A light-induced charge order mode in a metastable cuprate ladder

Using time-resolved resonant inelastic x-ray scattering, researchers observed that near-infrared light induces a metastable state in Sr$_{14}$Cu$_{24}$O$_{41}$ where equilibrium charge order partially melts and gives rise to a gapless, itinerant collective excitation, offering a new platform to investigate light-induced pairing instabilities.

The Gist

Imagine a complex building made of two different types of rooms: long, narrow hallways (called "chains") and wide, open staircases (called "ladders"). In this specific building, made of a material called Sr14Cu24O41, the "people" living inside are tiny electrical charges called holes.

Normally, these people stay in their own rooms. The hallway people stay in the hallways, and the ladder people stay on the ladders. They don't mix much, and they tend to line up in neat, rigid rows (this is called charge order). It's like a quiet library where everyone sits in assigned seats and follows a strict schedule.

The Light Switch

The scientists in this paper used a very fast, powerful flash of light (like a camera strobe) to zap the building. This light didn't just warm things up; it acted like a magical key that unlocked a secret door between the hallways and the staircases.

Suddenly, the "people" (holes) from the hallways rushed over to the staircases. This wasn't a temporary panic; once the light turned off, the doors stayed locked, and the people remained in the staircases for a surprisingly long time (nanoseconds). The building had entered a metastable state—a "hidden" configuration that doesn't naturally happen when the building is at rest.

The New Dance

In this new, crowded staircase state, something strange and exciting happened. The scientists used a special type of high-speed X-ray camera to watch how these charges moved.

In the normal state, the charges were stiff and orderly. But in this light-induced state, the charges started to dance.

• The Melting: The rigid, neat rows of charges began to melt. They weren't frozen in place anymore.
• The Wave: Instead of just sitting there, the charges started moving together in a synchronized wave. The scientists saw a new "mode" of movement—a collective ripple of charge that traveled up the ladder.
• The Speed: This wave moved incredibly fast, traveling at a speed similar to how individual particles usually move when they are free to roam.

The Analogy: From a Parade to a Mosh Pit

Think of the normal state as a military parade. Everyone is in a straight line, marching in perfect lockstep, very rigid and predictable.

When the light hits, it's like someone turns on a disco light and plays music. The rigid lines break down. The people aren't just marching anymore; they are jostling and flowing in a wave. But here's the twist: even though they are moving freely (itinerant), they are still moving in a coordinated wave pattern (collective mode) that didn't exist before. It's like a mosh pit that somehow organizes itself into a perfect, traveling ripple.

Why This Matters (According to the Paper)

The paper claims this is a rare discovery because:

1. It's a "Hidden" State: The material stays in this excited, dancing state for a long time without immediately falling back to sleep (equilibrium).
2. It's a New Kind of Order: Usually, when you melt a solid order (like ice turning to water), you just get a messy liquid. Here, melting the order created a new, gapless wave of movement. The charges became free to move but still moved together in a specific rhythm.
3. The Connection to Superconductivity: The authors suggest that this "dancing" state is very similar to what happens in materials that become superconductors (conduct electricity with zero resistance). By using light to force the charges into this specific, fluctuating dance, they might be creating a temporary environment where superconductivity could emerge, even if it doesn't happen naturally in this material at this temperature.

In short: The scientists used light to trick a material into a "hidden" state where its electrical charges stopped being rigid and started flowing together in a fast, organized wave. This wave is a new type of behavior that might help us understand how to make materials conduct electricity perfectly.

Technical Summary

Problem and Context
Optically excited quantum materials often exhibit transient nonequilibrium phenomena, such as photoinduced magnetic or charge-ordered phases. However, these driven states typically relax rapidly back to equilibrium due to dissipation and decoherence. A significant challenge in the field is realizing "hidden" or metastable electronic states that evade thermalization and persist for extended durations. While theoretical works have proposed mechanisms for light-induced states protected by Mott gaps or competing orders, long-lived nonequilibrium electronic states have remained experimentally elusive. Specifically, in the context of cuprate ladders, it is unclear whether trapped carriers in a metastable state exhibit emergent collective dynamics or incipient pairing, given the intrinsic tendency of these systems toward hole binding and superconductivity under pressure.

Methodology
The authors investigate the metastable state of the cuprate ladder compound $\text{Sr}_{14}\text{Cu}_{24}\text{O}_{41}$. This system possesses a self-doped ($p=0.06$) charge-ordered ground state where chain and ladder subunits are effectively decoupled. Previous work established that ultrafast near-infrared (1.55 eV) pump pulses induce a coherent transfer of holes from the chain reservoirs to the ladder subunits, creating a symmetry-protected metastable state that persists for nanoseconds.

To probe the charge dynamics within this metastable state, the authors employ time-resolved resonant inelastic x-ray scattering (tr-RIXS) at the O K-edge (530 eV) using the SwissFEL facility.

• Excitation: Samples are excited with 800 nm (1.55 eV), 100-fs optical pulses at fluences up to 8 mJ/cm².
• Probe: X-ray pulses are tuned to the upper Hubbard band (UHB) resonance (529.7 eV) to specifically probe the dynamics of correlated carriers in the ladders.
• Geometry: Measurements are performed in the $ac$ plane, varying the incident angle to scan momentum transfers ($q_{leg}$) along the ladder legs from 0 to 0.28 r.l.u., accessing the tail of the charge-order peak at $q_{CO} = (0, 1, 0.2)$.
• Analysis: The study utilizes high-resolution tr-RIXS (160 meV resolution) to construct energy-momentum maps. The data is analyzed by fitting momentum-dependent spectra with Gaussian and Lorentzian components to isolate collective modes from the background two-triplon continuum. Complementary time-resolved x-ray absorption spectroscopy (trXAS) confirms the metastable hole redistribution. Theoretical support is provided by Density Matrix Renormalization Group (DMRG) calculations on a two-leg extended Hubbard ladder and Random Phase Approximation (RPA) calculations to rule out plasmonic origins.

Key Results

1. Metastable Hole Redistribution: trXAS measurements confirm a prompt transfer of holes from chains to ladders following optical excitation. This results in an increased ladder hole concentration ($\Delta p \approx 0.03$) and a partial melting of the equilibrium charge order. This spectral reshaping remains stable for hundreds of picoseconds, confirming the metastable nature of the state.
2. Emergent Collective Mode: tr-RIXS measurements reveal a novel collective excitation that emerges only in the metastable state. This mode is centered at the charge-order wavevector ($q_{CO}$) and disperses up to 0.8 eV.
   • Dispersion: The mode exhibits a linear dispersion with a slope of approximately $2.1 \pm 0.3$ eV·Å, comparable to the quasiparticle velocity in the ladder.
   • Nature: The mode is identified as a charge collective mode rather than a magnetic excitation. Its energy scale and velocity far exceed those of magnetic excitations (e.g., $\Delta S = 1$ two-triplons) and are incompatible with a magnetic origin.
   • Exclusion of Alternatives: The authors rule out acoustic plasmons (which would disperse symmetrically about $q=0$) and particle-hole continuum edges (which would occur at much higher momenta for the given doping). RPA calculations confirm that plasmons do not generate modes near $q_{CO}$.
3. Charge Order Fluctuations: The emergence of this gapless mode is attributed to fluctuating charge order. While the static charge-order peak is partially suppressed, the spectral weight is redistributed to finite energies around $q_{CO}$. This indicates that the charge order melts into a dynamically fluctuating regime rather than a sliding state.
4. Theoretical Corroboration: DMRG calculations on a two-leg extended Hubbard ladder show that increasing hole doping from the equilibrium value ($p=0.06$) toward $p \approx 0.1$ drives a crossover from a state with suppressed charge fluctuations to one with significantly enhanced charge fluctuations. This theoretical crossover aligns with the experimental observation of the gapless mode in the photo-induced state.

Significance and Claims
The paper reports the observation of an emergent, gapless charge order mode in the metastable electronic phase of $\text{Sr}_{14}\text{Cu}_{24}\text{O}_{41}$. The authors claim that this finding demonstrates a regime where correlated carriers acquire itinerant character at finite momentum while the charge order becomes dynamically fluctuating.

The significance lies in the demonstration that light can steer a strongly correlated material into a long-lived metastable state characterized by distinct collective dynamics absent in equilibrium. The authors suggest that this state, featuring fluctuating charge order and itinerant carriers, offers a platform to explore light-induced pairing instabilities. Given that cuprate ladders exhibit strong hole pairing tendencies and compete with superconductivity, the authors posit that such fluctuating states could potentially be driven toward metastable superconducting or $\eta$-paired condensates under suitable conditions, motivating future searches for hidden condensates in spin and charge structure factors.