Ultrafast decoupling of the pseudogap from superconductivity in a pressurized cuprate

Abstract: The relationship between the pseudogap and superconductivity remains a central puzzle in the physics of cuprates. Hydrostatic pressure provides a clean tuning parameter free from chemical disorder, yet probing the microscopic energy scales of these phases under compression has remained experimentally challenging. Here, we utilize ultrafast optical spectroscopy to construct the high-pressure phase diagram of the underdoped cuprate Bi$2$Sr$_2$CaCu$_2$O${8+δ}$ up to 37 GPa. Our results reveal a striking dichotomy within the pseudogap state: while the onset temperature $T^*$ rises monotonically with pressure, the energy gap $Δ{\mathrm{PG}}$ is continuously suppressed. In contrast, the critical temperature $T{\mathrm{c}}$ and the superconducting gap $Δ{\mathrm{SC}}$ trace a correlated dome-like trajectory, demonstrating that superconductivity evolves independently from the pseudogap. Furthermore, an abrupt collapse of the gap ratio $2Δ{\mathrm{SC}}/k_{\mathrm{B}}T_{\mathrm{c}}$ near 8 GPa marks a pressure-driven dimensional crossover, quenching two-dimensional phase fluctuations to stabilize global three-dimensional coherence. Upon reaching 37 GPa, the superconducting condensate is completely quenched into an insulating-like state. By resolving the extended phase evolution, our findings disentangle the pseudogap and superconducting orders, establishing a rigorous experimental basis for the pairing mechanism of high-temperature superconductivity.

• The paper demonstrates that while the pseudogap onset temperature (T*) increases with pressure above 14 GPa, the pseudogap energy gap (∆PG) is steeply suppressed.
• The study reveals a pressure-induced transition from 2D fluctuating superconductivity to 3D phase coherence, marked by a collapse of the superconducting coupling ratio near 8 GPa.
• The research employs ultrafast pump-probe spectroscopy in a diamond anvil cell to temporally resolve competing relaxation channels, establishing a two-gap scenario in underdoped Bi2212.

Ultrafast Decoupling of the Pseudogap from Superconductivity in Pressurized Bi2212

Introduction and Motivation

Understanding the interplay between the pseudogap (PG) phase and superconductivity (SC) in cuprate high-temperature superconductors remains a central, unresolved issue. A major challenge is the presence of disorder and impurity scattering when the phase diagram is mapped using chemical doping, which obscures the intrinsic relationship between ordering phenomena in the CuO$_2$ planes. This work deploys hydrostatic pressure as a clean tuning parameter for underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi2212), enabling modulation of the electronic structure without introducing extrinsic disorder. By leveraging ultrafast pump-probe spectroscopy within a diamond anvil cell, the study achieves spectrally sensitive, time-resolved measurement of quasiparticle relaxation dynamics in the high-pressure regime inaccessible with conventional probes.

Experimental Approach

A two-color ultrafast optical spectroscopy setup was integrated with a diamond anvil cell to probe the non-equilibrium quasiparticle dynamics in high-quality single crystals of underdoped Bi2212 across a pressure range up to 37 GPa and a temperature range from 20 K to 300 K. The transient reflectivity response is decomposed using a bi-exponential model to temporally resolve relaxation channels associated with the pseudogap and superconductivity: a fast, positive component (APG) is attributed to PG dynamics, while a slower, negative component (A$_\text{SC}$) is assigned to the superconducting condensate. The extracted amplitudes and associated lifetimes across pressures and temperatures provide direct access to the evolution of T*, T$_c$, ∆$_\mathrm{PG}$, and ∆$_\mathrm{SC}$ in the high-pressure phase diagram.

Key Findings

Decoupling of Pseudogap and Superconductivity Under Pressure

A principal result is the experimental demonstration that the temperature onset of the pseudogap (T*) rises monotonically with pressure, exceeding 300 K above 14 GPa, while simultaneously, the magnitude of the pseudogap energy gap (∆$_\mathrm{PG}$) is continuously and steeply suppressed. In contrast, both the superconducting critical temperature (T$_2$0) and the superconducting gap (∆$_2$1) exhibit a non-monotonic, dome-like evolution: both reach a maximum at intermediate pressures (peaking near 98 K at 6 GPa) before declining and ultimately vanishing between 29 and 37 GPa where the system transitions into an insulating-like state.

This result violates the canonical scaling observed under chemical doping, where T* and ∆$_2$2 scale together and both decline with increased carrier concentration. Under hydrostatic pressure, T* and ∆$_2$3 are decoupled, with T* increasing despite a higher in-plane hole concentration, confirmed by independent Seebeck measurements.

Dimensional Crossover and Coupling Ratio Evolution

A notable abrupt decrease in the superconducting coupling ratio $_2$4 is observed near 8 GPa: below 6 GPa, the ratio is $_2$510, characteristic of strong underdoped correlations and pronounced phase fluctuations; between 6 and 11 GPa, it rapidly collapses to $_2$65 and approaches the d-wave weak-coupling BCS limit with further pressure. This marks a transition from two-dimensional (2D) phase fluctuating superconductivity to three-dimensional (3D) phase coherence, attributed to enhanced interlayer hopping and the recovery of antinodal spectral weight as ∆$_2$7 is reduced.

Spectral Competition and Two-Gap Scenario

Temporal separation of the relaxation channels supports a two-gap scenario over a single-gap preformed-pair paradigm. In the low-pressure regime, the growth of A$_2$8 at the superconducting transition occurs in conjunction with the attenuation of APG, indicating a direct competition for low-energy spectral weight. At high pressure, superconductivity is quenched while the pseudogap component persists, reinforcing the view that the two orders arise from distinct microscopic degrees of freedom and supporting a model of competing, rather than precursor, orders.

Pressure-Induced Evolution of the Normal State

Pressure-driven shrinkage of Cu–O plane spacing increases the hopping integral $_2$9, thereby enhancing the superexchange $_2$0 ($_2$1) without appreciably altering the on-site repulsion $_2$2. This strengthens local magnetic correlations (reflected in T*), but the bandwidth broadening lowers the effective correlation parameter $_2$3, driving the collapse of ∆$_2$4 and favoring coherent metallicity. At high enough pressure, out-of-plane charge transfer and orbital filling induce strong Coulomb repulsion and density-of-states depletion near the Fermi level, promoting the observed insulating-like ground state.

Implications and Future Directions

The spectroscopic disentanglement of pseudogap and superconducting order parameters under pressure directly constrains theoretical models of cuprate pairing. The violation of universal scaling between T*, ∆$_2$5, and hole doping underlines the role of pressure as a fundamentally different tuning parameter compared to chemical composition. These results suggest pseudogap and superconducting orders are not simply fluctuating versions of the same ground state but have different controlling variables: the pseudogap is correlated with spin exchange (local magnetism), while superconductivity is tuned by electronic itinerancy and phase stiffness.

The experimentally resolved pressure-driven dimensional crossover is likely to have ramifications for understanding the emergence of global phase coherence in other layered correlated systems. The observation of an insulating-like state at the highest pressures also invites comparison to pressure-induced metal-insulator transitions and Fermi surface reconstructions in other oxides.

Prospective future work could extend ultrafast spectroscopic approaches to higher pressures, doping levels, and other cuprate families, as well as pursue joint measurements (e.g., Raman, ARPES, and X-ray spectroscopy) to further dissect intertwined correlations. The role of interlayer tunneling and spectral weight transfer at the antinodes under external control parameters is a compelling avenue for investigating universal mechanisms in unconventional superconductors.

Conclusion

This study establishes, via ultrafast optical spectroscopy under hydrostatic pressure, a comprehensive phase diagram for underdoped Bi2212, convincingly decoupling the pseudogap and superconducting phenomena. The monotonic increase of T* concurrent with the suppression of ∆$_2$6, as well as the independent, dome-like behavior of T$_2$7 and ∆$_2$8, challenge single-gap precursor models. The pressure-tuned crossover from 2D fluctuating to 3D coherent superconductivity, and ultimately to a pressure-induced insulating state, provides rigorous experimental constraints for models of high-T$_2$9 pairing. These findings sharpen the distinction between spin- and charge-sector dynamics in cuprates and will inform both phenomenological and microscopic approaches to the mechanism of high-temperature superconductivity.