Anisotropic time-domain electronic response in cuprates driven by midinfrared pulses

F. Giusti, A. Montanaro, A. Marciniak, F. Randi, F. Boschini, F. Glerean, G. Jarc, H. Eisaki, M. Greven, A. Damascelli, A. Avella, and D. Fausti

Phys. Rev. B 104, 125121 – Published 14 September 2021

Abstract

Superconductivity in the cuprates is characterized by an anisotropic electronic gap of $d$ -wave symmetry. The aim of this work is to understand how this anisotropy affects the nonequilibrium electronic response of high- $T_{c}$ superconductors. Here we use a polarization selective time domain experiment to address the dynamics of electronic excitation of different symmetry in optimally doped ${Bi}_{2} {Sr}_{2} Y_{0.08} {Ca}_{0.92} {Cu}_{2} O_{8 + δ}$ and measure the nodal and antinodal nonequilibrium response resulting from photoexcitations with ultrashort pulses with photon energy comparable to the superconducting gap. The response to long wavelength photoexcitation with pump polarization along the Cu-Cu axis of the sample is discussed with the support of an effective $d$ -wave BCS model which suggests that such transient response could be ascribed to an increase of pair coherence in the antinodal region.

Received 10 December 2020
Revised 24 August 2021
Accepted 25 August 2021

DOI:https://doi.org/10.1103/PhysRevB.104.125121

Physics Subject Headings (PhySH)

Electronic structure Impurities in superconductors Nonlinear optics Superconducting fluctuations Superconducting gap Superconducting phase transition

Cuprates High-temperature superconductors

Infrared spectroscopy Methods in superconductivity

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

F. Giusti ¹, A. Montanaro ¹, A. Marciniak ¹, F. Randi ², F. Boschini ^3,4, F. Glerean¹, G. Jarc¹, H. Eisaki ⁵, M. Greven⁶, A. Damascelli³, A. Avella ⁷, and D. Fausti^1,*

¹Department of Physics, Università degli Studi di Trieste, 34127 Trieste, Italy and Elettra Sincrotrone Trieste S.C.p.A., 34127 Basovizza, Trieste, Italy
²Joseph Henry Laboratories of Physics, Princeton University, Princeton, New Jersey 08544, USA
³Quantum Matter Institute, University of British Columbia, Vancouver, BC, Canada V6T 1Z4 and Department of Physics & Astronomy, University of British Columbia, Vancouver, BC, Canada V6T 1Z1
⁴Centre Énergie Matériaux Télécommunications, Institut National de la Recherche Scientifique, Varennes, Québec, Canada J3X1S2
⁵Nanoelectronics Research Institute, National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568, Japan
⁶School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
⁷Dipartimento di Fisica “E.R. Caianiello,” Università degli Studi di Salerno, I-84084 Fisciano (SA), Italy and CNR-SPIN, UOS di Salerno, I-84084 Fisciano (SA), Italy

^*daniele.fausti@elettra.eu

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Vol. 104, Iss. 12 — 15 September 2021

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Figure 1
Polarization selection. Left column: sensitivity to the excitations in the first Brillouin zone for different Raman symmetries [(a) $A_{1 g}$ , (c) $B_{2 g}$ , and (e) $B_{1 g}$ )]. They represent the weightings $K_{i} (k)$ of the light-scattering transition for polarization orientations transforming as the three considered symmetries in a $D_{4 h}$ crystal [14], and they are defined as (a) $K_{A 1 g} (k) = 0.5 [\cos (k x) + cos (k x)]$ , (c) $K_{B 1 g} (k) = 0.5 [\cos (k x) - cos (k x)]$ , and (e) $K_{B 2 g} (k) = 0.5 [\sin (k x) - \sin (k x)]$ . Right column: results of the pump-probe experiment at $T = 80 K$ (below $T_{c}$ ) for different excitation fluences. (b) No polarization selection (the dominant contribution is $A_{1 g}$ ), (d) $B_{1 g}$ , and (f) $B_{2 g}$ . Three excitation fluences are considered: $0.09 mJ c m^{- 2}$ (blue line) corresponds to the commonly dubbed “linear” response regime, whereas 0.2 and $0.5 mJ c m^{- 2}$ (green and red line, respectively) refer to the “nonlinear” response regime associated with strong perturbation of the SC gap. The inset of panels (d,f) represent sketches of the Cu-O layer of cuprates (the orange dots represent the Cu atoms and the gray ones the oxygen atoms) and the polarization of the incoming and selected probe beams (arrows).
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Figure 2
Measurement correspondence. Correspondence between “standard” pump-probe polarization configurations used to measure $B_{1 g}$ and $B_{2 g}$ signals (on the left) and birefringence measurements (on the right). The colored dots on the left represent the copper (orange) and oxygen (gray) atoms, whereas the arrows show the polarization of the incoming probe beam and the polarization selection after the sample. In the right panel the polarizations of the birefringence measurement are shown: The black line represents the incoming probe and the gray ones the two final polarization selections after the sample.
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Figure 3
Measurement comparison. Comparison between a pump-probe measurement performed in $B_{2 g}$ configuration (orange line) and a birefringence measurement (black line, obtained by subtracting the polarization components along the Cu-Cu axes), both in superconducting phase (a), (c) and in pseudogap (b),(d). The measurements have been performed in two different pump fluence regimes [ $0.2 mJ / c m^{2}$ in (a), (b) and $1.3 mJ / c m^{2}$ in (c), (d)]. The signals have been rescaled in order to verify the proportionality between the two measurements.
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Figure 4
Temperature dependence for different pump photon energies. Temperature-dependent pump-probe measurements, in $B_{2 g}$ and $B_{1 g}$ configurations, at low fluence ( $0.09 mJ c m^{- 2}$ ). Top row: $B_{2 g}$ measurements with photoexcitation energies of (a) 170 and (c) 70 meV. Panels (b,d) display the values of $γ (T)$ and $η (T)$ [Eq. (2)] obtained from the data in (a), (c), respectively. The dashed gray lines highlight the critical temperature $T_{c}$ . Bottom row (e)–(h): same analysis for measurements in the $B_{1 g}$ configuration.
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Figure 5
High-fluence measurements. Temperature-dependent pump-probe measurements, in $B_{2 g}$ and $B_{1 g}$ configurations, with high fluence excitations ( $0.4 mJ c m^{- 2}$ ). First row: $B_{2 g}$ measurements with different excitation photon energies [(a) 170 and (c) 70 meV]. The graphs (b), (d) display the values of γ(T) and η(T) [Eq. (6)] obtained from the data in (a), (c), respectively. The dashed gray lines represent the critical temperature $T_{c}$ . The bottom row (e)–(h) shows the same analysis for measurements in the $B_{1 g}$ configuration.
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Figure 6
Theoretical effective model. In (a), (b), the dynamics of $λ_{i} = \int_{BZ} | Λ (k) | \cdot | K_{i} (k) | d k$ and $ϕ_{i} = | \int_{BZ} Λ (k) \cdot K_{i} (k) d k |$ are displayed, where $i = A_{1 g}, B_{1 g}, B_{2 g}$ and $K_{i} (k)$ represent the weightings of the light-scattering transition defined in Fig. 1. The blue line represents the $A_{1 g}$ selection, the orange line the $B_{1 g}$ one, and the green curve the $B_{2 g}$ one. The dashed line shows the time evolution of the pump pulse. In (c), (d), random noise with amplitude $δ = π$ was added to the pair operator phase, in order to simulate an initial pseudogap state. In (e)–(j) the noise dependence of three quantities λ in blue, ϕ in orange, and the superconducting gap with the red diamonds) is analyzed for two time delays: at the equilibrium (e)–(g) and immediately after the pump excitation (h)–(j).
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