The rare-earth tritellurides ($R$Te$_3$, where $R$ = La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Y) form a charge density wave state consisting of a single unidirectional charge density wave for lighter $R$, with a second unidirectional charge density wave, perpendicular and in addition to the first, also present at low temperatures for heavier $R$. We present a quantum oscillation study in magnetic fields up to 65T that compares the single charge density wave state with the double charge density wave state both above and below the magnetic breakdown field of the second charge density wave. In the double charge density wave state it is observed that there remain several small, light pockets with the largest occupying around 0.5% of the Brillouin zone. By applying magnetic fields above the independently determined magnetic breakown field, the quantum oscillation frequencies of the single charge density wave state are recovered, as expected in a magnetic breakdown scenario. Measurements of the electronic effective mass do not show any divergence or significant increase on the pockets of Fermi surface observed here as the putative quantum phase transition between the single and double charge density wave states is approached.
We calculated electron susceptibility of rare-earth tritelluride compounds RTe$_3$ as a function of temperature, wave vector and electron-dispersion parameters. Comparison of results obtained with the available experimental data on the transition temperature and on the wave vector of a charge-density wave in these compounds allowed us to predict values and the evolution of electron-dispersion parameters with the variation of atomic number of rare-earth element R.
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 …
Slow oscillations of the in-plane magnetoresistance are observed in the rare-earth tritellurides and proposed as an effective tool to determine the parameters of electronic structure in various strongly anisotropic quasi-two-dimensional compounds. These oscillations do not originate from the small Fermi surface pockets, as revealed usually by the Shubnikov-de-Haas oscillations, but from the entanglement of close frequencies due to a finite interlayer transfer integral $t_z$, which allows to estimate its value. For TbTe$_3$ and GdTe$_3$ we obtain the estimate $t_z\approx 1$ meV.
We show that the isotropic conductivity in the normal state of rare-earth tritelluride RTe_3 compounds is broken by the occurrence of the unidirectional charge density wave (CDW) in the (a,c) plane below the Peierls transition temperature. In contrast with quasi-one-dimensional systems, the resistivity anomaly associated with the CDW transition is strong in the direction perpendicular to the CDW wave vector Q (a-axis) and very weak in the CDW wave vector Q direction (c-axis). We qualitatively explain this result by calculating the electrical conductivity for the electron dispersion with moment…
The charge density wave transition is investigated in the bi-layer family of rare earth tritelluride RTe_3 compounds (R = Sm, Gd, Tb, Dy, Ho, Er, Tm) via high resolution x-ray diffraction and electrical resistivity. The transition temperature increases monotonically with increasing lattice parameter from 244(3) K for TmTe_3 to 416(3) K for SmTe_3. The heaviest members of the series, R = Dy, Ho, Er, Tm, are observed to have a second transition at a lower temperature, which marks the onset of an additional CDW with wavevector almost equal in magnitude to the first, but oriented in the perpendicu…
The Fermi surface of rare-earth tri-tellurides ({\it R}Te$_{3}$) is investigated in terms of the nesting driven charge-density wave formation using positron annihilation and first-principles LMTO calculations. Fermi surface nesting is revealed as a strong candidate for driving charge-density wave formation in these compounds. The nesting vector obtained from positron annihilation experiments on GdTe$_{3}$ is determined to be ${\mathbf q} = (0.28\pm0.02,0,0) {\mathbf a}^{*}$, (${\mathbf a}^{*}=2π/{\mathbf a}$), in excellent agreement with previous experimental and theoretical studies.
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 fre…
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.
We performed resonant soft X-ray diffraction on known charge density wave (CDW) compounds, rare earth tri-tellurides. Near the $M_5$ (3d - 4f) absorption edge of rare earth ions, an intense diffraction peak is detected at a wavevector identical to that of CDW state hosted on Te$_2$ planes, indicating a CDW-induced modulation on the rare earth ions. Surprisingly, the temperature dependence of the diffraction peak intensity demonstrates an exponential increase at low temperatures, vastly different than that of the CDW order parameter. Assuming 4f multiplet splitting due to the CDW states,we pres…
Time-domain identification of distinct mechanisms for competing charge density waves in a rare-earth tritelluride
Massachusetts Institute of Technology（麻省理工学院）；Tsung-Dao Lee Institute, School of Physics and Astronomy, and Zhangjiang Institute for Advanced Study, Shanghai Jiao Tong University（上海交大）；Stanford University（斯坦福大学）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）；ETH Zürich（苏黎世联邦理工学院）；Harvard University（哈佛大学）
Even though the rare-earth tritellurides are tetragonal materials with a quasi two dimensional (2D) band structure, they have a "hidden" 1D character. The resultant near-perfect nesting of the Fermi surface leads to the formation of a charge density wave (CDW) state. We show that for this band structure, there are two possible ordered phases: A bidirectional "checkerboard" state would occur if the CDW transition temperature were sufficiently low, whereas a unidirectional "striped" state, consistent with what is observed in experiment, is favored when the transition temperature is higher. This …
Charge density wave (CDW) states in solids bear an intimate connection to underlying fermiology. Modification of the latter by a suitable perturbation provides an attractive handle to unearth novel CDW states. Here, we combine extensive magnetotransport experiments and first-principles electronic structure calculations on a non-magnetic tritelluride LaTe$_{3}$ single crystal to uncover phenomena rare in CDW systems: $(i)$ hump-like feature in the temperature dependence of resistivity at low temperature under application of magnetic field, which moves to higher temperature with increasing field…
The antiferromagnetic transition is investigated in the rare-earth (R) tritelluride RTe3 family of charge density wave (CDW) compounds via specific heat, magnetization and resistivity measurements. Observation of the opening of a superzone gap in the resistivity of DyTe3 indicates that additional nesting of the reconstructed Fermi surface in the CDW state plays an important role in determining the magnetic structure.
We report the evolution of a charge density wave (CDW) state in the quasi-2D rare-earth tritellurides ($R$Te$_3$ for $R$=Er,Tm) as a function of in-plane uniaxial stress. Measurements of the elastocaloric effect, resistivity, and elastoresistivity allow us to demonstrate the importance of in-plane antisymmetric strain on the CDW and to establish a phase diagram. We show that modest tensile stress parallel to the in-plane $a$-axis can reversibly switch the direction of the ordering wavevector between the two in-plane directions. This work establishes $R$Te$_3$ as a promising model system for th…
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 estimat…
Revealing the nature of the charge density wave order of ErTe$_3$ via Raman scattering under anisotropic strain
Université Paris Cité, CNRS, Laboratoire Matériaux et Phénomènes Quantiques（巴黎西岱大学，法国国家科学研究中心，物质与现象量子实验室）；Institut de Physique et Chimie des Matériaux de Strasbourg (UMR 7504), Université de Strasbourg and CNRS（斯特拉斯堡材料物理与化学研究所（联合研究单位7504），斯特拉斯堡大学和法国国家科学研究中心）；Department of Applied Physics, Stanford University（斯坦福大学应用物理系）；Geballe Laboratory for Advanced Materials, Stanford University（斯坦福大学格伯勒先进材料实验室）；Stanford Institute for Materials and Energy Sciences, SLAC（斯坦福材料与能源科学研究所，SLAC）
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 lat…
Distinct amplitude mode dynamics upon resonant and off-resonant excitation across the charge density wave energy gap in LaTe3 investigated by time- and angle-resolved photoemission spectroscopy
HoTe$_{3}$, a member of the rare-earth tritelluride ($R$Te$_{3}$) family, and its Pd-intercalated compounds, Pd$_x$HoTe$_{3}$, where superconductivity (SC) sets in as the charge-density wave (CDW) transition is suppressed by the intercalation of a small amount of Pd, are investigated using angle-resolved photoemission spectroscopy (ARPES) and electrical resistivity. Two incommensurate CDWs with perpendicular nesting vectors are observed in HoTe$_{3}$ at low temperatures. With a slight Pd intercalation ($x$ = 0.01), the large CDW gap decreases and the small one increases. The momentum dependenc…
We review possible mechanisms for energy transfer based on 'rare' or 'non-perturbative' effects, in physical systems that present a many-body localized phenomenology. The main focus is on classical systems, with or without quenched disorder. For non-quantum systems, the breakdown of localization is usually not regarded as an issue, and we thus aim at identifying the fastest channels for transport. Next, we contemplate the possibility of applying the same mechanisms in quantum systems, including disorder free systems (e.g. Bose-Hubbard chain), disordered many-body localized systems with mobilit…
There has been a recent renewal of interest in charge-density-wave (CDW) phenomena, primarily driven by the emergence of two-dimensional (2D) layered CDW materials, such as 1T-TaS2, characterized by very high transition temperatures to CDW phases. In the extensively studied classical bulk CDW materials with quasi-1D crystal structure, the charge carrier transport exhibits intriguing sliding behavior, which reveals itself in the frequency domain as "narrowband" and "broadband" noise. Despite the increasing attention on physics of 2D CDWs, there have been few reports of CDW sliding, specifically…
We systematically investigate the ground-state and the spectral properties of antiferromagnets on a kagomé lattice with several common types of the planar anisotropy: $XXZ$, single-ion, and out-of-plane Dzyaloshinskii-Moriya. Our main focus is on the role of nonlinear, anharmonic terms, which are responsible for the quantum order-by-disorder effect and for the corresponding selection of the ground-state spin structure in many of these models. The $XXZ$ and the single-ion anisotropy models exhibit a quantum phase transition between the ${\bf q}\!=\!0$ and the $\sqrt{3}\times\!\sqrt{3}$ states a…
