logo CRAS
Comptes Rendus. Physique
Photoinduced charge density wave phase in 1T-TaS 2 : growth and coarsening mechanisms
Comptes Rendus. Physique, Volume 22 (2021) no. S2, pp. 139-160.

Part of the special issue: Physics of ultra-fast phenomena

Recent experiments have shown that the high-temperature incommensurate (I) charge density wave (CDW) phase of 1T-TaS 2 can be photoinduced from the lower-temperature, nearly commensurate CDW state. In a first step, several independent regions exhibiting I-CDW phase modulations nucleate and grow. After coalescence, these regions form a multidomain I-CDW phase that undergoes coarsening dynamics, i.e. a progressive increase of the domain size or I-CDW correlation length. Using time-resolved X-ray diffraction, we show that the wave vector of the photoinduced I-CDW phase is shorter than in the I-CDW phase at equilibrium, and progressively increases towards its equilibrium value as the correlation length increases. We interpret this behaviour as a consequence of a self-doping of the photoinduced I-CDW, following the presence of trapped electrons in the vicinity of CDW dislocation sites. Putting together results of the present and past experiments, we develop a scenario in which the I-CDW dislocations are created during the coalescence of the I-CDW phase regions.

Plusieurs expériences récentes ont montré que les impulsions laser dans les domaines optique ou proche infrarouge permettent de déclencher des transitions entre états à onde de densité de charge (ODC) dans 1T-TaS 2 . Nous nous intéressons ici à la transition entre l’état à ODC presque commensurable (NC) et l’état à ODC incommensurable (I), habituellement observé au-dessus de 350 K. Lors de cette transition, plusieurs régions présentant les modulations de l’état I se forment et se développent. Lorsque la coalescence a lieu, ces régions se muent en domaines de la phase I photoinduite de 1T-TaS 2 , caractérisés chacun par un phasage particulier de l’ODC I. La phase I ainsi fragmentée en domaines subit alors une dynamique de mûrissement, c’est-à-dire une augmentation progressive de la taille de domaine ou encore de la longueur de corrélation de l’ODC I. En utilisant la diffraction des rayons X résolue en temps, nous montrons que le vecteur d’onde de l’ODC I photoinduite est plus court que dans l’ODC I observée à l’équilibre thermodynamique. Celui-ci s’allonge progressivement vers sa valeur d’équilibre, en même temps que la longueur de corrélation de l’ODC I augmente. Nous attribuons ce comportement à un autodopage de l’ODC I photoinduite, dû à la présence d’électrons piégés au voisinage de dislocations de l’ODC I. En réalisant une synthèse des résultats des différentes expériences menées jusqu’à présent, nous développons un scénario dans lequel les dislocations de l’ODC I sont créées au moment de la coalescence.

Online First:
Published online:
DOI: 10.5802/crphys.89
Keywords: Photoinduced phase transitions, Pump–probe X-ray diffraction, Charge density wave compounds, Topological defects, Transition metal dichalcogenides
Amélie Jarnac 1; Vincent L. R. Jacques 2; Laurent Cario 3; Etienne Janod 3; Steven L. Johnson 4; Sylvain Ravy 2; Claire Laulhé 1

1 Université Paris-Saclay, Synchrotron Soleil, 91190, Saint-Aubin, France
2 Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405, Orsay, France
3 Institut des Matériaux Jean Rouxel, Université de Nantes, CNRS, 2 rue de la Houssinière, 44322 Nantes Cedex 03, France
4 Institute for Quantum Electronics, Eidgenossische Technishe Hochschule (ETH) Zürich, 8093 Zürich, Switzerland
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
@article{CRPHYS_2021__22_S2_139_0,
     author = {Am\'elie Jarnac and Vincent L.~R. Jacques and Laurent Cario and Etienne Janod and Steven L. Johnson and Sylvain Ravy and Claire Laulh\'e},
     title = {Photoinduced charge density wave phase in {1T-TaS}$_2$: growth and coarsening mechanisms},
     journal = {Comptes Rendus. Physique},
     pages = {139--160},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {22},
     number = {S2},
     year = {2021},
     doi = {10.5802/crphys.89},
     language = {en},
}
TY  - JOUR
AU  - Amélie Jarnac
AU  - Vincent L. R. Jacques
AU  - Laurent Cario
AU  - Etienne Janod
AU  - Steven L. Johnson
AU  - Sylvain Ravy
AU  - Claire Laulhé
TI  - Photoinduced charge density wave phase in 1T-TaS$_2$: growth and coarsening mechanisms
JO  - Comptes Rendus. Physique
PY  - 2021
DA  - 2021///
SP  - 139
EP  - 160
VL  - 22
IS  - S2
PB  - Académie des sciences, Paris
UR  - https://doi.org/10.5802/crphys.89
DO  - 10.5802/crphys.89
LA  - en
ID  - CRPHYS_2021__22_S2_139_0
ER  - 
%0 Journal Article
%A Amélie Jarnac
%A Vincent L. R. Jacques
%A Laurent Cario
%A Etienne Janod
%A Steven L. Johnson
%A Sylvain Ravy
%A Claire Laulhé
%T Photoinduced charge density wave phase in 1T-TaS$_2$: growth and coarsening mechanisms
%J Comptes Rendus. Physique
%D 2021
%P 139-160
%V 22
%N S2
%I Académie des sciences, Paris
%U https://doi.org/10.5802/crphys.89
%R 10.5802/crphys.89
%G en
%F CRPHYS_2021__22_S2_139_0
Amélie Jarnac; Vincent L. R. Jacques; Laurent Cario; Etienne Janod; Steven L. Johnson; Sylvain Ravy; Claire Laulhé. Photoinduced charge density wave phase in 1T-TaS$_2$: growth and coarsening mechanisms. Comptes Rendus. Physique, Volume 22 (2021) no. S2, pp. 139-160. doi : 10.5802/crphys.89. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.89/

[1] E. Dagotto Correlated electrons in high-temperature superconductors, Rev. Mod. Phys., Volume 66 (1994), pp. 763-840 | DOI

[2] M. Imada; A. Fujimori; Y. Tokura Metal–insulator transitions, Rev. Mod. Phys., Volume 70 (1998), pp. 1039-1263 | DOI

[3] K. Nasu Photoinduced Phase Transitions, World Scientific Publishing, Singapore, 2004

[4] K. Yonemitsu; K. Nasu Theory of photoinduced phase transitions in itinerant electron systems, Phys. Rep., Volume 465 (2008), pp. 1-60 | DOI

[5] J. Zhang; R. D. Averitt Dynamics and control in complex transition metal oxides, Annu. Rev. Mater. Res., Volume 44 (2014), pp. 19-43 | DOI

[6] D. N. Basov; R. D. Averitt; D. Hsieh Towards properties on demand in quantum materials, Nat. Mater., Volume 16 (2017), pp. 1077-1088 | DOI

[7] E. Janod; J. Tranchant; B. Corraze; M. Querre; P. Stoliar; M. Rozenberg; T. Cren; D. Roditchev; V. T. Phuoc; M.-P. Besland; L. Cario Resistive switching in mott insulators and correlated systems, Adv. Funct. Mater., Volume 25 (2015), pp. 6287-6305 | DOI

[8] A. Singer; S. K. K. Patel; R. Kukreja; V. Uhlíř; J. Wingert; S. Festersen; D. Zhu; J. M. Glownia; H. T. Lemke; S. Nelson; M. Kozina; K. Rossnagel; M. Bauer; B. M. Murphy; O. M. Magnussen; E. E. Fullerton; O. G. Shpyrko Photoinduced enhancement of the charge density wave amplitude, Phys. Rev. Lett., Volume 117 (2016), 056401 | DOI

[9] V. L. R. Jacques; C. Laulhé; N. Moisan; S. Ravy; D. L. Bolloc’h Laser-induced charge-density-wave transient depinning in chromium, Phys. Rev. Lett., Volume 117 (2016), 156401

[10] P. Stoliar; J. Tranchant; B. Corraze; E. Janod; M.-P. Besland; F. Tesler; M. Rozenberg; L. Cario A leaky-integrate-and-fire neuron analog realized with a mott insulator, Adv. Funct. Mater., Volume 27 (2017), 1604740 | DOI

[11] C. Adda; B. Corraze; P. Stoliar; P. Diener; J. Tranchant; A. Filatre-Furcate; M. Fourmigué; D. Lorcy; M.-P. Besland; E. Janod; L. Cario Mott insulators: a large class of materials for leaky integrate and fire (LIF) artificial neuron, J. Appl. Phys., Volume 124 (2018), 152124 | DOI

[12] G. Grüner Density Waves in Solids, Perseus Publishing, Cambridge, MA, 2000

[13] F. Schmitt; P. Kirchmann; U. Bovensiepen; R. Moore; L. Rettig; M. Krenz; J.-H. Chu; N. Ru; L. Perfetti; D. Lu; M. Wolf; I. Fisher; Z.-X. Shen Transient electronic structure and melting of a charge density wave in TbTe 3 , Science, Volume 321 (2008), pp. 1649-1652 | DOI

[14] A. Tomeljak; H. Schäfer; D. Städter; M. Beyer; K. Biljakovic; J. Demsar Dynamics of photoinduced charge-density-wave to metal phase transition in K 0.3 MoO 3 , Phys. Rev. Lett., Volume 102 (2009), 066404 | DOI

[15] R. Yusupov; T. Mertelj; V. V. Kabanov; S. Brazovskii; P. Kusar; J.-H. Chu; I. R. Fisher; D. Mihailovic Coherent dynamics of macroscopic electronic order through a symmetry-breaking transition, Nat. Phys., Volume 6 (2010), pp. 681-684 | DOI

[16] M. Eichberger; H. Schäfer; M. Krumova; M. Beyer; J. Demsar; H. Berger; G. Moriena; G. Sciaini; R. J. D. Miller Snapshots of cooperative atomic motions in the optical suppression of charge density waves, Nature, Volume 468 (2010), pp. 799-802 | DOI

[17] S. Hellmann; M. Beye; C. Sohrt; T. Rohwer; F. Sorgenfrei; H. Redlin; M. Kallaäne; M. Marczynski-Bühlow; F. Hennies; M. Bauer; A. Föhlisch; L. Kipp; W. Wurth; K. Rossnagel Ultrafast melting of a charge-density wave in the mott insulator 1T-TaS 2 , Phys. Rev. Lett., Volume 105 (2010), 187401 | DOI

[18] T. Rohwer; S. Hellmann; M. Wiesenmayer; C. Sohrt; A. Stange; B. Slomski; A. Carr; Y. Liu; L. Avila; M. Kalläne; S. Mathias; L. Kipp; K. Rossnagel; M. Bauer Collapse of long-range charge order tracked by time-resolved photoemission at high momenta, Nature, Volume 471 (2011), pp. 490-493 | DOI

[19] E. Möhr-Vorobeva; S. L. Johnson; P. Beaud; U. Staub; R. Desouza; C. Milne; G. Ingold; J. Demsar; H. Schaefer; A. Titov Nonthermal melting of a charge density wave in TiSe 2 , Phys. Rev. Lett., Volume 107 (2011), 036403 | DOI

[20] S. Hellmann; T. Rohwer; M. Kalläne; K. Hanff; C. Sohrt; A. Stange; A. Carr; M. Murnane; H. Kapteyn; L. Kipp; M. Bauer; K. Rossnagel Time-domain classification of charge-density-wave insulators, Nat. Commun., Volume 3 (2012), 1069 | DOI

[21] T.-R. T. Han; Z. Tao; S. D. Mahanti; K. Chang; C.-Y. Ruan; C. D. Malliakas; M. G. Kanatzidis Structural dynamics of two-dimensional charge-density waves in CeTe 3 investigated by ultrafast electron crystallography, Phys. Rev. B, Volume 86 (2012), 075145

[22] N. Erasmus; M. Eichberger; K. Haupt; I. Boshoff; G. Kassier; R. Birmurske; H. Berger; J. Demsar; H. Schwoerer Ultrafast dynamics of charge density waves in 4H b –TaSe 2 probed by femtosecond electron diffraction, Phys. Rev. Lett., Volume 109 (2012), 167402 | DOI

[23] P. Zhu; J. Cao; Y. Zhu; J. Geck; Y. Hidaka; S. Pjerov; T. Ritschel; H. Berger; Y. Shen; R. Tobey; J. P. Hill; X. J. Wang Dynamic separation of electron excitation and lattice heating during the photoinduced melting of the periodic lattice distortion in 2H-TaSe 2 , Appl. Phys. Lett., Volume 103 (2013), 071914

[24] T. Huber; S. O. Mariager; A. Ferrer; H. Schäfer; J. A. Johnson; S. Grübel; A. Lübcke; L. Huber; T. Kubacka; C. Dornes; C. Laulhé; S. Ravy; G. Ingold; P. Beaud; J. Demsar; S. L. Johnson Coherent structural dynamics of a prototypical charge-density-wave-to-metal transition, Phys. Rev. Lett., Volume 113 (2014), 026401 | DOI

[25] A. Zong; A. Kogar; Y.-Q. Bie; T. Rohwer; C. Lee; E. Baldini; E. Ergeçen; M. B. Yilmaz; B. Freelon; E. J. Sie; H. Zhou; J. Straquadine; P. Walmsley; P. E. Dolgirev; A. V. Rozhkov; I. R. Fisher; P. Jarillo-Herrero; B. V. Fine; N. Gedik Evidence for topological defects in a photoinduced phase transition, Nat. Phys., Volume 15 (2019), pp. 27-31 | DOI

[26] A. Zong; P. E. Dolgirev; A. Kogar; E. Ergeçen; M. B. Yilmaz; Y.-Q. Bie; T. Rohwer; I.-C. Tung; J. Straquadine; X. Wang; Y. Yang; X. Shen; R. Li; J. Yang; S. Park; M. C. Hoffmann; B. K. Ofori-Okai; M. E. Kozina; H. Wen; X. Wang; I. R. Fisher; P. Jarillo-Herrero; N. Gedik Dynamical slowing-down in an ultrafast photoinduced phase transition, Phys. Rev. Lett., Volume 123 (2019), 097601 | DOI

[27] M. Trigo; P. Giraldo-Gallo; M. E. Kozina; T. Henighan; M. P. Jiang; H. Liu; J. N. Clark; M. Chollet; J. M. Glownia; D. Zhu; T. Katayama; D. Leuenberger; P. S. Kirchmann; I. R. Fisher; Z. X. Shen; D. A. Reis Coherent order parameter dynamics in SmTe 3 , Phys. Rev. B, Volume 99 (2019), 104111 | DOI

[28] S. Sun; L. Wei; Z. Li; G. Cao; Y. Liu; W. J. Lu; Y. P. Sun; H. Tian; H. Yang; J. Li Direct observation of an optically induced charge density wave transition in 1T-TaSe 2 , Phys. Rev. B, Volume 92 (2015), 224303

[29] T.-R. T. Han; F. Zhou; C. D. Malliakas; P. M. Duxbury; S. D. Mahanti; M. G. Kanatzidis; C.-Y. Ruan Exploration of metastability and hidden phases in correlated electron crystals visualized by femtosecond optical doping and electron crystallography, Sci. Adv., Volume 1 (2015), e1400173

[30] K. Haupt; M. Eichberger; N. Erasmus; A. Rohwer; J. Demsar; K. Rossnagel; H. Schwoerer Ultrafast metamorphosis of a complex charge-density wave, Phys. Rev. Lett., Volume 116 (2016), 016402 | DOI

[31] L. L. Guyader; T. Chase; A. H. Reid; R. K. Li; D. Svetin; X. Shen; T. Vecchione; X. J. Wang; D. Mihailovic; H. A. Dürr Stacking order dynamics in the quasi-two-dimensional dichalcogenide 1T-TaS 2 probed with mev ultrafast electron diffraction, Struct. Dyn., Volume 4 (2017), 044020 | DOI

[32] C. Laulhé; T. Huber; G. Lantz; A. Ferrer; S. O. Mariager; S. Grübel; J. Rittmann; J. A. Johnson; V. Esposito; A. Lübcke; L. Huber; M. Kubli; M. Savoini; V. L. R. Jacques; L. Cario; B. Corraze; E. Janod; G. Ingold; P. Beaud; S. L. Johnson; S. Ravy Ultrafast formation of a charge density wave state in 1T-TaS 2 : observation at nanometer scales using time-resolved X-ray diffraction, Phys. Rev. Lett., Volume 118 (2017), 247401 | DOI

[33] G. Lantz; C. Laulhé; S. Ravy; M. Kubli; M. Savoini; K. Tasca; E. Abreu; V. Esposito; M. Porer; A. Ciavardini; L. Cario; J. Rittmann; P. Beaud; S. L. Johnson Domain-size effects on the dynamics of a charge density wave in 1T-TaS 2 , Phys. Rev. B, Volume 96 (2017), 224101 | DOI

[34] S. Vogelgesang; G. Storeck; J. G. Horstmann; T. Diekmann; M. Sivis; S. Schramm; K. Rossnagel; S. Schäfer; C. Ropers Phase ordering of charge density waves traced by ultrafast low-energy electron diffraction, Nat. Phys., Volume 14 (2018), pp. 184-190 | DOI

[35] L. Stojchevska; I. Vaskivskyi; T. Mertelj; P. Kusar; D. Svetin; S. Brazovskii; D. Mihailovic Ultrafast switching to a stable hidden quantum state in an electronic crystal, Science, Volume 344 (2014), pp. 177-180 | DOI

[36] Y. A. Gerasimenko; P. Karpov; I. Vaskivskyi; S. Brazovskii; D. Mihailovic Intertwined chiral charge orders and topological stabilization of the light-induced state of a prototypical transition metal dichalcogenide, NPJ Quantum Mater., Volume 4 (2019), 32 | DOI

[37] A. Kogar; A. Zong; P. E. Dolgirev; X. Shen; J. Straquadine; Y.-Q. Bie; X. Wang; T. Rohwer; I.-C. Tung; Y. Yang; R. Li; J. Yang; S. Weathersby; S. Park; M. E. Kozina; E. J. Sie; H. Wen; P. Jarillo-Herrero; I. R. Fisher; X. Wang; N. Gedik Light-induced charge density wave in LaTe 3 , Nat. Phys., Volume 16 (2019), pp. 159-163 | DOI

[38] D. Mihailovic The importance of topological defects in photoexcited phase transitions including memory applications, Appl. Sci., Volume 9 (2019), 890 | DOI

[39] J. A. Wilson; F. J. di Salvo; S. Mahajan Charge-density waves and superlattices in the metallic layered transition metal dichalcogenides, Adv. Phys., Volume 24 (1975), pp. 117-201 | DOI

[40] T. Ishiguro; H. Sato Electron microscopy of phase transformations in 1T-TaS 2 , Phys. Rev. B, Volume 44 (1991) no. 5, pp. 2046-2060 | DOI

[41] A. Spijkerman; J. L. de Boer; A. Meetsma; G. A. Wiegers; S. van Smaalen X-ray crystal-structure refinement of the nearly commensurate phase of 1T-TaS 2 in (3 + 2)-dimensional superspace, Phys. Rev. B, Volume 56 (1997) no. 21, pp. 13757-13767 | DOI

[42] K. Rossnagel On the origin of charge-density waves in selected layered transition-metal dichalcogenides, J. Phys. Condens. Matter, Volume 23 (2011), 213001 | DOI

[43] W. L. McMillan Landau theory of charge-density waves in transition-metal dichalcogenides, Phys. Rev. B, Volume 12 (1975), pp. 1187-1196 | DOI

[44] K. Momma; F. Izumi Vesta 3 for three-dimensional visualization of crystal, volumetric and morphology data, J. Appl. Crystallogr., Volume 44 (2011), pp. 1272-1276 | DOI

[45] S. Ravy; C. Laulhé; J. P. Itié; P. Fertey; B. Corraze; S. Salmon; L. Cario High-pressure X-ray diffraction study of 1T-TaS 2 , Physica B, Volume 407 (2012), pp. 1704-1706 | DOI

[46] A. Beal; H. Hughes; W. Liang The reflectivity spectra of some group va transition metal dichalcogenides, J. Phys., C, Solid State Phys., Volume 8 (1975), pp. 4236-4248 | DOI

[47] M.-A. Tordeux; J. Barros; A. Bence; P. Brunelle; N. Hubert; M. Labat; A. Nadji; L. Nadolski; P. Lebasque; J.-P. Pollina; C. Evain Low-alpha operation for the soleil storage ring, Proceedings of the 2012 International Particle Accelerator Conference (IPAC12) (2012), pp. 1608-1610

[48] B. Henke; E. Gullikson; J. Davis X-ray interactions: photoabsorption, scattering, transmission, and reflection at e = 50–30000 eV, z = 1–92, At. Data Nucl. Data Tables, Volume 54 (1993), pp. 181-342 | DOI

[49] K. Medjoubi; S. Hustache; F. E. Picca; J. Bérar; N. Boudet; F. Bompard; P. Breugnon; J.-C. Clémens; A. Dawiec; P. Delpierre; B. Dinkenspiler; S. Godiot; J.-P. Logier; M. Menouni; C. Morel; M. Nicolas; P. Pangaud; E. Vigeolas Performance and applications of the CdTe- and Si-XPAD3 photon counting 2D detector, J. Instrum., Volume 6 (2011), C01080

[50] J.-P. Ricaud; P. Betinelli-Deck; J. Bisou; X. Elattaoui; C. Laulhé; P. Monteiro; L. S. Nadolski; G. Renaud; S. Ravy; M. Silly; F. Sirotti The timbel synchronization board for time-resolved experiments at synchrotron soleil, Proceedings of the 2011 International Conference on Accelerator and Large Experimental Physics Control Systems (ICALEPCS2011) (2011), pp. 1036-1038

[51] L. Perfetti; P. A. Loukakos; M. Lisowski; U. Bovensiepen; H. Berger; S. Biermann; P. S. Cornaglia; A. Georges; M. Wolf Time evolution of the electronic structure of 1T-TaS 2 through the insulator–metal transition, Phys. Rev. Lett., Volume 97 (2006), 067402 | DOI

[52] L. Perfetti; P. A. Loukakos; M. Lisowski; U. Bovensiepen; M. Wolf; H. Berger; S. Biermann; A. Georges Femtosecond dynamics of electronic states in the mott insulator 1T-TaS 2 by time resolved photoelectron spectroscopy, New J. Phys., Volume 10 (2008), 053019

[53] L. Rettig; R. Cortés; J.-H. Chu; I. R. Fisher; F. Schmitt; R. G. Moore; Z.-X. Shen; P. S. Kirchmann; M. Wolf; U. Bovensiepen Persistent order due to transiently enhanced nesting in an electronically excited charge density wave, Nat. Commun., Volume 7 (2016), 10459 | DOI

[54] P. Monceau Electronic crystals: an experimental overview, Adv. Phys., Volume 61 (2012), pp. 325-581 | DOI

[55] F. E. Picca Ghkl’s documentation [https://people.debian.org/~picca/hkl/hkl.html], Université Paris-Saclay (Synchrotron SOLEIL), 91190, Saint-Aubin, France

[56] C. Thomsen; H. T. Grahn; H. J. Maris; J. Tauc Surface generation and detection of phonons by picosecond light pulses, Phys. Rev. B, Volume 34 (1986), pp. 4129-4138 | DOI

[57] S. Lee; G. J. Williams; M. I. Campana; D. A. Walko; E. C. Landahl Picosecond X-ray strain rosette reveals direct laser excitation of coherent transverse acoustic phonons, Sci. Rep., Volume 6 (2016), 19140

[58] Structural Phase Transitions in Layered Transition Metal Compounds (K. Motizuki, ed.), Springer, Netherlands, 1986 | DOI

[59] C. B. Scruby; P. M. Williams; G. S. Parry The role of charge density waves in structural transformations of 1T-TaS 2 , Philos. Mag., Volume 31 (1975), pp. 255-274 | DOI

[60] K. Nakanishi; H. Takatera; Y. Yamada; H. Shiba The nearly commensurate phase and effect of harmonics on the successive phase transitions in 1T-TaS 2 , J. Phys. Soc. Japan, Volume 43 (1977), pp. 1509-1517 | DOI

[61] J. van Landuyt; G. van Tendeloo; S. Amelinckx Electron diffraction study of inter- and intrapolytypic phase transition in transition metal dichalcogenides. III. complementary diffraction studies and lattice imaging of the deformation waves, Phys. Status Solidi A, Volume 36 (1976), pp. 757-777 | DOI

[62] J. A. Wilson; F. J. di Salvo; S. Mahajan Charge-density waves in metallic, layered, transition-metal dichalcogenides, Phys. Rev. Lett., Volume 32 (1974), pp. 882-885 | DOI

[63] L. F. Mattheiss Band structures of transition-metal-dichalcogenide layer compounds, Phys. Rev. B, Volume 8 (1973), pp. 3719-3740 | DOI

[64] J.-D. Su; A. R. Sandy; J. Mohanty; O. G. Shpyrko; M. Sutton Collective pinning dynamics of charge-density waves in 1T-TaS 2 , Phys. Rev. B, Volume 86 (2012), 205105

[65] A. J. Bray Theory of phase-ordering kinetics, Adv. Phys., Volume 51 (2002), pp. 481-587 | DOI

[66] D. Feinberg; J. Friedel Elastic and plastic deformations of charge density waves, J. Phys. (France), Volume 49 (1988), pp. 485-496 | DOI

[67] H. Toyoki Pair annihilation of pointlike topological defects in the ordering process of quenched systems, Phys. Rev. A, Volume 42 (1990), pp. 911-917 | DOI

[68] D. Toussaint; F. Wilczek Particle-antiparticle annihilation in diffusive motion, J. Chem. Phys., Volume 78 (1983), pp. 2642-2647 | DOI

[69] P. Papon; J. Leblond; P. H. E. Meijer The Physics of Phase Transitions: Concepts and Applications, Springer, Netherlands, 2006 | Zbl

[70] K. Maki; X. Z. Huang Phase vortices in charge-density-wave conductors, Phys. Rev. B, Volume 37 (1988), pp. 8668-8673 | DOI

Cited by Sources: