[Paper Review] Revealing strong coupling of collective modes between superconductivity and pseudogap in cuprate superconductor by terahertz third harmonic generation

J. Y. Yuan, Lianping Shi+22 more|arXiv (Cornell University)|Nov 13, 2022

Physics of Superconductivity and Magnetism4 citations

TL;DR

This study uses terahertz third harmonic generation (THG) spectroscopy to reveal strong dynamical coupling between the Higgs mode in superconductivity and a collective mode in the pseudogap phase of YBa₂Cu₃O₆₊ₓ thin films. A beating structure in the real-time THG waveform near Tc, along with spectral splitting of 16% in frequency, provides direct evidence of strong coupling, indicating the pseudogap is a distinct phase rather than a precursor to superconductivity.

ABSTRACT

The study of interaction between different degrees of freedom in solids is of fundamental importance to understand the functionalities of materials. One striking example of such interaction is the intertwined coupling or competition between superconductivity (SC), charge density wave (CDW), pseudogap state (PG), and other exotic phases in cuprate superconductors. Recent emergence of nonlinear Terahertz (THz) third harmonic generation (THG) spectroscopy provides a powerful tool for exploring the collective (Higgs) modes of superconductivity order parameters, and its interaction with intertwined/competing phases. In this study, we report on nonlinear THz THG spectroscopy of the YBa$_2$Cu$_3$O$_{6+x}$ (YBCO) thin films with different doping. We identify a characteristic temperature $T_{THG}$, below which third order suscepetility $χ^{(3)}$ emerges. Notably, the $T_{THG}$ is coincident with the crossover temperature $T^*$ of pseudogap in a wide range doping of phase diagram. Upon entering the superconducting state, THG increases sharply but exhibits an abnormal dip feature near $T_c$ which is more clearly seen in optimally doped sample. Strikingly, we observe a beating structure directly in the measured real time waveform of THG signal. Fourier transformation of the time domain waveform gives two separate modes below and above original THG frequency. The observation strongly indicates that an additional mode, presumably Higgs mode, appears at $T_c$ and couples to the mode already developed below $T^*$. The strong coupling effect offers new insight into the interplay between superconductivity and pseudogap. The result unambiguously suggests that the pseudogap phase is not a precursor of superconductivity but represents a distinct order.

Motivation & Objective

• To investigate the interplay between superconductivity and the pseudogap phase in cuprates using nonlinear terahertz spectroscopy.
• To determine whether the pseudogap state is a precursor to superconductivity or a distinct broken-symmetry phase.
• To probe collective modes in the superconducting and pseudogap states via third harmonic generation in the terahertz regime.
• To identify the nature of the observed nonlinear response and its temperature dependence across the phase diagram.
• To explore the role of strong coupling between Higgs mode and pseudogap collective mode in driving nonlinear optical responses.

Proposed method

• Employed terahertz third harmonic generation (THG) spectroscopy on YBa₂Cu₃O₆₊ₓ thin films with varying doping levels.
• Conducted temperature-dependent THG measurements to track the emergence of nonlinear susceptibility χ⁽³⁾.
• Analyzed real-time waveforms of the THG signal to detect beating patterns indicative of coupled oscillations.
• Performed Fourier transformation of time-domain THG signals to resolve frequency components and extract splitting.
• Used polarization-dependent measurements to assess the symmetry of the hybridized modes.
• Correlated the onset temperature of THG (T_THG) with established phase transition temperatures (T*, Tc) across the doping phase diagram.

Experimental results

Research questions

• RQ1 Is the pseudogap phase a precursor to macroscopic superconductivity or a distinct broken-symmetry phase?
• RQ2 What is the nature of the collective mode observed in the pseudogap regime and how does it couple to the superconducting Higgs mode?
• RQ3 Does the observed beating pattern in the THG waveform near Tc indicate strong dynamical coupling between two distinct modes?
• RQ4 How does the strength of coupling between the Higgs mode and pseudogap mode vary with doping and temperature?
• RQ5 What is the microscopic origin of the third harmonic signal in the normal state above Tc, and is it related to charge density fluctuations?

Key findings

• A characteristic temperature T_THG was identified below which third-order susceptibility χ⁽³⁾ emerges, coinciding with the pseudogap crossover temperature T* across a wide doping range.
• The THG signal increases sharply upon entering the superconducting state but exhibits an abnormal dip near Tc, most clearly observed in the optimally doped sample.
• A beating structure was directly observed in the real-time THG waveform near Tc, indicating coherent coupling between two oscillating modes.
• Fourier analysis revealed two distinct frequency components below and above the original THG frequency, confirming the presence of a hybridized mode.
• The spectral splitting Δω/ω reached 16%, indicating a remarkably strong coupling between the Higgs mode and the pseudogap collective mode.
• The polarization dependence of the hybridization is isotropic, consistent with the isotropic nature of both the Higgs mode and the pseudogap response.