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Ultrafast optical control of charge orders in kagome metals

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Pith's one-line read Ultrafast optical pump pulses can control the charge orders of the kagome metals $A$V$_3$Sb$_5$: linearly polarized light biases the real charge density waves and resonantly enhances charge nematicity, while circularly polarized light…

desk verdict A well-executed tDHF study with genuinely new pump-polarization predictions for kagome charge order; the quantitative 2.5 eV resonance rests on a single U1 value and needs a robustness check, but the paper deserves a serious referee. read the letter →

arxiv 2411.10447 v1 pith:7FXMWQ6O submitted 2024-11-15 cond-mat.str-el cond-mat.mes-hallcond-mat.mtrl-sci

Yu-Ping Lin , Vidya Madhavan , Joel E. Moore This is my paper · ORCID
classification cond-mat.str-elcond-mat.mes-hallcond-mat.mtrl-sci
keywords kagomemetalschargedensitywavesultrafastopticalcontrolnematicityimaginaryloopcurrentstime-dependentHartree-FockRabiresonance
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Ultrafast light pulses can steer the competing charge orders in the kagome metals $A$V$_3$Sb$_5$ ($A =$ K, Rb, Cs), according to time-dependent Hartree-Fock simulations of a minimal spinless-fermion Hubbard model at the $p$-type Van Hove filling. Starting from the equilibrium tri-hexagonal real charge density wave (rCDW), the polarization of the pump decides the outcome: linear polarization breaks the sixfold symmetry and favors one of the three rCDW directions, while circular polarization suppresses all three rCDW components and generates imaginary CDWs (iCDWs) that carry charge loop currents. The paper also finds that an emergent charge nematicity peaks at a resonant pump frequency $\omega_c \approx 2.5$ (eV), understood through a Rabi-oscillation-like coupling between the rCDW and the nematic state. If these predictions hold in the real materials, pump-probe experiments can use pulse shape and frequency to select among competing orders rather than only melt them.

What carries the argument

The machinery is time-dependent Hartree-Fock applied to a spinless-fermion nearest-neighbor Hubbard model on the kagome lattice at filling $n_f=5/12$ with interaction $U_1=t_1=1$, whose mean-field ground state is the $3\mathbf{Q}$ tri-hexagonal rCDW. The pump pulse enters as a Gaussian-envelope time-dependent gauge field through the Peierls substitution, and its linear or circular polarization determines which lattice symmetries are broken during the dynamics. The argument is carried by the computed evolution of the charge-order amplitudes $\Delta_\alpha$ — the real and imaginary CDWs at the three $\mathbf{M}_\alpha$ points plus the $\Gamma$-point charge nematicity — and the resonant enhancement of the nematicity is explained by a Rabi-oscillation-like two-level model in which the drive transfers weight from the rCDW to the nematic state near $\omega_c\approx2.5$.

What would settle it

Scan a single crystal of RbV$_3$Sb$_5$ with linearly polarized pump pulses of fixed fluence and center frequency swept across 1–3 eV, and measure a rotation-symmetry-breaking charge response (for example by time-resolved X-ray diffraction or optical birefringence) within the first picosecond; the central claim is falsified if no resonant enhancement of charge nematicity appears near 2.5 eV, or if a circularly polarized pulse produces no loop-current signal (for example in time-resolved Kerr rotation).

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Extended reading notes

Core claim

The central claim is that ultrafast optical pumping is an effective control knob for the charge orders of the kagome metals $A$V$_3$Sb$_5$. The paper studies the post-pump dynamics of the $3\mathbf{Q}$ tri-hexagonal rCDW ground state and finds that the pump polarization dictates which order wins: linearly polarized pumps break the $C_{6v}$ symmetry down to $C_{2v}$, giving a directional preference to the rCDW and enhancing the flat-band component, while the injected energy peaks at $\omega_c \approx 2.5$ and the emergent charge nematicity is maximally enhanced there. Circularly polarized pumps break time-reversal symmetry, uniformly suppress all three rCDW components, and trigger $3\mathbf{Q}$ imaginary CDWs whose charge loop currents are weaker and less stable than the nematic order because the cubic free-energy phase term penalizes the required phase configuration. The authors connect these results directly to pump-probe experiments through explicit unit conversions, and they reproduce the directional preference already seen in laser-coupled STM data on RbV$_3$Sb$_5$.

Load-bearing premise

The load-bearing premise is that a spinless-fermion nearest-neighbor Hubbard model treated at Hartree-Fock level captures the essential charge-order physics of the real kagome metals, so that the predicted resonant nematicity, directional preferences, and light-induced loop currents survive the additional electron-phonon coupling, spin degrees of freedom, and three-dimensional structure present in $A$V$_3$Sb$_5$.

Editorial extensions

If this is right

  • Linearly polarized pump pulses parallel to $\mathbf{M}_2$ select the $\alpha=2$ directional component of the rCDW, while a perpendicular pump drives the opposite preference, reproducing and extending the laser-coupled STM observation on RbV$_3$Sb$_5$.
  • At the resonant frequency $\omega_c\approx2.5$ the injected energy peaks, the emergent charge nematicity is maximally enhanced, and the rCDW is maximally suppressed, giving a frequency-selective experimental signature.
  • Increasing the pump amplitude softens the rCDW collective-mode oscillations under linear polarization, shifting the major spectral peak to lower frequency.
  • Circularly polarized pumps uniformly suppress all three rCDW components and generate $3\mathbf{Q}$ imaginary CDWs with charge loop currents, whose flat-band component can exceed the $p$-type component and whose sign flips with pump helicity.
  • All of these effects occur on a roughly 0.33 ps timescale after a ~33 fs pulse at fluences of $0.001$–$0.6~\mathrm{mJ/cm^2}$, placing them within reach of current pump-probe techniques.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the nematic resonance is interpreted as a Rabi-like transfer between the rCDW and the nematic state, scanning the resonance position under doping, pressure, or strain could measure the rCDW-to-nematic gap and pin down the interaction energy scale more directly than equilibrium probes.
  • If the circularly pumped iCDW carries loop currents without closing a topological gap, time-resolved Kerr rotation should show a helicity-dependent transient signal, providing a background-free probe of loop-current order that is stronger than static probes of the weak equilibrium iCDW.
  • The symmetry-based mechanism suggests the same polarization rules may transfer to other kagome CDW materials with different microscopic parameters, and a direct test would be to run the same pump protocol on a model that includes electron-phonon coupling to see whether the resonant frequency and directional selection survive quantitative changes.
  • The predicted uniform rCDW suppression under an out-of-plane linear pump offers a way to isolate the in-plane charge-order response from interlayer effects in the layered materials, which could be checked by comparing in-plane and out-of-plane pump geometries in trXRD.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. This manuscript studies the nonequilibrium dynamics of a spinless-fermion nearest-neighbor Hubbard model on the kagome lattice at filling nf = 5/12 with U1 = t1 = 1, using time-dependent Hartree-Fock theory. Starting from a 3Q tri-hexagonal rCDW ground state, the authors apply linearly and circularly polarized pump pulses and analyze the post-pump charge orders. They report that linearly polarized pulses induce a directional preference of the rCDW (consistent with a laser-coupled STM experiment), enhance the flat-band rCDW, and generate charge nematicity with a resonant enhancement at omega_c ~ 2.5 interpreted via a Rabi-like two-level model. Circularly polarized pulses uniformly suppress the rCDW and induce imaginary CDWs with charge loop currents. The paper includes unit conversions to experimental time and energy scales and a detailed numerical implementation in the Supplemental Material.

Significance. If the reported phenomena are robust, the paper provides concrete, falsifiable predictions for pump-probe experiments on AV3Sb5: a frequency-tunable resonance in charge nematicity, a polarization-dependent directional selection of the CDW, and a circular-polarization-induced loop-current order. The numerical implementation is careful: RK4 time stepping with explicit projector enforcement and energy-conservation checks, and the parameter conversions to experimental units are clearly documented. The directional-preference result already connects to an existing STM experiment. However, the quantitative claims, especially the omega_c ~ 2.5 resonance, rest on a single interaction value and a heuristic resonance explanation, which limits the material-specific significance until the parameter sensitivity is established.

major comments (2)
  1. [Pump pulse and dynamics; Fig. 4] The resonance peak at omega_c ~ 2.5 is computed only for U1 = t1 = 1. No scan over U1 is presented, despite the fact that in mean-field theory the collective-mode spectrum and any resonance position generally depend on U1 and on the mean-field gap. Because the abstract claims 'effective control over charge orders in the kagome metals AV3Sb5' and states that the results 'can be directly compared to pump-probe experiments,' the single-U1 calculation is a load-bearing gap. Please provide a U1 sensitivity scan (for example, U1 = 0.5, 0.75, 1.25, 1.5) showing whether the resonance and the iCDW emergence survive, or explicitly reframe the predictions as model-specific rather than material-specific.
  2. [Linearly polarized pump (Rabi-like model)] The Rabi-like model invoked in the linearly polarized pump section is not a derivation: the two-level parameters epsilon' and g' are never computed from the Hubbard Hamiltonian, and no charge-nematic spectral weight is shown to peak near omega_c ~ 2.5. As written, the 'resonance' is an analogy applied after the fact. To make the explanation load-bearing, compute epsilon' from the mean-field excitation spectrum (for example, the pole of the charge-nematic susceptibility in the ground state) and compare it with the observed resonance; alternatively, present the two-level model as a purely illustrative analogy and state explicitly that the numerical resonance is the primary evidence.
minor comments (4)
  1. [Supplemental Material Sec. IV C 1] The phrase '1-higher-2-lower CN' is used without definition; please define it in terms of which sublattice densities are enhanced or suppressed.
  2. [Eq. (2) and surrounding text] The symbol A is overloaded: A(t) is the gauge field, Ac is the pump amplitude, and A also denotes the alkali-metal species K, Rb, Cs. This makes the notation harder to follow, particularly in the figure captions.
  3. [Abstract and Fig. 6] The wording 'triggers imaginary CDWs' is stronger than the plotted result, since Fig. 6 shows the iCDW is small and decays rapidly; please qualify it as a transient induced order to match the magnitude shown.
  4. [Supplemental Material Sec. II A] The identification '1 energy unit = 1 eV' is stated without discussion; please add one sentence on the uncertainty of this assumption and how the conclusions would shift if the band width differed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central dynamical results are new time-dependent Hartree-Fock outputs, and the self-citations are interpretational rather than load-bearing.

full rationale

The central results (directional rCDW preference, flat-band enhancement, resonant charge nematicity at ωc≈2.5, uniform rCDW suppression and emergent iCDW under circular polarization) are obtained by time-dependent Hartree-Fock evolution of the Hubbard model (1), with the initial TrH mean-field ground state computed in the paper's own Supplemental Material (SM Sec. I). The pump enters only through the Peierls substitution (3), and no parameter is fitted to the target observables. The ωc scan is a genuine sweep: the resonance at 2.5 is a simulation output, and the Rabi-oscillation-like model is invoked after the fact as an interpretation, not used to derive or fit the resonance frequency. Self-citations [10,35,41] appear only when explaining why a 1Q preference or a 2-higher-1-lower CN decays faster; these energy-ordering statements do not generate the simulated order parameters. External benchmarks, especially the observed directional preference in laser-coupled STM [30] and the pump-probe measurements [23–29], are independent of the model's own outputs. The acknowledged omission of electron-phonon coupling and three-dimensional structure is a robustness caveat, not a circular reduction. No equation in the paper is equivalent by construction to its own output; the derivation chain is self-contained.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim rests on a minimal model and a mean-field time evolution; the only fitted/ad hoc quantities are representative model parameters (U1, nf) and pump pulse settings. No new physical entities are postulated. The main unverified assumption is the transferability of the spinless tDHF results to the real AV3Sb5 materials.

free parameters (3)
  • U1 (nearest-neighbor repulsion) = 1 (in units of t1=1)
    Chosen by hand as a representative interaction strength; the rCDW ground state and all pump dynamics depend on it. No material-specific fitting is performed.
  • nf (fermion filling) = 5/12
    Chosen so the Fermi level sits at the p-type Van Hove singularity, motivated by AV3Sb5. The nesting vectors and the resulting 3Q rCDW depend on this filling.
  • Pump pulse parameters (Ac, omega_c, sigma_t, t_c) = Ac in [0.02, 0.1]; omega_c in [1, 3]; sigma_t=3; t_c=25
    Pulse parameters are scanned or set for numerical convenience; the fluence range is matched to experiments (SM Sec. II B), but the parameters are not fitted to data.
assumptions (5)
  • domain assumption Spinless-fermion nearest-neighbor Hubbard model (t1=1, U1=1) captures the relevant charge-order physics of AV3Sb5.
    The paper chooses this model 'to avoid complication from potential spin orders' and calls it a 'representative simple electronic model'; all pump-dynamics results are computed within it (Eq. 1).
  • domain assumption Time-dependent Hartree-Fock theory remains accurate for the post-pump dynamics up to t=500 (0.329 ps).
    The dynamics is solved with Eq. (S56) and RK4; the paper states tDHF 'does not include all of the possible relaxation processes in the late-time dynamics' (Discussion), so the late-time evolution is an unverified assumption.
  • domain assumption The pump is described by a spatially uniform Gaussian gauge field via Peierls substitution (Eqs. 2-3); the system remains spatially uniform.
    The authors 'treat the system as spatially uniform, meaning we focus on the laser-illuminated spots' (main text); spatial inhomogeneity and 3D effects are neglected.
  • domain assumption The state remains 2x2 periodic in the studied regimes, allowing restriction to M-point and Gamma-point order parameters.
    SM Sec. IV A states 'our computation generally finds strong 2x2 periodicity in the real-space patterns', which justifies the order-parameter analysis.
  • standard math Wick's theorem and fermionic anticommutation relations are used to derive the mean-field energy and time evolution.
    Used in SM Sec. I A and III A to obtain E[P] and Eq. (S56).

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Cite this review

Pith. "Pith review of Ultrafast optical control of charge orders in kagome metals." pith.science (2026). https://pith.science/paper/7FXMWQ6O

@misc{pith2026241110447,
  author       = {Pith},
  title        = {Pith review of: Ultrafast optical control of charge orders in kagome metals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7FXMWQ6O}},
  note         = {Machine review of arXiv:2411.10447}
}
abstract

We show that ultrafast optical pump pulses provide effective control over charge orders in the kagome metals $A$V$_3$Sb$_5$ with $A=$ K, Rb, and Cs. Starting from the real charge density waves (rCDWs) at the $p$-type Van Hove singularity, we conduct a thorough analysis of the post-pump dynamics by time-dependent Hartree-Fock theory. Our analysis uncovers distinct dynamical phenomena under linearly and circularly polarized pumps. Linearly polarized pumps induce directional preferences in the rCDWs, accompanied by an enhancement in the flat band. Unexpectedly, charge nematicity also emerges and receives maximal enhancement at a resonant pump frequency, which we understand with a Rabi-oscillation-like model. On the other hand, circularly polarized pumps suppress the rCDWs uniformly and triggers imaginary CDWs (iCDWs) with charge loop currents. Our results can be directly compared to the pump-probe experiments on the kagome metals $A$V$_3$Sb$_5$.

Figures

Figures reproduced from arXiv: 2411.10447 by the authors.

Figure 2
Figure 2. FIG. 2. Kagome lattice and charge orders. (a) The lat [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Directional preference of the rCDWs under linearly [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Emergent CN under the linearly polarized pumps. [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figures from the paper (1 more)
Figure 6
Figure 6. Figure 6: FIG. 6. Dynamics under the circularly polarized pump. [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]

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    Ultrafast optical control of charge orders in kagome metals

    C. Butcher, in Numerical Methods for Ordinary Differ- ential Equations (John Wiley & Sons, Ltd, 2016). 8 Supplemental Material for “Ultrafast optical control of charge orders in kagome metals” CONTENTS I. Hartree-Fock theory 8 A. General formalism 8 B. Numerical scheme 10 C. I...

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    Real-space formalism 11

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    Comparison of model parameters to experimental setup 13 A

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    Projector condition 17

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    Numerical scheme 18

    Current orders 18 C. Numerical scheme 18

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    Runge-Kutta method 19

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    Implementation in this work 20 IV

    Algorithm 20 D. Implementation in this work 20 IV. Dynamics of charge orders 21 A. Types of charge orders 21

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    Computation of frequency spectrum 23 C

    Γ-point orders 22 B. Computation of frequency spectrum 23 C. Miscellaneous dynamics 23

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    Linearly polarized pump 23

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    HAR TREE-FOCK THEOR Y In this section, we provide a comprehensive introduction to the Hartree-Fock theory and its numerical scheme

    Circularly polarized pump 24 I. HAR TREE-FOCK THEOR Y In this section, we provide a comprehensive introduction to the Hartree-Fock theory and its numerical scheme. The specific implementation in our work is also explained. A. General formalism We begin with an introduction to ...

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    ) with ϵ1 < ϵ2 <

    Diagonalize the Hartree-Fock Hamiltonian HHF,m = UϵDϵU † ϵ , where Dϵ = diag(ϵ1, ϵ2, . . .) with ϵ1 < ϵ2 < . . . are the eigenvalues and Uϵ = ( ψ1, ψ2, . . .) are the eigenstates of HHF,m. (Optional) If the ODA is applied, diagonalize ˜HHF,m instead

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    ,1, 0, 0,

    Assemble the new density matrix Pm+1 = UϵDN U † ϵ , where DN = diag(1 , 1, . . . ,1, 0, 0, . . . ,0) selects the N lowest-lying eigenstates

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    Compose the new Hartree-Fock Hamiltonian HHF,m+1 = HHF[Pm+1]

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    Compute the new energy em+1 = Em+1/NDOF

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    Compute the desired physical observables

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    The criteria δe, δp= 10−15 are chosen in our computation, although the density-matrix elements may only converge to O(10−15) for large system sizes

    Check the convergence: Stop the iteration if the variations in the energy |em+1 −em| < δeand the density-matrix elements |Pm+1,ab − Pm,ab| < δpare small enough. The criteria δe, δp= 10−15 are chosen in our computation, although the density-matrix elements may only converge to ...

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    (Optional) Adopt the ODA [S47], which interpolates between Pm+1 and ˜Pm to minimize the energy. i. Compute the variation of the density matrix δPm = Pm+1 − ˜Pm and the Hartree-Fock Hamiltonian δHHF,m = HHF,m+1 − ˜HHF,m. ii. Consider the energy of an interpolation ˜Pm + λmδPm b...

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    The indices i and τ = 0, 1, 2 label the Bravais-lattice site and the three sublattices, respectively

    Real-space formalism To study the repulsive spinless fermions on the kagome lattice, we adopt a real-space formalism, where the fermionic basis is defined by the lattice sites a = iτ . The indices i and τ = 0, 1, 2 label the Bravais-lattice site and the three sublattices, resp...

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    (S21) 12 The site orders Piiτ τare real, which characterize the onsite charge densities

    Computation of charge orders To understand the ground states, we study the charge orders on the sites and bonds Pii′τ τ′ = ⟨c† i′τ ′ciτ ⟩. (S21) 12 The site orders Piiτ τare real, which characterize the onsite charge densities. Meanwhile, the bond orders Pii′τ τ′ with iτ ̸= i′...

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    The band-structure analysis is based on a noninteracting model ˜H = X ˜i˜i′ ˜τ ˜τ ′ ˜H˜i˜i′ ˜τ ˜τ ′c† ˜i˜τ c˜i′ ˜τ ′

    Band-structure analysis While the real-space formalism is already effective in understanding the interaction-driven ground states, further information can be gathered from the band-structure analysis in the momentum space. The band-structure analysis is based on a noninteracti...

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    Assume that the density matrix P (t) obeys the projector condition P 2(t) − P (t) = 0 at the time t

    Projector condition In the time-dependent Hartree-Fock theory, an important property is the preservation of projector conditionP 2 = P under the time evolution (S56). Assume that the density matrix P (t) obeys the projector condition P 2(t) − P (t) = 0 at the time t. Examining...

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    (S58) The first two terms in the second trace result from the time dependence of the noninteracting Hamiltonian H0(t) and the interaction U (t), respectively

    Energy change Another important property is the energy change d dt E[P ] = d dt 1 2 Tr(P (H0 + HHF[P ])) = d dt Tr P H0 + 1 2 VHF[P ] = Tr dP dt H0 + 1 2 VHF[P ] + Tr P dH0 dt + 1 2 dVHF[P ] dt = Tr dP dt H0 + 1 2 VHF[P ] + Tr P dH0 dt + 1 2 dVHF dt [P ] + 1 2 VHF dP dt . (S58...

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    I C 2, the current flowing between different states can be an important symmetry- breaking order

    Current orders As mentioned previously in Sec. I C 2, the current flowing between different states can be an important symmetry- breaking order. Moreover, the time evolution is achieved through these currents, so it is important to understand how to quantify them. Define the c...

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    However, in the numerical implementation, we need to introduce a small discrete time step ∆ t

    Defects in naive discrete time evolution In the time-dependent Hartree-Fock theory, the time-evolution equation (S56) is a differential equation of a contin- uous time t. However, in the numerical implementation, we need to introduce a small discrete time step ∆ t. As the time...

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    Here we adopt its fourth order version, known as the RK4

    Runge-Kutta method A powerful resolution to the discrete time errors is the famous Runge-Kutta method [S48–50]. Here we adopt its fourth order version, known as the RK4. For conceptual clarity, we first describe it in terms of a general ordinary 20 differential equation of a f...

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    Compute k1 = f (tm, ym)

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    Compute k2 = f (tm + ∆t/2, ym + [∆t/2]k1)

  73. [81]

    Compute k3 = f (tm + ∆t/2, ym + [∆t/2]k2)

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    Compute k4 = f (tm + ∆t, ym + ∆tk3)

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    We can see that the RK4 method averages the slopes at the tentative middle and end points, thereby reducing the error from the discrete time step

    Compute ym+1 = ym + (∆t/6)(k1 + 2k2 + 2k3 + k4). We can see that the RK4 method averages the slopes at the tentative middle and end points, thereby reducing the error from the discrete time step. Remarkably, it has been proven that the design of the RK4 method can reduce the e...

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    The time evolution begins with the initial iteration m = 0, where an initial density matrix Pm = P (tm = 0) is assigned

    Algorithm The time-dependent Hartree-Fock theory is again implemented as an iterative algorithm. The time evolution begins with the initial iteration m = 0, where an initial density matrix Pm = P (tm = 0) is assigned. To ensure the validity of the results, a small enough time ...

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    Get the time-dependent noninteracting Hamiltonian H0,m = H0(tm) and the interaction Um = U (tm)

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    Compose the Hartree-Fock Hamiltonian HHF,m = HHF[Pm](tm)

  79. [87]

    Compute the desired physical observables, including the energy

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    Note that there are still very small numerical errors in the projector condition and the energy conservation

    Perform the discrete time evolution by the RK4 method and get Pm+1. Note that there are still very small numerical errors in the projector condition and the energy conservation. To preserve the robustness of our computation, we enforce the projector condition with an error cri...

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    Here we consider the CDWs in the band basis and focus on the M points

    M-point orders We first discuss the M-point orders, which correspond to the 2 × 1 CDWs. Here we consider the CDWs in the band basis and focus on the M points. The wavefunctions at the p-type VHS ( p), the m-type VHS ( m), and the flat band (FB) take the form ψp Ma = [(δτ a)τ =...

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    These orders are 1 × 1 with zero transfer momentum qb = q = 0

    Γ-point orders We next discuss the charge orders at Γ. These orders are 1 × 1 with zero transfer momentum qb = q = 0. Instead of working in the band basis, here we conduct the analysis in the sublattice basis. The real orders can be either site or bond orders, which correspond...

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    S5) and (0, 1, 0) (Fig

    Linearly polarized pump We first present the results for the linearly polarized pumps with ep,0 = (1, 0, 0) (Fig. S5) and (0, 1, 0) (Fig. S6). As discussed in the main text, there exist the directional preferences of the rCDWs, the enhancement on the flat band, and the resonan...

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    Circularly polarized pump We next present the results for the circularly polarized pumps (Fig. S7). As discussed in the main text, there exist the uniform suppressions of the rCDWs and the emergence of the iCDWs. Notably, over the resonant frequency ωc > 2.5, the iCDWs seem to...

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