Two distinct kinetic regimes for the relaxation of light-induced superconductivity in $\mathrm{L}{\mathrm{a}}_{1.675}\mathrm{E}{\mathrm{u}}_{0.2}\mathrm{S}{\mathrm{r}}_{0.125}\mathrm{Cu}{\mathrm{O}}_4$

We address the kinetic competition between charge striped order and superconductivity in $\mathrm{L}{\mathrm{a}}_{1.675}\mathrm{E}{\mathrm{u}}_{0.2}\mathrm{S}{\mathrm{r}}_{0.125}\mathrm{Cu}{\mathrm{O}}_4$. Ultrafast optical excitation is tuned to a midinfrared vibrational resonance that destroys charge order and promptly establishes transient coherent interlayer coupling in this material. This effect is evidenced by the appearance of a longitudinal plasma mode reminiscent of a Josephson plasma resonance. We find that coherent interlayer coupling can be generated up to the charge-order transition $T_{\mathrm{CO}}\approx 80\mathrm{K}$, far above the equilibrium superconducting transition temperature of any single layer cuprate. Two key observations are extracted from the relaxation kinetics of the interlayer coupling. First, the plasma mode relaxes through a collapse of its coherence length and not its density. Second, two distinct kinetic regimes are observed for this relaxation, above and below spin-order transition $T_{\mathrm{SO}}\approx 25\mathrm{K}$. In particular, the temperature-independent relaxation rate observed below $T_{\mathrm{SO}}$ is anomalous and suggests coexistence of superconductivity and stripes rather than competition. Both observations support arguments that a low temperature coherent stripe (or pair density wave) phase suppresses $c$-axis tunneling by disruptive interference rather than by depleting the condensate.

Figure 1

Phase diagram of LESCO and transient response at 5, 30, and 100 K. (a) Phase diagram of LESCO, based on Ref. [28] indicating regions of bulk superconductivity (SC) and static spin (SO) and charge (CO) order. The static stripes suppress $c$-axis coupling of the $\mathrm{Cu}{\mathrm{O}}_2$ planes (inset cartoon, left), with bulk superconductivity restored at dopings in which the stripe order is reduced (inset cartoon, right). (b) The raw transient reflectivity changes measured 1.8 ps after MIR excitation. At 5 K (b.1) and 30 K (b.2), an edge is apparent at 1.5–2 THz. The black lines indicate the reflectivity spectrum (rescaled) due to a longitudinal plasma mode, shown as a guide to the eye. Above the charge-ordered transition temperature $T_{\mathrm{CO}}$ no edge is observed [shown at 100 K; (b.3)]. (c) The size of the reflectivity edge remains approximately constant below the spin-order transition temperature $T_{\mathrm{SO}}$, but drops rapidly between $T_{\mathrm{SO}}$ and $T_{\mathrm{CO}}$ (dark gray circles). This trend is also reflected in the time domain, by the change in the THz amplitude $\Delta E\left(\tau \right)/E^{\max }$ measured at the peak of the response (light gray squares). The full delay traces $\Delta E\left(\tau \right)/E^{\max }$ are shown in Fig. 4.

Figure 2

Transient optical properties at 5 and 30 K. Upon MIR excitation, LESCO 1/8 develops a high-mobility state, shown 2.8 ps after excitation at 5 K (red, first row) and at the peak of the response at 30 K (blue, second row). The equilibrium response is shown in gray. The transient state can be fit (black lines) by a longitudinal plasma mode, as described in the main text. (a) The mode is characterized by a zero crossing in the real dielectric function, ${\varepsilon }_1\left(\omega \right)$. (b) The Ohmic conductivity ${\sigma }_1\left(\omega \right)$ remains insulating, showing only a small enhancement at lowest frequencies. (c) The inductive conductivity ${\sigma }_2\left(\omega \right)$ becomes positive and diverging towards low frequency. (d) The pump-induced changes $\Delta {\sigma }_2\left(\omega \right)={\sigma }_2\left(\omega \right)-{\sigma }_2^{\mathrm{eq}}\left(\omega \right)$ diverge as $1/\omega$ (dotted line).

Figure 3

Time dependence of the transient response. (a) The real dielectric function ${\varepsilon }_1\left(\omega \right)$ (alternating circle and square dots) as a function of pump-probe delay at 5 K (a.1), 35 K (a.2), and 65 K (a.3). The response is fit with a single longitudinal mode, as described in the main text (solid black and dashed lines). The drop in coherence length causes a flattening in the low frequency ${\varepsilon }_1\left(\omega \right)$. (b, top) The $c$-axis coherence length of the transient plasma as a function of delay for three temperatures: 5 K (circles), 35 K (squares), and 65 K (triangles). The length is expressed in units of the $\mathrm{Cu}{\mathrm{O}}_2$ plane spacing. The decay can be fit with a double exponential (dashed lines) with time constants 2 ps (1 ps) and 45 ps (4 ps) at 5 K (35 K). (b, bottom) The plasma frequency ${\omega }_P$ redshifts at early times, decaying to a constant value following single exponential (dashed lines) of 2 ps (1 ps) at 5 K (35 K).

Figure 4

Temperature dependence of the transient lifetime. (a) The time profile of the transient state as a function of pump-probe delay. The vertical axis indicates the transient change of the peak of the THz probe field. For clarity, each point shown represents an average of ten delay measurements. The lifetime of the transient state was extracted using a double exponential fit (dashed lines), with each exponential given roughly equal weight, 50% ± 10%. (b) An Arrhenius plot of the relaxation rate as a function of temperature. The short lifetime ${\tau }_1$ (dark blue squares) and the long lifetime ${\tau }_2$(light blue circles) track the decay of the coherence length of the transient plasma. [Lifetimes used in the fits shown in Fig. 3 are plotted in red.] The lifetime of the transient state remains temperature independent (horizontal gray dashed line) below the spin-order transition temperature, $T_{\mathrm{SO}}\approx 25\mathrm{K}$. Above this transition, the lifetime exhibits an exponential temperature dependence, with an energy scale of 4 meV for ${\tau }_2$ and $0.8\mathrm{meV}$ for ${\tau }_1$ (gray dashed line).