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1. Interplay of Quantum and Thermal Fluctuations in Two-Dimensional Randomly Pinned Charge Density Waves

   O'Brien, Matthew C; Fradkin, Eduardo (October 2024, 2410.16375)

   The interplay between quantum and thermal fluctuations in the presence of quenched random disorder is a long-standing open theoretical problem which has been made more urgent by advances in modern experimental techniques. The fragility of charge density wave order to impurities makes this problem of particular interest in understanding a host of real materials, including the cuprate high-temperature superconductors. To address this question, we consider the quantum version of an exactly solvable classical model of two-dimensional randomly pinned incommensurate charge density waves first introduced by us in a recent work, and use the large-N technique to obtain the phase diagram and order parameter correlations. Our theory considers quantum and thermal fluctuations and disorder on equal footing by accounting for all effects non-perturbatively, which reveals a novel crossover between under-damped and over-damped dynamics of the fluctuations of the charge density wave order parameter. 

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2. Endotaxial stabilization of 2D charge density waves with long-range order

   https://doi.org/10.1038/s41467-024-45711-3  

   Sung, Suk Hyun; Agarwal, Nishkarsh; El_Baggari, Ismail; Kezer, Patrick; Goh, Yin Min; Schnitzer, Noah; Shen, Jeremy M; Chiang, Tony; Liu, Yu; Lu, Wenjian; et al (December 2024, Nature Communications)

   Abstract Charge density waves are emergent quantum states that spontaneously reduce crystal symmetry, drive metal-insulator transitions, and precede superconductivity. In low-dimensions, distinct quantum states arise, however, thermal fluctuations and external disorder destroy long-range order. Here we stabilize ordered two-dimensional (2D) charge density waves through endotaxial synthesis of confined monolayers of 1T-TaS₂. Specifically, an ordered incommensurate charge density wave (oIC-CDW) is realized in 2D with dramatically enhanced amplitude and resistivity. By enhancing CDW order, the hexatic nature of charge density waves becomes observable. Upon heating via in-situ TEM, the CDW continuously melts in a reversible hexatic process wherein topological defects form in the charge density wave. From these results, new regimes of the CDW phase diagram for 1T-TaS₂are derived and consistent with the predicted emergence of vestigial quantum order. 

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3. Melting of the charge density wave by generation of pairs of topological defects in UTe2

   https://doi.org/10.1038/s41567-024-02429-9  

   Aishwarya, Anuva; May-Mann, Julian; Almoalem, Avior; Ran, Sheng; Saha, Shanta R.; Paglione, Johnpierre; Butch, Nicholas P.; Fradkin, Eduardo; Madhavan, Vidya (March 2024, Nature Physics)

   Topological defects are singularities in an ordered phase that can have a profound effect on phase transitions and serve as a window into the order parameter. Examples of topological defects include dislocations in charge density waves and vortices in a superconductor or pair density wave, where the latter is a condensate of Cooper pairs with finite momentum. Here we demonstrate the role of topological defects in the magnetic-field-induced disappearance of a charge density wave in the heavy-fermion superconductor UTe2. We reveal pairs of topological defects of the charge density wave with positive and negative phase winding. The pairs are directly correlated with zeros in the charge density wave amplitude and increase in number with increasing magnetic field. A magnetic field generates vortices of the superconducting and pair density wave orders that can create topological defects in the charge density wave and induce the experimentally observed melting of this charge order at the upper critical field. Our work reveals the important role of magnetic-field-generated topological defects in the melting of the charge density wave order parameter in UTe2 and provides support for the existence of a pair density wave order on the surface. 

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4. Nonequilibrium dynamics of spontaneous symmetry breaking into a hidden state of charge-density wave

   https://doi.org/10.1038/s41467-020-20834-5  

   Zhou, Faran; Williams, Joseph; Sun, Shuaishuai; Malliakas, Christos D.; Kanatzidis, Mercouri G.; Kemper, Alexander F.; Ruan, Chong-Yu (January 2021, Nature Communications)

   Abstract Nonequilibrium phase transitions play a pivotal role in broad physical contexts, from condensed matter to cosmology. Tracking the formation of nonequilibrium phases in condensed matter requires a resolution of the long-range cooperativity on ultra-short timescales. Here, we study the spontaneous transformation of a charge-density wave in CeTe₃from a stripe order into a bi-directional state inaccessible thermodynamically but is induced by intense laser pulses. With ≈100 fs resolution coherent electron diffraction, we capture the entire course of this transformation and show self-organization that defines a nonthermal critical point, unveiling the nonequilibrium energy landscape. We discuss the generation of instabilities by a swift interaction quench that changes the system symmetry preference, and the phase ordering dynamics orchestrated over a nonadiabatic timescale to allow new order parameter fluctuations to gain long-range correlations. Remarkably, the subsequent thermalization locks the remnants of the transient order into longer-lived topological defects for more than 2 ns. 

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5. Revealing the order parameter dynamics of 1T-TiSe$$_2$$ following optical excitation

   https://doi.org/10.1038/s41598-022-19319-w  

   Huber, Maximilian; Lin, Yi; Dale, Nicholas; Sailus, Renee; Tongay, Sefaattin; Kaindl, Robert A.; Lanzara, Alessandra (December 2022, Scientific Reports)

   Abstract The formation of a charge density wave state is characterized by an order parameter. The way it is established provides unique information on both the role that correlation plays in driving the charge density wave formation and the mechanism behind its formation. Here we use time and angle resolved photoelectron spectroscopy to optically perturb the charge-density phase in 1T-TiSe $$_2$$ 2  and follow the recovery of its order parameter as a function of energy, momentum and excitation density. Our results reveal that two distinct orders contribute to the gap formation, a CDW order and pseudogap-like order, manifested by an overall robustness to optical excitation. A detailed analysis of the magnitude of the the gap as a function of excitation density and delay time reveals the excitonic long-range nature of the CDW gap and the short-range Jahn–Teller character of the pseudogap order. In contrast to the gap, the intensity of the folded Se $$_{4p}$$ 4 p * band can only give access to the excitonic order. These results provide new information into the the long standing debate on the origin of the gap in TiSe $$_2$$ 2  and place it in the same context of other quantum materials where a pseudogap phase appears to be a precursor of long-range order. 

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