Photoinduced Charge Order Melting

• The paper reports the ultrafast collapse of charge order, with direct measurements (e.g., Δ₍CDW₎ reduction in 1T-TaS₂) observed within sub-picosecond timescales.
• Experiments use advanced pump–probe techniques like TR-XPS and TR-ARPES to capture detailed charge order dynamics and transient phase formation.
• The study demonstrates selective photoinduced control over nonequilibrium phases by decoupling electronic and lattice subsystems, offering insights for engineering novel quantum states.

Photoinduced melting of charge order refers to the rapid destabilization or destruction of a spatial modulation in the electronic charge density—such as a charge-density wave (CDW) or other forms of charge order—triggered by intense, ultrafast optical excitation. Modern ultrafast spectroscopies have provided direct access to the real-time evolution of the order parameter, revealing that photoexcitation can drive a system across symmetry-breaking phase transitions on femto- to picosecond time scales. These processes are of central importance in correlated electron systems, where the charge order interacts with spin, lattice, and orbital degrees of freedom, and where nonequilibrium routes can potentially stabilize novel transient phases.

1. Experimental Probes and Protocols

Photoinduced melting of charge order is primarily studied using time-resolved pump–probe spectroscopies capable of elemental, chemical, and atomic site selectivity. In particular, femtosecond time-resolved core-level photoemission spectroscopy (TR-XPS) and time- and angle-resolved photoemission spectroscopy (TR-ARPES) have been deployed to monitor electronic structure changes with sub-picosecond time resolution. For example, in the charge-density-wave/Mott insulator 1T-TaS₂, a 120 fs, 1.55 eV optical pump excites the system, followed by a ∼700 fs (FWHM) x-ray probe pulse at ∼156 eV (FLASH free-electron laser), enabling direct measurement of the Ta 4f core-level splitting as the CDW order parameter (Hellmann et al., 2010).

Key setup parameters:

Method	Temporal Resolution	Energy Resolution	Selectivity
TR-XPS	~700 fs	~300 meV	Atomic-site (core-level)
TR-ARPES	~30 fs	~20-30 meV	Momentum and band-resolved

These experiments follow a pump–probe scheme: the pump pulse excites the material, then the probe pulse tracks the subsequent evolution of the relevant order parameter or band structure. By tuning the probe (x-ray photon energy or emission angle), researchers target specific electronic states, momentum sectors, or atomic sites within the ordered structure.

2. Charge Order Dynamics and Timescales

Photoinduced melting of charge order occurs via multiple, temporally distinct stages:

1. Prompt Collapse (sub-picosecond): Directly after strong optical excitation, the order parameter (e.g., the CDW-induced core-level splitting Δ₍CDW₎) drops nearly instantaneously, evidencing the rapid destruction of long-range order. For 1T-TaS₂, Δ₍CDW₎ falls from ~0.62 eV to ~0.47 eV within 700 fs of photoexcitation, marking the loss of macroscopic charge order (Hellmann et al., 2010).
2. Quasi-equilibration (∼1 ps): Following the initial collapse, the system evolves into a metastable, quasi-equilibrium state in which the long-range order is lost, but short-range or domain-like order persists (Δ₍CDW₎ stabilizes at an intermediate value, e.g., 0.54 eV). This marks partial recovery of order on a timescale set by electron–phonon coupling and energy flow to the lattice.
3. Persistence of New Phases (10s of ps): The transient, domain-like or nearly-commensurate phase persists long after the initial processes, indicating the presence of kinetic barriers that inhibit immediate recovery of the original long-range order.

These stages are well-captured by a two-temperature model, in which the electron and lattice temperatures (Tₑ, Tₗ) are governed by coupled differential equations:

$C_e \frac{dT_e}{dt} = -G (T_e - T_l) + S(t)$

$C_l \frac{dT_l}{dt} = G (T_e - T_l)$

Here, $C_e$ and $C_l$ are the electron and lattice heat capacities, $G$ is the electron–phonon coupling constant, and $S(t)$ describes the instantaneous energy deposition from the pump.

3. Nature of the Photoinduced Phase Transition

The ultrafast melting of charge order constitutes a nonequilibrium phase transition, frequently driving the system from a commensurate, long-range ordered phase (e.g., CCDW in 1T-TaS₂) to a nearly commensurate or domain-based phase (NCCDW), distinguished by:

• Loss of long-range phase coherence: Large, well-ordered domains give way to spatially limited regions of order interrupted by discommensurations.
• Partial retention of local structure: Within domains, the short-range order and underlying structural motifs (e.g., David-star clusters in TaS₂) can persist, but are separated by fluctuating or disordered boundaries.
• Mismatch with thermal transitions: The nonequilibrium state accessed via femtosecond pulses is distinct from those created by temperature changes; for example, comparison to equilibrium phase diagrams shows that the observed Δ₍CDW₎ after photoexcitation falls into an NCCDW-like region (Hellmann et al., 2010).

This separation of electronic and structural responses demonstrates that charge order can be selectively decoupled from the periodic lattice distortion (PLD) on femtosecond timescales, enabling phase transitions inaccessible by conventional routes.

4. Coupling Between Electronic and Lattice Degrees of Freedom

An essential aspect of ultrafast charge order melting is the decoupling—and eventual recoupling—of the electronic and lattice subsystems:

• Initial Decoupling: The electronic order (e.g., charge modulation, band splitting) collapses almost immediately upon pump excitation, while the underlying lattice distortion (PLD, atomic displacements) relaxes on the much slower, characteristic timescale of phonons (~1 ps or longer). This is observed both in site-sensitive TR-XPS and momentum-resolved TR-ARPES, the latter showing band collapse before measurable relaxation of structural modulation (Petersen et al., 2010).
• Electron–Phonon Thermalization: After the rapid electron heating, equilibration with the lattice leads to the formation of a new quasi-equilibrium state, with coupled short-range charge and lattice order.
• Order Parameter Mapping: The CDW order parameter is tracked via the splitting of site-specific core-level spectra (Δ₍CDW₎), while its time-dependent recovery is used to identify the stages of melting and re-formation of local order.

A critical insight derived from these observations is that selective ultrafast manipulation of electronic and lattice orders is achievable, providing tools to engineer nonequilibrium material phases.

5. Implications for Correlated Electron Systems and Nonequilibrium Control

Ultrafast melting of charge order by optical excitation provides a window into:

• Dynamics of Coupled Order Parameters: Demonstrating that electron–lattice coupling can be transiently overcome, so that charge order and lattice distortion can evolve on distinct time scales. This feature is essential for understanding nonequilibrium dynamics in correlated systems with intertwined orders.
• Interaction Between Mott Physics and CDW Order: In Mott–CDW systems, the prompt collapse of both the CDW order parameter and the Mott gap suggests a strong feedback mechanism in which the destruction of charge modulation facilitates rapid closure of electronic gaps, highlighting the role of electronic correlations.
• Access to Nonthermal Phases: The ability to induce transitions to domain-like or hidden phases on demand via pulsed excitation offers routes to control symmetry, order, and functional properties in quantum materials. These phases may exhibit properties inaccessible in equilibrium, opening research directions in ultrafast phase engineering.

Furthermore, the application of site- and element-selective probes such as FEL-based TR-XPS holds transformative potential for the "movie" visualization of ultrafast local electron dynamics in solids.

6. Modeling and Quantitative Analysis

Crucial quantitative descriptions employed in these studies include:

• Order parameter extraction: Direct definition in terms of measured core-level spectral features, e.g.,

$\Delta_{CDW} = E_c - E_b$

where $E_c$ and $E_b$ are the Ta 4f binding energies associated with different atomic sites in the CDW lattice.

• Two-temperature model dynamics: As outlined above, used to connect energy deposition, transfer, and eventual lowering of the order parameter over specific time scales.
• Comparison to equilibrium phase diagrams: Mapping post-pump Δ₍CDW₎ to positions in the T–Δ₍CDW₎ diagram distinguishes between the commensurate, nearly commensurate, and incommensurate phases.

Phenomenon	Timescale	Measurement	Interpretation
Electronic collapse	<700 fs	Ta 4f splitting	Prompt loss of long-range charge order
Electron–phonon	~900 fs – 1 ps	Δ₍CDW₎ partial recovery	Equilibration to quasi-equilibrium (NCCDW)
Persistent domains	>10 ps	Stable Δ₍CDW₎	Long-lived, domain-like short-range order

These models and quantitative tools enable detailed mapping of photoinduced phase transitions, offering a paradigm for uncovering and controlling nonequilibrium phenomena in complex materials.

7. Broader Significance and Future Directions

The ultrafast melting of charge order under photoexcitation represents a benchmark for investigating the interplay of strong correlations, lattice coupling, and symmetry-breaking in complex quantum systems. This research establishes:

• Experimental methods for capturing the atomic-site and momentum-resolved evolution of order parameters with sub-picosecond resolution.
• Theoretical frameworks (e.g., two-temperature models, spectral mapping) for quantifying energy flow and order parameter dynamics.
• Foundational insights into the separation and recombination of electronic and lattice degrees of freedom after strong perturbations.

This approach is broadly applicable to studies of superconductors, Mott and Peierls systems, wigner crystals, and quantum materials with intertwined spin, charge, orbital, and lattice orders. Looking ahead, the ability to photoinduce and track symmetry-breaking transitions will be essential for the design of next-generation electronic and photonic devices with on-demand phase functionalities.