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Charge transport in materials has an impact on a wide range of devices based on semiconductor, battery or superconductor technology. Charge transport in sliding Charge Density Waves (CDW) differs from all others in that the atomic lattice is directly involved in the transport process. To obtain an overall picture of the structural changes associated to the collective transport, the large coherent X-ray beam generated by an X-ray free-electron laser (XFEL) source was used. The CDW phase can be retrieved over the entire sample from diffracted intensities using a genetic algorithm. For currents below threshold, increasing shear deformation is observed in the central part of the sample while longitudinal deformation appears above threshold when shear relaxes. Shear thus precedes longitudinal deformation, with relaxation of one leading to the appearance of the other. Moreover, strain accumulates on surface steps in the sliding regime, demonstrating the strong pinning character of these surface discontinuities. The sliding process of nanometric CDW is based on an impressive spatial coherence involving the macroscopic sample dimensions., Comment: 20 pages, 5 figures

Magnetic quantum oscillations (MQO) of Hall coefficient are measured in rare-earth tritelluride TmTe$_{3}$ and shown to be much stronger and persist to higher temperature than the Shubnikov oscillations. It is general for MQO in strongly anisotropic metals, and the combined measurements of Hall and diagonal magnetoresistance provide useful informations about the electronic structure. The ratio of their MQO amplitudes depends linearly on magnetic field, and its slope gives a simple and accurate measurement tool of the electron mean free time and its temperature dependence., Comment: 6 pages, 2 figures

The electronic orders appearing in condensed matter systems are originating from the precise arrangement of atoms constituting the crystal as well as their nature. This teneous relationship can lead to highly different phases in condensed matter, and drive electronic phase transitions. Here, we show that a very slight deformation of the crystal structure of TbTe$_3$ can have a dramatic influence on the electronic order that is stabilized. In particular, we show that the Charge Density Wave (CDW) developping along the $\vec{c}$ axis in the pristine state, switches to an orientation along $\vec{a}$ when the naturally orthorhombic system is turned into a tetragonal system. This is achieved by performing true biaxial mechanical deformation of a TbTe$_3$ sample from 250K to 375K, and by measuring both structural and electronic parameters with x-ray diffraction and transport measurements. We show that this switching transition is driven by the tetragonality parameter $a/c$, and that the transition occurs for $a=c$, with a coexistence region for $0.9985< a/c < 1.002$. The CDW transition temperature $T_c$ is found to have a linear dependence with $a/c$, with no saturation in the deformed states investigated here, while the gap saturates out of the coexistence region. The linear dependence of $T_c$ is accounted for within a tight-binding model. Our results question the relationship between the gap and $T_c$ in RTe$_3$ systems. More generally, our method of applying true biaxial deformation at cryogenic temperatures can be applied to many systems displaying electronic phase transitions, and opens a new route towards the study of coexisting or competing electronic orders in condensed matter.

We studied the in-plane angular magnetoresistance (AMR), in the normal state, of underdoped superconducting Sr1-xLaxCuO2 , which has the simplest crystal structure among cuprates. The measurements of two underdoped thin films with different dopings were performed in intense magnetic field H (up to 22 T). The longitudinal magnetoresistance at temperature T is negative and scales with H/T. For both samples, the AMR is anisotropic and shows an unexpected dependence on H intensity. While at the low magnetic field, one observes essentially twofold AMR oscillations for the more doped sample, fourfold ones start to grow under the high magnetic field, resulting in the coexistence of the two. For the less doped film at the low magnetic field, both twofold and fourfold AMR components exist. With the increase of the magnetic field, the fourfold component survives a pi/4 phase shift, during which its amplitude vanishes, at a magnetic field Hc such as: 16 T < Hc < 17 T. As a result, at the high magnetic field above Hc, the angular dependence of the in-plane magnetoresistance turns out to be the same for both samples. We tentatively ascribe the above features to the presence of anti-ferromagnetism in the CuO2 planes of underdoped Sr1-xLaxCuO2., Comment: 9 pages 5 figures

A recent experimental work has reported an excess of the non-linear conductivity in the charge density wave (CDW) sliding mode of the quasi one-dimensional compound (TaSe4)2I, when a magnetic field is applied co-linearly to the electric field [Gooth et al., Nature 575, 315 (2019)]. This result has opened a conceptual approach, where the CDW gap in (TaSe4)2I is opened between Weyl fermions of opposite chirality with the assumption that this compound is a Weyl semi-metal in its undistorted high temperature phase. We report measurements in the sliding state of (TaSe4)2I performed in similar conditions. We have found no increase in the magnetoconductivity. In our attempts for understanding this unsettling discrepancy, we stress the specific nature of the Peierls transition in (TaSe4)2I and the strong electron-phonon coupling present in this compound. Given the lack of further evidence, we think that it is premature to assert that (TaSe4)2I is an axionic insulator., Comment: 8 pages, 3 figures

We report a ground state with strongly coupled magnetic and charge density wave orders mediated via orbital ordering in the layered compound \tbt. In addition to the commensurate antiferromagnetic (AFM) and charge density wave (CDW) orders, new magnetic peaks are observed whose propagation vector equals the sum of the AFM and CDW propagation vectors, revealing an intricate and highly entwined relationship. This is especially interesting given that the magnetic and charge orders lie in different layers of the crystal structure where the highly localized magnetic moments of the Tb$^{3+}$ ions are netted in the Tb-Te stacks, while the charge order is formed by the conduction electrons of the adjacent Te-Te layers. Our results, based on neutron diffraction and resonant x-ray scattering reveal that the charge and magnetic subsystems mutually influence each other via the orbital ordering of Tb$^{3+}$ ions., Comment: 5 pages, 4 figures

We show that the charge density wave (CDW) ground state below the Peierls transition temperature, $T_{CDW}$, of rare-earth tritellurides is not at its equilibrium value, but depends on the time where the system was kept at a fixed temperature below $T_{CDW}$. This ergodicity breaking is revealed by the increase of the threshold electric field for CDW sliding which depends exponentially on time. We tentatively explain this behavior by the reorganization of the oligomeric (Te$_x$)$^{2-}$ sequence forming the CDW modulation., Comment: 10 pages, 5 figures, accepted in PRB

Collective charge-density wave (CDW) transport was measured under a high magnetic field in NbSe$_3$ microbridges which have been cut transversely and at an angle to the chains' direction. We give evidences that the CDW sliding is driven by the Hall voltage generated by the inter-chain current of normal carriers. We have discovered a re-entrance effect of the Hall-driven sliding above a crossover temperature at which the Hall constant has been known to change sign. For the narrow channel, cut at 45$^\circ$ relative to the chain axis, we observed an evolution from the Hall-driven sliding at low temperatures, to the conventional sliding at higher temperatures, which corroborates with falling of the Hall constant. In this course, the nonlinear contribution to the conductivity coming from the collective sliding changes sign. The quantization of Shapiro-steps, generated presumably by a coherent sequence of phase slips, indicates that their governing changes from the applied voltage to the current., Comment: 6 pages, 5 figures, accepted in PRB

The microscopic description of the CDW phase transition is still debated and remains controversial. The question is how to extend the Peierls picture to real systems in higher dimensions. A general tendency is found in the thermodynamic properties such as the specific heat jump DCp and the decrease of the longitudinal elastic stiffness constant DC11/C11 at the CDW phase transition in several materials, such as quasi-one dimensional (K0.3MoO3), transition metal dichalcogenide compounds (2H-NbSe2), rare earth tritellurides (TbTe3, ErTe3, HoTe3) and intermetallic compound (Lu5Ir4Si10). DCp and DC11/C11 increase as the temperature of the phase transition TCDW and TCDW2 respectively. The same tendency is found at the spin density phase transition in chromium and CuGeO3.Thermodynamic properties of almost all CDW systems, although it has been recognized to exhibit large fluctuations, follow the classical mean field BCS type behavior., Comment: 10 pages 3 figures

Our measurements of the Hall coefficient in rare-earth tritelluride compounds reveal a strong hysteresis between cooling and warming in the low temperature range where a second unidirectional charge density wave (CDW) occurs. We show that this effect results from the interplay between two instabilities: band crossing of the Te $p_{x}$ and $p_{y}$ orbitals at the Fermi level and CDW, which have a close energy gain and compete. Calculation of the electron susceptibility at the CDW wave vector with and without band anticrossing reconstruction of the electron spectrum yields a satisfactory estimation of the temperature range of the hysteresis in Hall effect measurements., Comment: 10 pages, 5 pages main text + 5 pages supplemental materials, 7 figures

Incommensurate charge density waves (CDW) have the extraordinary ability to display non-Ohmic behavior when submitted to an external field. The mechanism leading to this non trivial dynamics is still not well understood, although recent experimental studies tend to prove that it is due to solitonic transport. Solitons could come from the relaxation of the strained CDW within an elastic-to-plastic transition. However, the nucleation process and the transport of these charged topological objects have never been observed at the local scale until now. In this letter, we use in-situ scanning x-ray micro-diffraction with micrometer resolution of a NbSe$_3$ sample designed to have sliding and non-sliding areas. Direct imaging of the charge density wave deformation is obtained using an analytical approach based on the phase gradient to disentangle the transverse from the longitudinal components over a large surface of a hundred microns size. We show that the CDW dissociates itself from the host lattice in the sliding regime and displays a large transverse deformation, ten times larger than the longitudinal one and strongly dependent on the amplitude and the direction of the applied currents. This deformation continuously extends across the macroscopic sample dimensions, over a distance 10 000 times greater than the CDW wavelength despite the presence of strong defects while remaining strongly pinned by the lateral surfaces. This 2D quantitative study highlights the prominent role of shear effect that should play a significant role in the nucleation of solitons.

We report measurements of the magnetoresistance in the charge density wave (CDW) state of rare-earth tritellurides, namely TbTe$_3$ and HoTe$_3$. The magnetic field dependence of magnetoresistance exhibits a temperature dependent crossover between a conventional quadratic law at high $T$ and low $B$ and an unusual linear dependence at low $T$ and high $B$. We present a quite general model to explain the linear magnetoresistance taking into account the strong scattering of quasiparticles on CDW fluctuations in the vicinity of "hot spots" of the Fermi surface (FS) where the FS reconstruction is the strongest., Comment: 6 pages, 5 figures

The long-time thermal relaxation of (TMTTF)$_2$Br, Sr$_{14}$Cu$_{24}$O$_{41}$ and Sr$_2$Ca$_{12}$Cu$_{24}$O$_{41}$ single crystals at temperatures below 1 K and magnetic field up to 10 T is investigated. The data allow us to determine the relaxation time spectrum of the low energy excitations caused by the charge-density wave (CDW) or spin-density wave (SDW). The relaxation time is mainly determined by a thermal activated process for all investigated materials. The maximum relaxation time increases with increasing magnetic field. The distribution of barrier heights corresponds to one or two Gaussian functions. The doping of Sr$_{14-x}$Ca$_{x}$Cu$_{24}$O$_{41}$ with Ca leads to a drastic shift of the relaxation time spectrum to longer time. The maximum relaxation time changes from 50 s (x = 0) to 3000 s (x = 12) at 0.1 K and 10 T. The observed thermal relaxation at x=12 clearly indicates the formation of the SDW ground state at low temperatures.

We report a strong difference in the sliding properties of the bidirectional charge density wave (CDW) in the two-dimensional rare earth tritelluride ErTe$_3$ which occurs below $T_{CDW1}=265$ K with a wave vector along $c$-axis and below $T_{CDW2}=165$ K with a wave vector along $a$-axis; the excess current carried by the motion of the CDW is 10 times less for the lower CDW compared with the value of the upper one. We tentatively explain this result by a stronger pinning of the lower temperature CDW intricated with the upper one, which inhibits its motion and may generate a phase slippage lattice., Comment: 7 pages, 9 figures, accepted in PRB

Slow oscillations (SlO) of the in-plane magnetoresistance with a frequency less than 4 T are observed in the rare-earth tritellurides and proposed as an effective tool to explore the electronic structure in various strongly anisotropic quasi-two-dimensional compounds. Contrary to the usual Shubnikov-de-Haas oscillations, SlO originate not from small Fermi-surface pockets, but from the entanglement of close frequencies due to a finite interlayer transfer integral, either between the two Te planes forming a bilayer or between two adjacent bilayers. From the observed angular dependence of the frequency and the phase of SlO we argue that they originate from the bilayer splitting rather than from the Fermi-surface warping. The SlO frequency gives the value of the interlayer transfer integral $\approx 1$ meV for TbTe$_3$ and GdTe$_3$., Comment: 10 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1504.06064

We report on sliding Charge Density Wave (CDW) in the quasi two-dimensional TbTe$_3$ system probed by coherent x-ray diffraction combined with {\it in-situ} transport measurements. We show that the non-Ohmic conductivity in TbTe$_3$ is made possible thanks to a strong distortion of the CDW. Our diffraction experiment versus current shows first that the CDW remains undeformed below the threshold current I$_S$ and then suddenly rotates and reorders by motion above threshold. Contrary to quasi-one dimensional systems, the CDW in TbTe$_3$ does not display any phase shifts below I$_S$ and tolerates only slow spatial variations of the phase above. This is a first observation of CDW behavior in the bulk in a quasi-two dimensional system allowing collective transport of charges at room temperature., Comment: submitted to PRB