Non-thermal separation of electronic and structural orders in a persisting charge density wave

Journal name:
Nature Materials
Year published:
Published online

The simultaneous ordering of different degrees of freedom in complex materials undergoing spontaneous symmetry-breaking transitions often involves intricate couplings that have remained elusive in phenomena as wide ranging as stripe formation1, unconventional superconductivity1, 2, 3, 4, 5, 6, 7 or colossal magnetoresistance1, 8. Ultrafast optical, X-ray and electron pulses can elucidate the microscopic interplay between these orders by probing the electronic and lattice dynamics separately9, 10, 11, 12, 13, 14, 15, 16, 17, but a simultaneous direct observation of multiple orders on the femtosecond scale has been challenging. Here we show that ultrabroadband terahertz pulses can simultaneously trace the ultrafast evolution of coexisting lattice and electronic orders. For the example of a charge density wave (CDW) in 1T-TiSe2, we demonstrate that two components of the CDW order parameter—excitonic correlations and a periodic lattice distortion (PLD)—respond very differently to 12-fs optical excitation. Even when the excitonic order of the CDW is quenched, the PLD can persist in a coherently excited state. This observation proves that excitonic correlations are not the sole driving force of the CDW transition in 1T-TiSe2, and exemplifies the sort of profound insight that disentangling strongly coupled components of order parameters in the time domain may provide for the understanding of a broad class of phase transitions.

At a glance


  1. CDW phase transition in 1T-TiSe2 and its low-energy spectral fingerprint.
    Figure 1: CDW phase transition in 1T-TiSe2 and its low-energy spectral fingerprint.

    a, The periodic lattice distortion associated with the CDW (space group: ) causes a doubling of the unit cell of the undistorted high-temperature structure (pale spheres in the background, space group: ), in all three spatial dimensions. The structure is viewed along the c axis. The dashed line frames the unit cell in the CDW phase. b, Schematic electronic band structure above (upper panel) and below (lower panel) Tc. Back-folding of the 3d-like conduction bands at the L point onto the zone centred 4p-like valence bands by qCDW yields a gapped structure24 (blue). c, Imaginary part of the dielectric function measured by terahertz time-domain spectroscopy, revealing characteristic in-plane polarized transverse optical phonons in the normal (red curves) and the CDW phase (blue curves). Arrows indicate phonon resonances that are observable only in the presence of the PLD. d, Mid-infrared energy loss function −Im(1/ɛ) in the normal (T  =  300 K, red curve) and the CDW phase (T  =  10 K, blue curve) according to the model function of ref. 20. The spectrum at T  =  10 K results from a numerical adaption to the infrared reflectance of our sample (Supplementary Fig. 1).

  2. Ultrafast photoinduced dynamics of the mid-infrared electronic response.
    Figure 2: Ultrafast photoinduced dynamics of the mid-infrared electronic response.

    a,b, Two-dimensional colour maps of the transient energy loss function −Im(1/ɛ) versus photon energy and delay time at T  =  10 K, following near-infrared excitation with Φ  =  20 μJ cm−2 (a) and Φ  =  330 μJ cm−2 (b). Dashed lines are guides to the eye indicating the centre frequency of the plasmon pole. c,d, Transient change in the free carrier density n (c) and the carrier scattering time τ (d) extracted from two-dimensional terahertz time-domain spectroscopy at various pump fluences. The change in n measured for Φ  =  7 μJ cm−2 is upscaled by a factor of 120 for quantitative comparison with the situation at Φ  =  170 μJ cm−2 (c). Horizontal dotted line in d: τ  =  τN. e,f, Number of free carriers n (e) and carrier scattering time τ (f) as a function of Φ at tD  =  0.2 ps measured at T  =  10 K. Vertical shaded lines indicate the threshold fluence Φth ≍ 40 μJ cm−2 required for transient suppression of the electronic correlations. Horizontal dotted line in e: critical density nc  =  4 × 1020 cm−3. Grey dashed line: Linear regression of n(Φ) in the high-fluence regime (Φ  >  0.14 mJ cm−2). Horizontal dotted line in f: τ  =  τN.

  3. Terahertz phonon spectrum during ultrafast melting of the electronic order.
    Figure 3: Terahertz phonon spectrum during ultrafast melting of the electronic order.

    a, Imaginary part of the terahertz dielectric function at select delay times tD after optical excitation with Φ  =  0.33 mJ cm−2 and T  =  10 K. The phonon resonance originating from the back-folded acoustic branch remains visible (black arrows) at all times, proving the persistence of the PLD. The elevated conductivity of photoexcited charge carriers found at a delay time of 1.5 ps (compare Fig. 2b) accounts for the increased background compared with the other spectra. b, The same measurement for T  =  150 K. The effective suppression of the PLD-related phonon (red crosses) for tD  =  0 and 3 ps attests to a complete melting of the PLD.

  4. CDW amplitude oscillations following a perturbation of the electronic order.
    Figure 4: CDW amplitude oscillations following a perturbation of the electronic order.

    a, Oscillatory component ΔAosc(tD) of the pump-induced terahertz transmission change ΔA(tD) recorded at T  =  10 K and various Φ. ΔA is spectrally integrated over an energy window from 40 meV to 140 meV. Vertical grey lines mark the maxima of the waveform recorded with Φ  =  3 μJ cm−2. The black vertical line and the black arrow indicate the time difference required for three full oscillation cycles during persistent (Φ  =  3 μJ cm−2) and suppressed (Φ  =  67 μJ cm−2) electronic order. b, A representatively selected frequency spectrum of the oscillations observed with Φ  =  7 μJ cm−2 identifies the well-known A1g CDW amplitude mode16. c, Maximum amplitude of ΔAosc as a function of Φ. The slope flattens at a fluence coinciding with Φth (shaded vertical line).


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Author information


  1. Department of Physics, University of Regensburg, 93040 Regensburg, Germany

    • M. Porer,
    • U. Leierseder,
    • J.-M. Ménard &
    • R. Huber
  2. Molecular and Surface Physics, University of Bielefeld, 33615 Bielefeld, Germany

    • H. Dachraoui &
    • U. Heinzmann
  3. Department of Physics, University of Crete and FORTH/IESL, Heraklion, Crete 71110, Greece

    • L. Mouchliadis &
    • I. E. Perakis
  4. Institute of Physics, Ilmenau University of Technology, 98684 Ilmenau, Germany

    • J. Demsar
  5. Institute of Experimental and Applied Physics, University of Kiel, 24098 Kiel, Germany

    • K. Rossnagel
  6. Present address: Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany.

    • H. Dachraoui


M.P., H.D., U.H. and R.H. planned the project; M.P., U.L. and J.-M.M. performed terahertz measurements; M.P., J.D., U.H., J.-M.M., K.R. and R.H. analysed data; K.R. and U.H. provided bulk samples; M.P. prepared thin-film samples; M.P., L.M. and I.E.P. elaborated the theoretical model; M.P., J.D., K.R., I.E.P. and R.H. wrote the paper. All authors contributed to discussions and gave comments on the manuscript.

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