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

I. Madan, P. Kusar, V. V. Baranov, M. Lu-Dac, V. V. Kabanov, T. Mertelj, and D. Mihailovic

Phys. Rev. B 93, 224520 – Published 30 June 2016

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 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 ${La}_{1.9} {Sr}_{0.1} {CuO}_{4}$ and compare the data to a simulation based on the time-dependent Ginzburg-Landau theory, using the 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 the 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.

Received 17 January 2016
Revised 4 June 2016

DOI:https://doi.org/10.1103/PhysRevB.93.224520

Physics Subject Headings (PhySH)

High-temperature superconductors

Reflectivity Time-dependent Ginzburg-Landau theory Ultrafast pump-probe spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

I. Madan^1,2,*, P. Kusar¹, V. V. Baranov^1,3, M. Lu-Dac¹, V. V. Kabanov¹, T. Mertelj^1,4, and D. Mihailovic^1,2,4

¹Complex Matter Department, Jozef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
²Jozef Stefan International Postgraduate School, Jamova 39, 1000 Ljubljana, Slovenia
³Department of Physics, University of Antwerp, Groenenborgerlaan 171, 2020 Antwerp, Belgium
⁴CENN Nanocentre, Jamova 39, 1000 Ljubljana, Slovenia

^*Corresponding author: ivan.madan@ijs.si

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Issue

Vol. 93, Iss. 22 — 1 June 2016

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Images

Figure 1
(a) The system trajectory (depicted by the silver ball) in a temporally evolving potential. In the rapid quench scenario (A), the potential changes faster than the system can follow. The opposite is true in the slow quench scenario (B). (b) A schematic diagram of the pulse sequence. The time delays $Δ t_{D - P}, Δ t_{D - pr}$ and $Δ t_{P - pr}$ refer to delays between the D, $P$ and pr pulses depicted in blue, red and green respectively. The $S / N$ phase boundary moves with velocity $v_{ψ}$ towards the surface. Vortices are created in the wake of the temperature front whose position is given by $T (r, t) = T_{c}$ .
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Figure 2
(a) The transient reflectivity $Δ R / R$ for ${La}_{1.9} {Sr}_{0.1} {CuO}_{4}$ at 4 K as a function of $Δ t_{P - pr}$ , for different $Δ t_{D - P}$ . The D pulse fluence is $F_{D} = 12 μ J / {cm}^{2}$ , which is approximately three times above the destruction threshold $(F_{T} ≃ 4.2 μ J / {cm}^{2})$ [12]. The red shaded curve indicates the pseudogap signal measured above $T_{c}$ . (b) Superconducting component extracted from data in (a) by subtracting $Δ t_{D - P} = 0.2$ ps line. This dataset is used to extract the evolution of the initial quasiparticle decay rate. (c) Black squares—the amplitude of the superconducting component $A_{S}$ extracted from (a) after subtraction of the PG. The blue squares are $1 / τ_{QP}$ as a function of $Δ t_{D - P}$ . The recovery of the system is schematically divided into phase transition region (blue background) where order parameter is not thermal, and into the thermal diffusion (orange background) where the transition is effectively over and order parameter is defined solely by the temperature.
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Figure 3
Comparison of experimentally measured data [circles, values of fluence are 4 (black), 9 (red), 12 (green), 18 (blue), 24 (cyan), and 34 (magenta) $μ J / {cm}^{2}]$ and the calculated $A_{S}$ obtained within different formulations of the problem (solid lines): the TDGL solution with the initial conditions described by (a) $ψ (0, z) = \sqrt{1 - T_{bath} / T_{c}}$ , (b) Eq. (3), (c) Eq. (4) (represented in Fig. 5), (d) $ψ_{fluc} (0, z) = κ z$ .
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Figure 4
Three surfaces showing the calculated time evolution of the logarithm of $T_{e}$ (yellow), $T_{p}$ (blue), and $T_{L}$ (green) as a function of incident fluence. The initial temperature of the sample is 4 K. $T_{p}$ and $T_{L}$ are very close, but $T_{e}$ reaches in excess of 400 K. The blue lines correspond to fluences used in the experiment. The red lines indicate where $T_{e}, T_{p}$ , and $T_{L}$ cross $T_{c} = 28$ K. $T_{e}$ is used in the modeling of the order parameter. Fast quench corresponds to $F < 5 F_{th} ≃ 23 μ J / {cm}^{2}$ .
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Figure 5
The initial conditions that take into account fluctuations of the order parameter according to Eq. (4) (blue surface) and the partially suppressed (yellow surface) order parameter in the region $F (z) < F_{T}$ in agreement with Eq. (3). The flat region near $z = 0$ at $F / F_{T} > 4$ corresponds to the slow quench conditions.
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