude mode enables us to determine the local modification of the effective potential even when the system is in a long-lived prethermal state. We then show that this chirped amplitude mode is an experimentally observable quantity since the photoinduced (super)current in pump-probe experiments serves as an efficient proxy for the order parameter dynamics, including the chirped dynamics. Our result is based on the attractive Hubbard model using dynamical mean-field theory within the symmetry-broken state after a excitation across the superconducting gap. Since the collective response involves long timescales, we extend the hierarchical low-rank compression method for nonequilibrium Green's functions to symmetry-broken states and show that it serves as an efficient representation despite long-lived memory kernels.
We study the effect of critical fluctuations on the (B,T)(B,T)(B,T) phase diagram in extreme type-II superconductors in zero and finite magnetic field. In zero magnetic field the critical fluctuations are transverse phase fluctuations of the complex scalar Ginzburg-Landau order parameter, which when excited thermally will induce topological line defects in the form of closed vortex loops into the system. The distribution function D(p)D(p)D(p) of vortex loops of perimeter p changes from an exponential function $D(p)\ensuremath{\sim}{p}^{\ensuremath{-}\ensuremath{\alpha}}\mathrm{exp}[\ensuremath{-}\ensuremath{\varepsilon}{(T)p/k}_{B}T]$ to a power law distribution $D(p)\ensuremath{\sim}{p}^{\ensuremath{-}\ensuremath{\alpha}}$ at the zero-field critical temperature T=Tc.{T=T}_{c}.T=Tc​. We find that the long-wavelength vortex-line tension vanishes as $\ensuremath{\varepsilon}(T)\ensuremath{\sim}|T\ensuremath{-}{T}_{c}{|}^{\ensuremath{\gamma}};\ensuremath{\gamma}\ensuremath{\approx}1.45,$ as $\stackrel{\ensuremath{\rightarrow}}{T}{T}_{c}.$ At T=Tc,{T=T}_{c},T=Tc​, an extreme type-II superconductor suffers an unbinding of large vortex loops of order the system size. When this happens, the connectivity of the thermally excited vortex tangle of the system changes abruptly. The loss of phase stiffness in the Ginzburg-Landau order parameter, the anomaly in specific heat, the loss of vortex-line tension, and the change in the connectivity of the vortex tangle are all found at the same temperature, the critical temperature of the superconductor. At zero magnetic field, unbinding of vortex loops of order the system size can be phrased in terms of a global U(1)\mathrm{U}(1)U(1)-symmetry breaking involving a local complex disorder field which is dual to the order parameter of the usual Ginzburg-Landau theory. There is one parameter in the theory that controls the width of the critical region, and for the parameters we have used, we show that a vortex-loop unbinding gives a correct picture of the zero-field transition even in the presence of amplitude fluctuations. A key result is the extraction of the anomalous scaling dimension of the dual field directly from the statistics of the vortex-loop excitations of the Ginzburg-Landau theory in the phase-only approximation. A scaling analysis of the vortex lattice melting line is carried out, yielding two different scaling regimes, namely, a high-field scaling regime and a distinct low-field three-dimensional XY critical scaling regime. We also find indications of an abrupt change in the connectivity of the vortex tangle in the vortex liquid along a line TL(B),{T}_{L}(B),TL​(B), which at low enough fields appears to coincide with the vortex line lattice melting transition line within the resolution of our numerical calculations. We study the temperature at which this phenomenon takes place as a function of system size and shape. Our results show that this temperature decreases and appears to saturate with increasing system size, and is insensitive to aspect ratios of the systems on which the simulations are performed, for large enough systems.
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.
This chapter investigates the critical behavior of high-temperature superconductors that are suddenly driven far from equilibrium conditions. Bi2Sr2CaCu2O8+δ is excited with a femtosecond laser pulse, and the subsequent nonequilibrium dynamics of the mid-infrared conductivity is monitored. The collected data allow discrimination of temperature regimes where superconductivity is coherent, fluctuating, or vanishingly small. Above the transition temperature Tc, the recovery to equilibrium conditions displays power-law behavior and scaling properties. Partial agreement is found between the scaling law of the optimal doped sample and the time-dependent Ginzburg–Landau (TDGL) model. Inherent limits of TDGL call for nonequilibrium field theories treating fluctuations, mode coupling, and fast degrees of freedom on an equal footing. These results open a timely connection between superconducting condensates and Bose–Einstein condensates of ultracold atoms.