Photoenhanced metastable c-axis electrodynamics in stripe-ordered cuprate La1.885Ba0.115CuO4.

Quantum materials are amenable to nonequilibrium manipulation with light, enabling modification and control of macroscopic properties. Light-based augmentation of superconductivity is particularly intriguing. Copper-oxide superconductors exhibit complex interplay between spin order, charge order, and superconductivity, offering the prospect of enhanced coherence by altering the balance between competing orders. We utilize terahertz time-domain spectroscopy to monitor the c-axis Josephson plasma resonance (JPR) in La2-xBaxCuO4 (x = 0.115) as a direct probe of superconductivity dynamics following excitation with near-infrared pulses. Starting from the superconducting state, c-axis polarized excitation with a fluence of 100 μJ/cm2 results in an increase of the far-infrared spectral weight by more than an order of magnitude as evidenced by a blueshift of the JPR, interpreted as resulting from nonthermal collapse of the charge order. The photoinduced signal persists well beyond our measurement window of 300 ps and exhibits signatures of spatial inhomogeneity. The electrodynamic response of this metastable state is consistent with enhanced superconducting fluctuations. Our results reveal that La2-xBaxCuO4 is highly sensitive to nonequilibrium excitation over a wide fluence range, providing an unambiguous example of photoinduced modification of order-parameter competition.

High-temperature superconductivity in the cuprates can coexist or compete with a multitude of other phenomena, including charge and spin order, pair density waves, and the pseudogap (1–4), all of which have observable signatures in the linear or transient electrodynamic response (5). A key question for the cuprates is the extent to which the underlying interactions can be manipulated to alter the macroscopic properties. Ultrafast pump–probe spectroscopy provides a unique means to initiate and interrogate nonequilibrium dynamics and property control in superconductors (6, 7).

Evidence of transiently enhanced interlayer tunneling has been reported in several cuprates following selective phonon pumping (8–10) or intense near-infrared excitation (11). In these experiments, the c-axis Josephson plasma resonance (JPR) serves as a reporter of the interlayer tunneling which, in general, scales with the superfluid spectral weight (12). Upon applying intense near-infrared pump excitation starting above the transition temperature Tc, Nicoletti et al. (11) observed a blueshift of the plasma resonance relative to the below Tc equilibrium response. The plasma resonance decayed after several picoseconds and was interpreted in terms of transient superconductivity. Similar dynamics were subsequently observed in both La2−xBaxCuO4 and YBa2Cu3O6+x over a range of doping levels and excitation conditions. More recently, in La2−xBaxCuO4 (x = 0.095), a longer-lived (>50 ps) collective response was observed subsequent to photoexcitation at T < Tc in which the JPR appeared to split into 2 distinct longitudinal modes (13), reminiscent of the static electrodynamic response in bilayer cuprates (14–16). Further, no pump-induced effect was observed above Tc. Notably, the x = 0.095 material does not exhibit robust charge or stripe order (17).

In this report, we clarify the details of the photoinduced order parameter control in the cuprates, by performing temperature and fluence-dependent c-axis measurements on materials with equilibrium signatures of phase competition. We present near-infrared pump, THz probe experiments of La2−xBaxCuO4 (x = 0.115), for which we observe distinct dynamics above and below Tc. The doping x = 0.115 is close to the anomalous x = 1/8 composition where 3D superconductivity is maximally suppressed by robust charge and stripe order (2, 18–20). At x = 0.115, charge order, spin order, and 3D superconductivity onset at Tco = 53 K, Tso = 40 K, and Tc = 13 K, respectively (17). In this compound Tc is high enough to enable initiating dynamics from within the superconducting state. The La1.885Ba0.115CuO4 crystal was cut and polished to expose the a-c plane with a large area of 5 mm × 5 mm. Temperature-dependent Fourier transform infrared spectroscopy (FTIR) measurements were carefully performed to provide a baseline static characterization of the electrodynamic response (see for details).

The static and dynamic reflectivity of LBCO were measured as a function of temperature and fluence using terahertz time-domain spectroscopy (0.15 to 2 THz). As shown in Fig. 1, both the near-infrared pump (1.55 eV) and the THz probe pulses are polarized along the c axis. The static THz reflectivity is plotted in Fig. 1, showing a flat response at 30 K (gray line, with a slight upturn below 0.5 THz). In the superconducting state (7 K, blue curve) a sharp reflectivity edge emerges around 200 GHz, a hallmark of the interlayer JPR effect in agreement with previous studies for this doping (11).

Fig. 1.

(A) Schematic of the 1.55-eV pump THz probe experiment on LBCO crystal with pump and probe polarization along c axis. The illustration depicts the superconducting state with electron pairs tunneling along the c axis. (B) Equilibrium THz reflectivity above and below TC at 30 and 7 K, respectively. The dotted line is beyond our experimentally accessible spectral range and is a guide to the eye. (C) Time-dependent relative change in the THz electric field amplitude after excitation at various pump fluences (at 7 K). (D) Temperature versus hole doping phase diagram of L2−xBaxCuO4. Adapted with permission from ref. 17. Regions of the phase diagram include bulk superconductivity (SC) at onset temperature Tc, spin ordering (SO) at temperature Tso, charge ordering at Tco, and low-temperature structural transition TLT. The initial temperature at 7 K for x = 0.115 is plotted in red, and the color dots mark the estimated lattice temperature after pump excitation and e-ph thermalization has occurred (colors corresponding to pump fluences shown in C).

For the dynamics measurements, we first performed 1-dimensional scans, where the photoinduced change in the peak electric field of the single-cycle THz pulse (ΔE/E) is measured as a function of pump-probe delay. These raw unprocessed data unambiguously highlight important features of the electrodynamic response. Fig. 1 plots 1-dimensional scans (ΔE/E peak scans) for various fluences, starting from an initial temperature of 7 K, well into the superconducting state. The dynamics exhibit a long-lived response with an initial risetime of several picoseconds. The magnitude of the ΔE/E signal slightly increases from 50 to 100 μJ/cm2, followed by a strong decrease in amplitude at higher fluences up to 760 μJ/cm2. The observed fluence dependence indicates dynamics that are distinct from a photoinduced decrease in the condensate density with a commensurate increase in the quasiparticle density. In that scenario, ΔE/E would increase in magnitude with increasing fluence.

Calculations using the 2-temperature model of the initial electron-phonon (e-ph) thermalization (see for details) indicate a rise in the final temperature that increases with fluence (after several picoseconds when the plateau in the data in Fig. 1 is reached). Fig. 1 displays the phase diagram of LBCO (reproduced from ref. 17) with color-coded dots (corresponding to the fluences used in Fig. 1) indicating the final temperature after thermalization. Clearly, the amplitude of ΔE/E decreases with increasing fluence as Tco is approached after the initial e-ph thermalization. This indicates that the strongest photoinduced response occurs for fluences that do not heat the sample above Tco. We refer to 50 to 380 µJ/cm2 as the low-fluence regime where the quasiequilibrium temperature stays below Tco. The data in Figs. 2 and 3 reveal that the dynamics are dramatically different for low- and high-fluence (>380 µJ/cm2) regimes spanning Tco. The difference in dynamics is evident in Fig. 1, where the 760-μJ/cm2 data exhibit an exponential decay in contrast to the plateau apparent in the low-fluence data.

Fig. 2.

Extracted c-axis THz optical properties of LBCO at different pump–probe delays after photoexcitation (colored) with 100 µJ/cm2 and at equilibrium (gray). All data have been taken at 7 K below TC except for the green curves in A and F which were taken at 20 K. (A) Reflectivity at 7 K before (gray) and after photoexcitation (colored) at different pump–probe delays. Plotted in green is the equilibrium (dotted) reflectivity and largest photoinduced change (solid) in reflectivity at 20 K. (B) Loss function −Im(1/ε). Dashed gray line is beyond our spectral resolution and is a guide to the eye. (C) Spectral evolution of the loss function after photoexcitation. (D and E) Real and imaginary parts of the THz conductivity. (F) Peak of ΔE/E THz transient after photoexcitation at 7 and 20 K.

Fig. 3.

Extracted c-axis THz optical properties of LBCO at different pump–probe delays after photoexcitation (colored) with 9 mJ/cm2 and at equilibrium (gray). All data taken at 30 K above TC and below TCO. (A) Reflectivity and (B) loss function, −Im(1/ε) at different pump–probe delays. (C) Spectral evolution of the loss function after photoexcitation. (D and E) Real and imaginary parts of the THz conductivity at different pump–probe delays. (F) Time-dependent relative changes in THz electric field after photoexcitation. (Inset) Display of maximum ΔE/E value at 30 K as a function of pump fluence.

We now discuss the full spectroscopic response of the dynamics, considering first low-fluence optical excitation of LBCO (100 μJ/cm2) obtained starting from an initial temperature of 7 K. The optical properties of the photoexcited region were extracted using a layered model to account for the penetration depth mismatch between the pump and probe beams (see ). Fig. 2 shows the photoinduced reflectivity (blue curve at 10 ps, red curve at 300 ps), revealing a large reflectivity increase extending out to 1 THz, corresponding to an increase in the plasma frequency from ∼0.2 to 0.9 THz. This is more clearly revealed in Fig. 2 showing the loss function −Im(1/ε) (where ε = ε1 +iε2 is the c-axis dielectric response) which peaks at the plasma frequency. Importantly, there is no sign of decay of the photoinduced state over the measured temporal window, indicating a metastable state that persists beyond 300 ps. Fig. 2 show the associated c-axis optical conductivity (σ = σ1 + iσ2) highlighting an important observation. Namely, there is a peak in σ1 at 0.3 THz signifying dissipation in the c-axis THz transport. In contrast, in equilibrium for a superconductor, σ1 at frequencies greater than zero but less than twice the superconducting gap approaches zero (solid gray line in Fig. 2). This origin of the peak in σ1 arising after photoexcitation will be discussed below. Finally, the solid green line in Fig. 2 shows the spectral response at 10 ps delay for a fluence of 100 μJ/cm2 taken at an initial temperature of 20 K––that is, above Tc. There is an increase in the reflectivity, arguably with the development of a weak plasma edge. However, as shown in Fig. 2, the response is much smaller and shorter lived in comparison to dynamics initiated from within the superconducting state. In short, the emergence of a robust metastable state upon low-fluence photoexcitation requires starting from the superconducting state while remaining below Tco after e-ph thermalization.

To complete the data discussion, we now consider the high-fluence dynamics. Fig. 3 shows the spectroscopic results for high-fluence excitation at 9 mJ/cm2 which leads to a final temperature greater than Tco. Fig. 3 reveals an increased reflectivity starting from an initial temperature of 30 K. At early times a broad peak emerges in the loss function (shown in Fig. 3 ) that rapidly broadens and decays on an ∼10-ps timescale. There is a corresponding increase in σ1 and σ2 (Fig. 3 ), although there are no well-defined peaks as for the low-fluence results. Fig. 3 reveals the rapid decay in the transient ΔE/E with 9-mJ/cm2 excitation, with the inset showing a saturation of the dynamics with increasing fluence. The plateau in the ΔE/E scans following the initial exponential decay is presumably associated with heating, leading to a broad and featureless optical conductivity from 0.1 to 1.5 THz. The broadened plasma edge that appears after the arrival of the pump pulse is qualitatively in agreement with the previous study by Nicoletti et al. (11). Given the relatively small value of σ1, this could indicate the presence of enhanced superconducting correlations associated with the unambiguous transient blueshift of the plasma frequency. Summarizing, the high-fluence transient response evolves at temperatures above Tco and is short-lived in contrast to the low-fluence metastable results presented in Fig. 2, implying that the 2 features correspond to distinct states.

We now discuss the origin and nature of the low-fluence photoinduced metastable electrodynamic response (Fig. 2). For 100 μJ/cm2, the temperature following e-ph thermalization is ∼35 K. In equilibrium, 35 K is within the charge-ordered, nonsuperconducting region that is spectrally featureless at THz frequencies. In contrast, the low-fluence metastable state produced by c-axis excitation exhibits unique spectroscopic features in the loss function −Im(1/ε) (Fig. 2 ) and conductivity (Fig. 2 ) that are indicative of a nonequilibrium metastable state. Importantly, the plasma frequency (ωp) is blueshifted by a factor of 4.5 upon photoexcitation (from 0.2 → 0.9 THz) corresponding to an increase of the low-energy spectral weight (Σ) by a factor of 20 (i.e., Σ p2). This is a robust observation, independent of the microscopic origin of the electrodynamic response. Additionally, the spectral weight must originate from energies beyond the 1.5-THz regime probed here because the equilibrium condensate spectral weight (Fig. 4) is far too small to account for the factor of 20 increase. A change in the c-axis response may also arise from structural distortions affecting interlayer coupling independent of a change in the in-plane superfluid density (21). Although our measurements are not directly sensitive to structural distortions, we estimate the metastable phase to be at ∼35 K which is still below the low-temperature orthorhombic to tetragonal transition occurring at 53 K (22). As such, this is not likely to be the cause of the increase in Σ. We next show that a more likely scenario for the increase in Σ is photoinduced collapse of charge/stripe order whereby spectral weight originally at energies above the charge density wave (CDW) gap scale is made available for enhanced c-axis transport.

Fig. 4.

(A) Plot of the superfluid density ρs versus the product of the zero-frequency conductivity (σdc) and the superconducting transition temperature Tc for several dopings of LBCO (σdc is the conductivity measured just above the superconducting transition). The values for x = 0.95 and x = 0.145 were taken from ref. 22. The dashed line is the universal scaling relation for cuprates ρs = 120σdcTc found by Homes et al. (23) (B) Schematic of anisotropic effective medium theory along the c axis with regions of different dielectric constants ε1 and ε2 and filling fractions f1 and f2, respectively. The superconducting volume is depicted with dark ellipses and the transformed region is in blue. (C) Real (red) and imaginary (blue) parts of the THz conductivity after photoexcitation with 100 µJ/cm2 at 7 K. Experimental data are plotted with dots and the effective medium model with solid lines.

A well-known approximate scaling relationship (valid for both c-axis and ab plane) for the cuprates is ρo = 120σdcTc, where ρo is the superfluid density (2) and σdc is the zero-frequency conductivity measured just above Tc (23). Fig. 4 shows the product σdcTc versus ρo for x = 0.115 doping measured in this study, and for x = 0.95 and x = 0.145 taken from ref. 22 For x = 0.115 at 7 K, the JPR appears near the renormalized superconducting plasma frequency ω′p = 6.7 cm−1 (200 GHz). The unscreened plasma frequency is given by ωp = ω′p giving a superfluid density ρo ≡ ωp2 = 1.3 × 103 cm−2 (This is taken to be very near the superfluid density at T = 0 K.) The conductivity just above Tc = 13 K is taken as σdc ∼ 0.8 Ω−1⋅cm−1, estimated from transport measurements on a similar doping of x = 0.11 (24). As seen in Fig. 4, the x = 0.115 doping is consistent with ρo = 120 σdcTc plotted as a dashed line. We now extend this concept to the photoinduced metastable state which, as described above, exhibits a large increase in spectral weight.

From the photoinduced blueshift of the plasma edge (ω′e ∼ 0.9 THz or 30 cm−1) it is possible to determine the photoinduced density ρe. This estimate from experimental data gives ρe = 2.7 × 104 cm−2, yielding ρe/ρo ∼ 20 as mentioned above. We now assume the validity of the scaling relation ρe = 120 σcoTco where σco ∼ 3 Ω−1⋅cm−1 is the conductivity just above the charge-ordering temperature (Tco = 53 K). From this we obtain ρe/ρo ∼ σcoTco/σcTc ∼ 15, in reasonable agreement with experiment. The product σcoTco is plotted in Fig. 4 as a red data point and lies on the dashed line given by ρs = 120 σdcTc. This suggests that c-axis spectral weight initially tied up in charge order is released upon photoexcitation leading to the blueshift of the plasma edge. We note that the precise microscopic reason for the photoinduced collapse of charge order upon c-axis interband excitation is not understood and is a topic for future investigation, beyond the scope of the present study.

The peak in the loss function cannot be simply described as an enhanced plasma edge with increased interlayer tunneling arising from the collapse of the charge order. This is because we have a peak in σ1 at a nonzero frequency (Fig. 2). In principle, 2 inequivalent junctions (with different interlayer spacing) do yield 2 distinct longitudinal JPRs at different frequencies. For example, Sm-doped La2−xSrxCuO4 (LSCO), is composed of a stack of inequivalent Josephson junctions. Out-of-phase oscillations of the 2 longitudinal modes result in a transverse mode with a resonance frequency intermediate to the 2 JPRs with a corresponding peak in σ1 (16, 25). In such a case, the spectral weight would be associated with a pure superfluid response, which is certainly intriguing since our LBCO sample is (as discussed above) at ∼35 K following e-ph equilibration (i.e., ∼2.7 Tc). It is, however, not clear how photoexcitation could lead to uniform creation of a well-defined microscopic bilayer structure, although spectroscopic aspects of this are present in the non–charge-ordered LBCO (x = 0.095) (13). However, for x = 0.115, charge-order collapse plays a dominant role as described above. As such, we consider an alternative scenario based on photoinduced mesoscopic inhomogeneity.

The simplest effective medium theory for an anisotropic layered crystal (appropriate to c-axis cuprates) is schematically depicted in Fig. 4 where regions are transformed into a metastable state (blue) while others remain untransformed (dark ellipses). The domain boundaries of the 2 different phases are along the a-b plane giving rise to regions with differing c-axis coupling strengths. The dark horizontal stripes represent the insulating barriers between CuO2 planes which give rise to the Josephson effect along the c axis. The effective dielectric response εeff is given as 1/εeff = f1/ε1 + f2/ε2 where f1 and f2 are the volume fractions corresponding to regions with complex dielectric function ε1 and ε2, respectively (26). Taking f1 as the superconducting volume fraction (having the 7 K equilibrium response), and f2 as a Drude response (with a finite scattering rate of 0.36 THz) yields the fit to the experimental data shown in Fig. 4. For additional details regarding the model and fit we refer the reader to . Notably, the peak in σ1 corresponding to a photoinduced transverse mode is accurately reproduced with this model taking f1 = 0.02 ± 0.01 and f2 = 0.98 ± 0.01. While the general features of σ2 are reproduced by the effective medium model, an exact fit was not possible. We note that errors in extracting σ2 from experiment are generally more difficult in comparison to σ1 as this depends sensitively on changes in phase of the terahertz pulse.

Taking the fits as representative of the photoinduced state leads to some interesting conclusions. First, the preponderant component consisting of a Drude response is consistent with the picture presented above that the pump destroys the charge/spin order. Second, a small but nonnegligible superconducting volume fraction (∼2%) is required to obtain the spectral response in Fig. 4. This indicates that even though the temperature is more than 2 times greater than the equilibrium Tc, regions of superconductivity persist. Furthermore, the Drude response (associated with f2) is anomalous as it exhibits a small scattering rate of 0.36 THz. This is surprising for a nonsuperconducting c-axis response and has not been observed in the equilibrium c-axis response for any cuprate material. We suggest that the origin of this enhanced response arises from incipient superconducting correlations that enhance the c-axis conductivity as has been theoretically discussed (27, 28). This is consistent with the experimental observation that the observed metastability requires starting from an initial superconducting state and that a nonzero superconducting volume fraction persists after photoexcitation. Previous pump–probe studies on the cuprates have also observed long-lived dynamics after photoexcitation of the superconducting state, although the fluence dependence differs from what we have observed (29–31). In these studies the slow relaxation rate of the quasiparticles is described by a persistent phase separation along the CuO planes which may be a general feature in the cuprates and responsible for the long-lived state we observe. It will be important to pursue comparative experimental studies as a function of doping and excitation fluence and to gain additional insight into the nature of the metastability we have observed in LBCO. Such studies will also benefit from theoretical investigations of the origin of metastability in materials with competing order (32).

In summary, low-fluence photoexcitation favors the establishment of a long-lived state with superconductivity playing an important role. Additional experiments are required to fully characterize the observed metastable response and the effective medium description of mesoscale inhomogeneity that includes a superfluid response. Our results raise crucial theoretical questions including the origin of the superconductivity and the physics and surprisingly long lifetime of the metallic state. The observed long lifetime bodes well for performing additional experiments, including time-resolved nanoscopy to spatially resolve the photoinduced state.