Charge excitations were studied for stipe-ordered 214 compounds, La$_{5/3}$Sr$_{1/3}$NiO$_{4}$ and 1/8-doped La$_{2}$(Ba, Sr)$_{x}$CuO$_{4}$ using resonant inelastic x-ray scattering in hard x-ray regime. We have observed charge excitations at the energy transfer of 1 eV with the momentum transfer corresponding to the charge stripe spatial period both for the diagonal (nikelate) and parallel (cuprates) stripes. These new excitations can be interpreted as a collective stripe excitation or charge excitonic mode to a stripe-related in-gap state.
Stripe fluctuations in La2NiO4.17 have been studied by 139La NMR using the field and temperature dependence of the linewidth and relaxation rates. In the formation process of the stripes the NMR line intensity is maximal below 230K, starts to diminish around 140K, disappears around 50K and recovers at 4K. These results are shown to be consistent with, but completely complementary to neutron measurements, and to be generic for oxygen doped nickelates and underdoped cuprates.
Neutron and X-ray scattering studies have provided strong evidence for coupled spatial modulations of charge and spin densities in layered nickelates and cuprates. The accumulated results for La(2-x)Sr(x)NiO(4+d) are consistent with the strongly-modulated topological-stripe concept. Clues from Nd-doped La(2-x)Sr(x)CuO(4) suggest similar behavior for the cuprates. The experimental results are summarized, and features that conflict with an interpretation based on a Fermi-surface instability are emphasized. A rationalization for the differences in transport properties between the cuprates and nic…
We discuss heat transport in hole-doped manganites, nickelates and cuprates for which real-space charge ordering has been observed. We survey the thermal transport response to charge order in the various materials and the associated structural modifications, particularly distortions of the metal-oxygen polyhedra associated with localized charge, that may be a principal source of phonon damping.
Bulk magnetic order in two dimensional La4Ni3O8 nickelate with Ni1+/Ni2+ (d9/d8), isoelectronic with superconducting cuprates is demonstrated experimentally and theoretically. Magnetization, specific heat and 139La NMR evidence a transition at 105 K to an antiferromagnetic state. Theoretical calculations by DFT relate the transition to a nesting instability of the Fermi surface with ordering wave-vector Q = [1/3, 1/3, 0].
We analyze pressure effects on stripe states within a selfconsistent Hartree-Fock calculation for a model of a striped nickelates. The results show a transition induced by high pressure and predict possible new spin states. We describe characteristics in the phonon excitations at the predicted transition, based on a real-space random phase approximation.
New dielectric transitions are observed at common temperatures 32K and 245K, in isostructural $La_{2}CuO_{4+x}$ and $La_{5/3}Sr_{1/3}NiO_{4},$ that are signatures of local lattice (octahedral) instabilities. The present dielectric transitions reveal new aspects of the phase diagram of the perovskite cuprates and nickelates. They suggest that competition and coexistence of superconductivity with dielectricity occurs that is analogous to that between superconductivity and anti-ferromagnetism. These results also indicate that inhomogeneous electronic states, such as charge stripes and oxygen orde…
The low-frequency dielectric response of hole-doped insulators La_{2}Cu_{1-x}Li_{x}O_{4} and La_{2-x}Sr_{x}NiO_{4} shows a large dielectric constant ε^{'} at high temperature and a step-like drop by a factor of 100 at a material-dependent low temperature T_{f}. T_{f} increases with frequency and the dielectric response shows universal scaling in a Cole-Cole plot, suggesting that a charge glass state is realized both in the cuprates and in the nickelates.
The 2019 discovery of high temperature superconductivity in layered nickelate films, Nd$_{1-x}$SrNiO$_2$, has galvanized a community that has been studying nickelates for more than 30 years both as cuprate analogs and in their own right. On the surface, infinite layer nickelates, and their multilayer analogs, should be promising candidates based on our understanding of cuprates: square planar coordination and a parent d9 configuration that places a single hole in a dx2-y2 planar orbital makes nickelates seem poised for superconductivity. But creating crystals and films of sufficient quality of…
The recently discovered infinite-layer nickelates show great promise in helping to disentangle the various cooperative mechanisms responsible for high-temperature superconductivity. However, lack of antiferromagnetic order in the pristine nickelates presents a challenge for connecting the physics of the cuprates and nickelates. Here, by using a quantum many-body Green's function-based approach to treat the electronic and magnetic structures, we unveil the presence of many two- and three-dimensional magnetic stripe instabilities that are shown to persist across the phase diagram of LaNiO$_2$. O…
Recent discovery of superconductivity in the doped infinite-layer nickelates has renewed interest in understanding the nature of high-temperature superconductivity more generally. The low-energy electronic structure of the parent compound NdNiO$_{2}$, the role of electronic correlations in driving superconductivity, and the possible relationship betweeen the cuprates and the nickelates are still open questions. Here, by comparing LaNiO$_2$ and NdNiO$_2$ systematically within a parameter-free density functional framework, all-electron first-principles framework, we reveal the role Nd 4$f$ elect…
To describe quasi two-dimensional nickelates we introduce an effective Hamiltonian for $e_g$ electrons which includes the kinetic energy, on-site Coulomb interactions, spin-spin and Jahn-Teller (static) terms. The experimental stripe phases are correctly reproduced by the model. The mechanisms responsible for stripe formation are different than those reported in cuprates and manganites.
Low-valent nickelates R$_{n+1}$Ni$_n$O$_{2n+2}$ (R = rare earth) containing Ni$^{1+}$ (d$^{9}$) with a quasi-two-dimensional (quasi-2D) square planar coordination geometry possess structural and electronic properties that are similar to those of high-Tc cuprates, including superconductivity itself in the doped infinite layer ($n = \infty$) RNiO$_2$ system. Within this R$_{n+1}$Ni$_n$O$_{2n+2}$ nickelate family, the crystallographic isomorphs Pr$_4$Ni$_3$O$_8$ and La$_4$Ni$_3$O$_8$ exhibit singularly different ground states: Pr$_4$Ni$_3$O$_8$ is metallic and La$_4$Ni$_3$O$_8$ is a charge- and s…
Motivated by the recent discovery of superconductivity in doped NdNiO$_2$, we study the magnetic exchange interaction $J$ in layered $d^9$ nickelates from first principles. The mother compounds of the high-$T_{\rm c}$ cuprates belong to the charge-transfer regime in the Zaanen-Sawatzky-Allen diagram and have $J$ larger than 100 meV. While this feature makes the cuprates very different from other transition metal oxides, it is of great interest whether layered $d^9$ nickelates can also have such a large $J$. However, one complexity is that NdNiO$_2$ is not a Mott insulator due to carrier doping…
Low-valence nickelates $-$ including infinite-layer (IL) and trilayer (TL) compounds $-$ are longstanding candidates for mimicking the high-temperature superconductivity of cuprates. A recent breakthrough in the field came with the discovery of superconductivity in hole-doped IL nickelates. Yet, the degree of similarity between low-valence nickelates and cuprates is the subject of a profound debate for which soft x-ray spectroscopy experiments at the Ni $L$- and O $K$-edge provided critical input. In this review, we will discuss the essential elements of the electronic structure of low-valance…
We consider a Landau theory of coupled charge and spin-density wave order parameters as a simple model for the ordering that has been observed experimentally in the La_2NiO_4 and La_2CuO_4 families of doped antiferromagnets. The period of the charge-density wave is generically half that of the spin-density wave, or equivalently the charges form antiphase domain walls in the antiferromagnetic order. A sharp distinction exists between the case in which the ordering is primarily charge driven (which produces a sequence of transitions in qualitative agreement with experiment) or spin driven (which…
The discovery of superconductivity in infinite-layer nickelates is presently an important topic in condensed-matter physics, and potential similarities to and differences from cuprates are under intense debate. We determine general features of the charge excitation spectrum in nickelates from two opposite viewpoints: (i) Nickelates are regarded as strongly correlated electron systems like cuprate superconductors and thus can be described by the $t$-$J$ model, and (ii) electron correlation effects are not as strong as in cuprates, and thus, random-phase approximation (RPA) calculations may capt…
Trilayer nickelates, which exhibit a high degree of orbital polarization combined with an electron count (d8.67) corresponding to overdoped cuprates, have been identified as a promising candidate platform for achieving high-Tc superconductivity. One such material, La4Ni3O8, undergoes a semiconductor-insulator transition at ~105 K, which was recently shown to arise from the formation of charge stripes. However, an outstanding issue has been the origin of an anomaly in the magnetic susceptibility at the transition and whether it signifies formation of spin stripes akin to single layer nickelates…
Effective models are constructed for a newly discovered superconductor (Nd,Sr)NiO2, which has been considered as a possible nickelate analogue of the cuprates owing to the d9 electron configuration. Estimation of the effective interaction, which turns out to require a multiorbital model that takes account of all the orbitals involved on the Fermi surface, shows that the effective interactions are significantly larger than in the cuprates. A fluctuation exchange study for the model indicates that dx2-y2-wave superconductivity is likely to occur as in the cuprates, where the transition temperatu…
We study the temporal stability of stripe-type spin order in a layered nickelate with X-ray photon correlation spectroscopy and observe fluctuations on time scales of tens of minutes over a wide temperature range. These fluctuations show an anomalous temperature dependence: they slow down at intermediate temperatures and speed up both upon heating and cooling. This behavior appears to be directly connected with spatial correlations: stripes fluctuate slowly when stripe correlation lengths are large and become faster when spatial correlations decrease. A low-temperature decay of nickelate strip…
We investigate the consequences of the stripe formation in the nickelate La5/3Sr1/3NiO4 for the details of its crystal structure and electronic states. Our data are based on numerical simulations within density functional theory (DFT) and the generalized gradient approximation (GGA). The on-site Coulomb interaction is included in terms of the LDA+U scheme. Structure optimization of preliminary experimental data indicates a strong interaction between the structural and electronic degrees of freedom. In particular, we find a segregation of the diagonal filled stripes induced by a delicate interp…
Ground-state properties of layered nickelates are investigated based on the orbital-degenerate Hubbard model coupled with lattice distortions, by using umerical techniques. The Néel state composed of spin S=1 ions is confirmed in the undoped limit x=0. At x=1/2, novel antiferromagnetic states, called CE- and E-type phases, are found by increasing the Hund's coupling. (3 x^2 - r^2 / 3 y^2 - r^2)-type orbital ordering is predicted to occur in a checkerboard-type charge-ordered state. At x=1/3, both Coulombic and phononic interactions are found to be important, since the former stabilizes the spi…
Some recent evidence for the existence of dynamic, metallic stripes in the 214-family of cuprates is reviewed. The mechanism of stripe pinning is considered, and changes in the charge density within stripes between the pinned and dynamic phases is discussed. From a purely experimental perspective, dynamic charge stripes are fully compatible with nodal ``quasiparticles'' and other electronic properties common to all superconducting cuprates.
In materials science, much effort has been devoted to reproduce superconductivity in chemical compositions analogous to cuprate superconductors since their discovery over thirty years ago. This approach was recently successful in realising superconductivity in infinite-layer nickelates. Although differing from cuprates in electronic and magnetic properties, strong Coulomb interactions suggest infinite-layer nickelates have a propensity to various symmetry-breaking orders that populate the cuprates. Here we report the observation of charge density waves (CDWs) in infinite-layer NdNiO$_2$ films …
Revealing the predominant driving force behind symmetry breaking in correlated materials is sometimes a formidable task due to the intertwined nature of different degrees of freedom. This is the case for La2-xSrxNiO4+δ in which coupled incommensurate charge and spin stripes form at low temperatures. Here, we use resonant X-ray photon correlation spectroscopy to study the temporal stability and domain memory of the charge and spin stripes in La2-xSrxNiO4+δ. Although spin stripes are more spatially correlated, charge stripes maintain a better temporal stability against temperature change. More i…
The experimental observations of stripes in superconducting cuprates and insulating nickelates clearly show the modulation in charge and spin density. However, these have proven to be rather insensitive to the harmonic structure and (site or bond) ordering. Using 139La NMR in La2NiO4.17, we show that in the 1/3 hole doped nickelate below the freezing temperature the stripes are strongly solitonic and site ordered with Ni3+ ions carrying S=1/2 in the domain walls and Ni2+ ions with S=1 in the domains.
We investigate the electron density distribution and the stability of stripe phases in the realistic two-band model with hopping elements between e_g orbitals at Ni sites on the square lattice, and compare these results with those obtained for the doubly degenerate Hubbard model with two equivalent orbitals and diagonal hopping. For both models we determine the stability regions of filled and half-filled stripe phases for increasing hole doping x=2-n in the range of x<0.4, using Hartree-Fock approximation for large clusters. In the parameter range relevant to the nickelates, we obtain the most…
Origin of Spin Stripes in Bilayer Nickelate La$_3$Ni$_2$O$_7$
The Chinese University of Hong Kong（香港中文大学）；Johns Hopkins University（约翰斯·霍普金斯大学）；Stanford University（斯坦福大学）；SLAC National Accelerator Laboratory（斯坦福直线加速器中心）
Pr$_4$Ni$_3$O$_8$ is an overdoped analog of hole-doped layered cuprates. Here we show via ab initio calculations that Ce-doped Pr$_4$Ni$_3$O$_8$ (Pr$_3$CeNi$_3$O$_8$) has the same electronic structure as the antiferromagnetic insulating phase of parent cuprates. We find that substantial Ce-doping should be thermodynamically stable and that other 4+ cations would yield a similar antiferromagnetic insulating state, arguing this configuration is robust for layered nickelates of low enough valence. The analogies with cuprates at different $d$ fillings suggest that intermediate Ce-doping concentrat…
Recent quantum oscillation measurements on underdoped cuprates are shown to be consistent with the predictions of a mean field theory of the 1/8 magnetic antiphase stripe order proposed to occur in high-$T_c$ cuprates. In particular, for intermediate values of the stripe order parameter, the magneto-transport is found to be dominated by an electron pocket.
Layer-by-layer oxide molecular beam epitaxy has been used to synthesize cuprate-nickelate multilayer structures of composition (La$_2$CuO$_4$)$_m$/LaO/(LaNiO$_3$)$_n$. In a combined experimental and theoretical study, we show that these structures allow a clean separation of dopant and doped layers. Specifically, the LaO layer separating cuprate and nickelate blocks provides an additional charge that, according to density functional theory calculations, is predominantly accommodated in the interfacial nickelate layers. This is reflected in an elongation of bond distances and changes in valence…
We analyze theoretically the resonant inelastic x-ray scattering (RIXS) at the Ni K edge in the stripe-ordered state of La_{2-x}Sr_xNiO_4 at x=1/3. In the calculation of RIXS spectra, the stripe-ordered ground state is described within the Hartree-Fock approximation by using a realistic tight-binding model for Ni3dγand O2p_{x, y} orbitals, and the electron correlations in the electronic excitation processes are taken into account within the random-phase approximation. The calculated RIXS spectrum shows a tail toward the low-energy region when the momentum transfer of photons equals the stripe …
Charge and spin stripe order is a type of electronic crystal observed in certain layered cuprates associated with high-temperature superconductivity. Quantum-disordered stripes could be relevant for understanding the superconductivity. Here I discuss recent experimental characterizations of the stripe-ordered state in La(1.875)Ba(0.125)CuO(4), and compare them with properties of superconducting compositions.
Observation of correlated plasmons in low-valence nickelates
Brookhaven National Laboratory（布鲁克海文国家实验室）；Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理北京国家实验室）；Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory（斯坦福材料能源科学研究所，SLAC国家加速器实验室）；National Synchrotron Light Source II, Brookhaven National Laboratory（布鲁克海文国家实验室第二代同步辐射光源）；Shanghai Advanced Research in Physical Sciences (SHARPS)（上海物理科学研究前沿中心）
The quasi-two-dimensional nickelate La4Ni3O8 (La-438) is an anion deficient n=3 Ruddlesden-Popper (R-P) phase that consists of trilayer networks of square planar Ni ions, formally assigned as Ni1+ and Ni2+ in a 2:1 ratio. While previous studies on polycrystalline samples have identified a 105 K phase transition with a pronounced electronic and magnetic response but weak lattice character, no consensus on the origin of this transition has been reached. Here we show using synchrotron x-ray diffraction on high-pO2 floating-zone grown single crystals that this transition is driven by a real space …
We study the influence of disorder and lattice effects on the striped phase and the incommensurate spin fluctuations of the cuprates and nickelates. Starting from a phenomenological model of a discrete quantum string on a lattice with disorder, we derive the renormalisation group equations in leading order in the lattice and disorder strength. Three regimes are identified, the quantum membrane phase, the flat phase pinned by the lattice and the disorder pinned phase. We compare our results with measurements on nickelates and cuprates and find good agreement.
Recent experiments indicate that the tendency toward the formation of unidirectional charge density waves ("stripes") is common to various underdoped cuprates. We discuss momentum-resolved spectral properties of valence-bond stripes, comparing the situations of ideal and short-range stripe order, the latter being relevant for weak and/or disorder-pinned stripes. We find clear signatures of ordered stripes, although matrix element effects suppress most shadow band features. With decreasing stripe correlation length, stripe signatures are quickly washed out, the only remaining effect being a bro…
The discovery of infinite-layer nickelate superconductors has spurred enormous interest. While the Ni$^{1+}$ cations possess nominally the same 3$d^9$ configuration as Cu$^{2+}$ in cuprates, the electronic structure variances remain elusive. Here, we present a soft x-ray photoemission spectroscopy study on parent and doped infinite-layer Pr-nickelate thin films with a doped perovskite reference. By identifying the Ni character with resonant photoemission and comparison to density functional theory + U (on-site Coulomb repulsion energy) calculations, we estimate U ~5 eV, smaller than the charge…
We investigate the formation of charge domain walls in an electron-doped extended Hubbard model for the superconducting cuprates. Within an unrestricted Hartree-Fock approach, extended by the introduction of slave-bosons to obtain a more proper treatment of strong correlations, we demonstrate the occurrence of stripes in the (1,1) and (1,-1) directions having one doped electron per stripe site. The different filling, direction and width of these electron-doped stripes with respect to those obtained in the hole-doped systems have interesting observable consequences, which are discussed.
Based on the unrestricted Gutzwiller approximation we study the possibility that the diagonal incommensurate spin scattering in the spin glass phase of lanthanum cuprates originates from stripe formation. Similar to the metallic phase two types of diagonal stripe structures appear to be stable: (a) site-centered textures which have one hole per site along the stripe and (b) ferromagnetic stair-case structures which are the diagonal equivalent to bond-centered stripes in the metallic phase and which on average have a filling of 3/4 holes per stripe site. We give a detailed analysis of the stabi…
The correlated electronic structure of the infinite-layer compounds NdNiO$_2$ and SrCuO$_2$ at stoichiometry and with finite hole doping is compared. Key differences are elucidated from an advanced first-principles many-body perspective. Contrary to the charge-transfer insulating cuprate, the self-doped nickelate remains non-insulating even for large interaction strength, though the Ni-$d_{x^2-y^2}$ spectral weight is also gapped in that limit. Hybridization between Ni$(3d)$ and Nd$(5d)$ is crucial for the appearance of the self-doping band. Upon realistic hole doping, Sr$_{1-y}$CuO$_2$ shows …
The recent discovery of superconductivity in hole-doped planar nickelates R1-xSrNiO2 (R=Pr,Nd) raises the foundational question of how the electronic structure and electronic correlations of these Ni1+ compounds compare to those of the Cu2+ cuprate superconductors. Here, we present an Angle-Resolved Photoemission Spectroscopy (ARPES) study of the trilayer nickelate Pr4Ni3O8, revealing an electronic structure and Fermi surface very similar to that of the hole-doped cuprates but with a few critical differences. Specifically, the main portions of the Fermi surface are extremely similar to that of…
The search for oxide materials with physical properties similar to the cuprate high Tc superconductors, but based on alternative transition metals such as nickel, has grown and evolved over time. The recent discovery of superconductivity in doped infinite-layer nickelates RNiO2 (R = rare-earth element) further strengthens these efforts.With a crystal structure similar to the infinite-layer cuprates - transition metal oxide layers separated by a rare-earth spacer layer - formal valence counting suggests that these materials have monovalent Ni1+ cations with the same 3d electron count as Cu2+ in…
We study stripes in cuprates within the one-band and the three-band Hubbard model. Magnetic and charge excitations are described within the time-dependent Gutzwiller approximation. A variety of experiments (charge profile from resonant soft X-ray scattering, incommensurability vs. doping, optical excitations, magnetic excitations, etc.) are described within the same approach.
Based on the time-dependent Gutzwiller approximation we study the possibility that the diagonal incommensurate spin scattering in strongly underdoped lanthanum cuprates originates from antiferromagnetic domain walls (stripes). Calculation of the dynamic spin response for stripes in the diagonal phase yields the characteristic hour glass dispersion with the crossing of low energy Goldstone and high-energy branches at a characteristic energy Ecross at the antiferromagnetic wave-vector Q_{AF}. The high energy part is close to the parent antiferromagnet. Our results suggest that inelastic neutron …
Using the local density approximation and its combination with dynamical mean-field theory, we show that electronic correlations induce a single-sheet, cuprate-like Fermi surface for hole-doped 1/1 LaNiO3 /LaAlO3 heterostructures, even though both eg orbitals contribute to it. The Ni 3d 3z^2-1 orbital plays the role of the axial Cu 4s-like orbital in the cuprates. These two results indicate that "orbital engineering" by means of heterostructuring should be possible. As we also find strong antiferromagnetic correlations, the low-energy electronic and spin excitations in nickelate heterostructur…
The discovery of superconductivity in infinite-layer nickelates has attracted much attention due to their association to the high-$T_c$ cuprates. Cuprate superconductivity was first demonstrated in bulk samples and subsequently in thin films. In the nickelates, however, the situation has been reversed: although surging as a bulk phenomenon, nickelate superconductivity has only been reported in thin films so far. At the same time, the specifics of infinite-layer nickelates yield distinct interface and surface effects that determine their bulk vs thin-film behavior. In this paper, we provide an …
Within a model that supports stripe spin and charge order coexisting with a d$_{x^2-y^2}$-wave superconducting phase, we study the self-consistently obtained electronic structure and the associated transverse dynamical spin susceptibility. In the coexisting phase of superconducting and static stripe order, the resulting particle-hole continuum can strongly damp parts of the low-energy spin wave branches. This provides insight into recent inelastic neutron scattering data revealing the dispersion of the low-energy collective magnetic modes of lanthanum based cuprate superconductors.
Motivated by experiments on LBCO-1/8 which suggest that stripe order co-exists with two-dimensional pairing without inter-layer phase coherence over an extended range of temperatures, we determine the inter-layer Josephson coupling in the presence of stripe order. We employ a mean-field description of bond-centered stripes, with a zero-momentum superconducting condensate and alternating stripe directions pinned by the low-temperature tetragonal (LTT) lattice structure. We show that the Fermi-surface reconstruction arising from strong stripe order can suppress the Josephson coupling between adj…
Using a phenomenological lattice model of coupled spin and charge modes, we determine the spin susceptibility in the presence of fluctuating stripe charge order. We assume the charge fluctuations to be slow compared to those of the spins, and combine Monte Carlo simulations for the charge order parameter with exact diagonalization of the spin sector. Our calculations unify the spin dynamics of both static and fluctuating stripe phases and support the notion of a universal spin excitation spectrum in doped cuprate superconductors.
The discovery of superconductivity in the infinite-layer nickelates has opened new perspectives in the context of quantum materials. We analyze, via first-principles calculations, the electronic properties of La$_2$NiO$_3$F -- the first single-layer T'-type nickelate -- and compare these properties with those of related nickelates and isostructural cuprates. We find that La$_2$NiO$_3$F is essentially a single-band system with a Fermi surface dominated by the Ni-3$d_{x^2-y^2}$ states with an exceptional 2D character. In addition, the hopping ratio is similar to that of the highest $T_c$ cuprate…
We demonstrate that the strong anomalies in the high frequency LO-phonon spectrum in cuprate superconductors can in principle be explained by the enhanced electronic polarizability associated with the self-organized one dimensionality of metallic stripes. Contrary to the current interpretation in terms of transversal stripe fluctuations, the anomaly should occur at momenta parallel to the stripes. The doping dependence of the anomaly is naturally explained, and we predict that the phonon line-width and the spread of the anomaly in the transverse momentum decrease with increasing temperature wh…
The in-plane resistivity and out-of-plane resistivity of non-superconducting RBCO (R = Y, Tm) and Fe-doped Bi2212 single crystals are discussed. The comparison of electrical transport properties of the cuprates and quasi-one dimensional (1D) (TMTSF)2PF6 organic conductor suggests that RBCO and Bi2212 exhibit 1D transport properties, and the step rise at low temperatures in the resistivities of the cuprates and quasi-1D organic conductor is due to charge-density-wave ordering. We discuss also phonon-electron interactions in cuprates at low temperatures.
