The essential role of surface pinning in the dynamics of charge density waves submitted to external dc fields
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THE EUROPEAN PHYSICAL JOURNAL B
Regular Article
The essential role of surface pinning in the dynamics of charge density waves submitted to external dc fields Ewen Bellec 1,2,a , Vincent L.R. Jacques 2 , Jonathan Caillaux 2 , and David Le Bolloc’h 2 1 2
ESRF – The European Synchrotron, 71 Avenue des Martyrs, 38000 Grenoble, France Laboratoire de Physique des Solides, UMR 8502 CNRS, Universit´e Paris-Saclay, 91405 Orsay Cedex, France Received 24 April 2020 / Received in final form 4 June 2020 Published online 2 September 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. A charge density wave (CDW) submitted to an electric field displays a strong shear deformation because of pinning at the lateral surfaces of the sample. This CDW transverse pinning was recently observed but has received little attention from a theoretical point of view until now despite important consequences on electrical conductivity properties. Here, we provide a description of this phenomenon by considering a CDW submitted to an external dc electric field and constrained by boundary conditions including both longitudinal pinning due to electrical contacts and transverse surface pinning. A simple formula for the CDW phase is obtained in 3D by using the Green function and image charges method. In addition, an analytical expression of the threshold field dependence on both length and sample cross-section is obtained by considering the phase slip process. We show that the experimental data are well reproduced with this model and that bulk pinning can be neglected. This study shows that the dynamical properties of CDW systems could be mainly driven by boundary effects, despite the comparatively huge sample volumes.
1 Introduction When a sufficiently large electrical current is applied to a charge density wave (CDW) system, a non-linear current may be induced [1,2]. This current has a periodic structure both in time [3] and space [4,5] and is believed to be due to a collective transport of charge based on a traveling periodic array of topological 2π solitons [6]. The CDW can be described as an elastic medium evolving under the application of an external electric field [7]. When this field exceeds a threshold value Eth , the CDW periodicity is broken and a soliton is created reducing the total elastic energy. This phase-slip mechanism [8,9] has been widely discussed in the literature as a thermally activated nucleation [10,11] or as a quantum process [12,13]. The sliding CDW phenomenon was extensively studied as a function of temperature [14], under a continuous laser photo-illumination [15] or as a depinning process induced by a short laser pulse excitation [16]. In all these phenomena, CDW pinning plays a fundamental role. The aim of this paper is to theoretically treat pinning effects as a whole including pinning at lateral surfaces when the CDW is submitted to an applied field and the incidence of this pinning on the threshold electric field Eth as a function of sample dime
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