Real-time measurement of the emergence of superconducting order in a high-temperature superconductor

Abstract

Systems which rapidly evolve through symmetry-breaking transitions on timescales comparable to the fluctuation timescale of the single-particle excitations may behave very differently than under controlled near-ergodic conditions. A real-time investigation with high temporal resolution may reveal new insights into the ordering through the transition that are not available in static experiments. We present an investigation of the system trajectory through a normal-to-superconductor transition in a prototype high-temperature superconducting cuprate in which such a situation occurs. Using a multiple pulse femtosecond spectroscopy technique we measure the system trajectory and time-evolution of the single-particle excitations through the transition in La1.9Sr0.1CuO4 and compare the data to a simulation based on time-dependent Ginzburg-Landau theory, using laser excitation fluence as an adjustable parameter controlling the quench conditions in both experiment and theory. The comparison reveals the presence of significant superconducting fluctuations which precede the transition on short timescales. By including superconducting fluctuations as a seed for the growth of superconducting order we can obtain a satisfactory agreement of the theory with the experiment. Remarkably, the pseudogap excitations apparently play no role in this process.The study of the time evolution of complex systems through symmetry breaking transitions (SBT) is of great fundamental interest in different areas of physics [1][2][3]. An SBT of particular general interest is the normal-tosuperconducting (N → S) state transition in which a Lorentz non-invariant system breaks gauge invariance. [4] By studying the N → S transition in time-evolving systems, rather than by slowly varying the temperature through the transition, one can in principle gain new information on the dynamical behavior of elementary excitations which lead to the formation of a superconducting condensate and the collective ordering behavior, leading to new insights into non-ergodic phenomena of collectively ordered systems as well as the mechanism of superconductivity. Particularly, ergodicity breaking in rapidly evolving systems leads to the appearance of topological defects (vortices).The description of the dynamical behavior of the gauge non-invariant systems is given in the timedependent Ginzburg-Landau theory (TDGL theory). It has been first applied to the problem of non-equilibrium phase transitions by Kibble and Zurek who considered the appearance of topological defects throughout the transition.[5, 6] The Kibble-Zurek description has been indirectly confirmed to be correct by static experiments in which trapped vortices were studied. [7,8] In this paper, beyond previous static studies, we study realtime evolution of the superconducting order in the nonequilibrium phase transition. We investigate the applicability of TDGL theory to the phase transition problem and provide a minimal formulation sufficient to describe the data.The paper is organized in the following way: we ...

Dynamics of superconducting order parameter through ultrafast normal-to-superconducting phase transition in Bi2Sr2CaCu2O8+δ

“…To overcome this problem the standard two-pulse all-optical pump-probe technique was extended to a multi-pulse technique, which was shown to be instrumental in extracting the order parameter dynamics in a charge density wave compound 20 as well as in the prototypical cuprate superconductor 21 . Here we extend our previous study 21 of an ultrafast S→N→S transition in La 1.9 Sr 0.1 CuO 4 to Bi 2 Sr 2 CaCu 2 O 8+δ in search of universality, and also to uncover potential imporant differences in the two materials with substantially different critical temperatures and pseudogap/SC gap ratios. By means of the all-optical multi-pulse technique combined with the polarization selective optical probe we were able to separate the SC state recovery dynamics from the previously studied 22 PG state recovery dynamic and enable discrimination between relaxation in the nodal and anti-nodal BZ regions.…”

“…3c in Ref. [21]). The magnitude of the initial order parameter corresponds to the magnitude of the frozen SC fluctuations after the quench from the normal/PG to the SC state which is a function of the depth-dependent quenchrate (Eq.…”

“…(4) in Ref. [21]). In LSCO even better fit is possible using a phenomenological depth-dependent initial order parameter ψ BC (z):…”

“…In previous study 21 of the SC-order recovery in LSCO we have shown that the TDGL theory fails to consistently describe the ultrafast optical destruction of the SC condensate. On the other hand, the SC condensate recovery can be quantitatively modeled using a phenomenological response function and the Ginzburg-Landau time, τ GL , as the only free fit parameter assuming a finite magnitude of the initial depth-dependent order parameter (Fig.…”

“…As in the case of (La,Sr)CuO 4+δ (LSCO), we attribute the suppression of γ during the first part of the recovery to the critical slowing down of the SC fluctuations in the vicinity of the transition. 21 Upon the initial increase γ decreases on the nanosecond timescale indicating cooling of the probed volume: Since the effective temperature on longer timescales is far from the critical temperature the T -dependence of γ is no longer critical but determined by the Rothwarf-Taylor bottleneck dynamics.…”