Quenching of a charge-density-wave by enhanced lattice fluctuations

Electron-phonon coupling (EPC) stands at the origin of a broad variety of phenomena. In particular, it shapes the main functionalities of quantum materials, including superconductivity, hence it is a persistent subject of study. Strong EPC is also responsible for the manifestation of a charge-density wave (CDW) phase in many materials. Specifically, below a critical temperature, several low-dimensional materials display a new energetically favorable ground state, the CDW, formed simultaneously by a periodic modulation of the electronic charge density and a periodic distortion of the lattice, in the form of small displacements of the ion positions. While for weak EPC the phase transition from the CDW to the normal phase may be controlled by increasing the electronic entropy, in the case of a strong EPC the transition can be induced by the lattice entropy. These lattice-entropy-induced transitions are also called order-disorder transitions. Due to the complexity of such systems, however, a precise microscopic understanding of the CDW transition remains elusive and calls for further studies to gain a better understanding of the underlying processes. Quenching the CDW phase by external stimuli, such as ultrashort (~100 fs) light pulses, allows one to shed light on the CDW driving force by measuring the transition speed, which can be accessed by probing the ultrafast electron dynamics. This knowledge constitutes an essential step towards the development of next-generation electronic devices based on these materials.

In this work, we show that in the strongly-coupled CDW compound VTe₂, a light-induced phase transition is determined by an incoherent process that evolves on a timescale much slower than that expected for a conventional (electron-driven) transition. The experimental data were acquired using the time- and angle-resolved photoemission spectroscopy (TR-ARPES) endstation at the T-ReX facility of the FERMI free-electron laser.

ARPES allows us to monitor the evolution of the electronic band structure during the light-induced phase transition, as Fig. 1 shows. The main signature of the CDW phase is an energy gap in the electronic band structure, which gradually closes as the system approaches the normal state of the material. Following the ultrafast evolution of the CDW gap after an optical excitation by means of TR-ARPES  thus gives direct access to the material’s ground state. In particular, Fig. 1 shows the deformation of an originally flat band (panel a) towards a more bent band (panel c) within the first 500 fs after optical excitation, which signals a light-induced (partial) gap closure. This effect looks more evident when focusing on the difference between the two snapshots, which is shown in panel f (red areas indicate intensity increase, while blue areas intensity decrease).

Figure 1:  CDW band structure dynamics. a–c Selected ARPES spectra acquired along the K-M2-K direction at different pump-probe delays: (a) before the arrival of the pump, (b) and (c) respectively 100 and 500 fs after the arrival of the pump pulse. d–f Differential ARPES maps showing the changes in the photoemission intensity induced by the pump pulse. g, h The photoemission intensity from the momentum region delimited by the dashed lines in (c) and (f), plotted as a function of the pump-probe delay. (i) Evolution of the photoemission intensity extracted from the boxes reported in (h). The gray dashed line shows the pump-probe delay at which traces B and C reach their maximum change.

Recording the band structure at different time-delays after photoexcitation, one can follow the temporal evolution of the transition in a step-by-step manner (cf. Fig. 1c,e showing an intermediate situation reached 100 fs after photoexcitation). By following the intensity changes in a defined momentum region of the electronic band structure (cf. dashed lines in Fig. 1c,f), as shown in Fig. 1g-i, one can gain insights into the underlying microscopic processes. Implementing a three-temperature model, we successfully describe the CDW gap dynamics by considering the population of a subset of strongly coupled optical phonon modes, which determine an increase in lattice fluctuations, and hence in the transient disorder of the system as schematically illustrated in Fig. 2.

Figure 2: Sketch showing the partial loss of the long-range CDW order in consequence of the incoherent excitation of the strongly-coupled optical phonon modes. The light induced displacements of the vanadium atoms (red spheres) are depicted by the black arrows. (I) Before the arrival of the pump pulse the system is characterized by a well-defined CDW order and thus the three subsystems electrons, phonons and lattice are in equilibrium (T_e = T_p = T_l ≪ T_CDW). The energy injected by the pump in the system is initially absorbed by the electrons and then transferred to a subset of strongly-coupled optical phonon modes. (II) The excitation of these phonon modes, without a macroscopic phase coherence, leads to a partial loss of the CDW long-range order of the system. (III) After ≈ 2 ps from the arrival of the pump pulse, the three subsystems are again in equilibrium and from there on the relaxation dynamics is governed solely by heat diffusion.

In conclusion, we showed that the light-induced phase transition in VTe₂ can be fully described by considering the population of a subset of strongly coupled optical phonon modes, while only a marginal role is played by the excitation of the CDW amplitude modes. The excitation of strongly-coupled phonons, which occurs without a macroscopic phase coherence, has the effect of increasing the lattice fluctuations and thus increasing the transient disorder of the system. The microscopic picture we developed extends beyond the specific case of VTe₂ and can, in principle, be applied to other CDW systems. More generally, the results presented in this work highlight the need for a deeper understanding of the interplay between lattice fluctuations and the CDW phase, paving the way for further exploration of the non-equilibrium properties of strongly-coupled CDW systems.

Manuel Tuniz^1,2, Denny Puntel¹, Wibke Bronsch³, Francesco Sammartino¹, Gian Marco Pierantozzi², Riccardo Cucini², Fulvio Parmigiani^1,3,4, and Federico Cilento^3
1 Dipartimento di Fisica, Universitá degli Studi di Trieste, Trieste, Italy
² CNR - Istituto Officina dei Materiali (IOM), Unitá di Trieste, Trieste, Italy 
³ Elettra - Sincrotrone Trieste S.C.p.A., Trieste, Italy 
⁴ International Faculty, University of Cologne, Cologne, Germany 

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