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We review salient structural and electronic features associated with the concomitant Peierls–charge density wave (CDW) instabilities observed in most one-dimensional (1D) inorganic and organic electronic conductors. First of all, the genesis of these concepts is placed in an historical perspective. We then present basic experimental facts supporting the general description of these 1D electron–phonon coupled systems developed in the 1970s. In this framework we shall consider in particular the role of 1D fluctuations on both lattice and electronic degrees of freedom, and of the inter-chain Coulomb coupling between CDWs in stabilizing in 3D the Peierls transition at finite temperature. We also clarify, in relation with experimental findings, the various conditions of adiabaticity of the electron–phonon coupling. Finally we illustrate by recent structural measurements the pioneering work of Jacques Friedel on CDW elasticity and plasticity and CDW pinning to defects through the appearance of Friedel oscillations.

Scanning tunneling microscopy, low-energy electron diffraction, and helium atom scattering show a transition to a dimerizationlike reconstruction in the one-dimensional atomic chains on Bi(114) at low temperatures. One-dimensional metals are generally unstable against such a Peierls-like distortion, but neither the shape nor the spin texture of the Bi(114) Fermi contour favors the transition: Although the Fermi contour is one dimensional and thus perfectly nested, the very short nesting vector $2{k}_{F}$ is inconsistent with the periodicity of the distortion. Moreover, the nesting occurs between two Fermi contour branches of opposite spin, which is also expected to prevent the formation of a Peierls phase. Indeed, angle-resolved photoemission spectroscopy does not reveal any change in the electronic structure near the Fermi energy around the phase transition. On the other hand, distinct changes at higher binding energies are found to accompany the structural phase transition. This suggests that the transition of a strong-coupling type and that it is driven by phonon entropy rather than electronic entropy. This picture is supported by the observed short correlation length of the pairing distortion, the second-order-like character of the phase transition, and pronounced differences between the surface phonon spectra of the high- and low-temperature phases.

In materials with nearly commensurate band filling the electron liquid may spontaneously separate into components with distinct properties, yielding complex intra- and interunit cell ordering patterns and a reduced dimensionality. Polarization-dependent angle-resolved photoemission data with submicron spatial resolution demonstrate such an electronic self-organization in NbSe3, a compound considered to be a paradigm of charge order. The new data indicate the emergence of a novel order, and reveal the one-dimensional (1D) physics hidden in a material which naively could be considered the most three dimensional of all columnar chalcogenides. The 1D physics is evidenced by a new selection rule—in two polarizations we observe two strikingly different dispersions each closely resembling apparently contradicting results of previous studies of this material., The work at Lausanne and Geneva is supported by the Swiss NSF. M.A.V. acknowledges financial support from Spanish MICIN Postdoctoral Mobility Program. S.P. acknowledges C’NANO Ile-de-France, DIM NanoK, for the support of the Nanospecs project. Work in Spain was supported by a MINECO (Grants FIS2015-64886-C5-4-P and CTQ2015-64579-C3-3-P), Generalitat de Catalunya (2017SGR1506 and 2017SGR1289), and XRQTC. E.C. acknowledges support from MINECO through the Severo Ochoa Centers of Excellence Program under Grant No. SEV-2015-0496. ICN2 is funded by the CERCA Program/ Generalitat de Catalunya, and supported by the Severo Ochoa program from Spanish MINECO (Grant No. SEV- 2017-0706). P.A. acknowledges support from the Maria de Maeztu Units of Excellence Program under Grant MDM- 2017-0767. S.C. gratefully acknowledges the Becas Chile program (CONICYT PAI/INDUSTRIA 72090772) for a doctoral grant at the Universitat de Barcelona. Synchrotron SOLEIL is supported by the Centre National de la Recherche Scientifique (CNRS) and the Commissariat à l’Energie Atomique et aux energies Alternatives (CEA).

We present a generic grand-canonical theory for the Peierls transition in atomic wires deposited on semiconducting substrates such as In/Si(111) using a mean-field solution of the one-dimensional Su-Schrieffer-Heeger model. We show that this simple low-energy effective model for atomic wires can explain naturally the occurrence of a first-order Peierls transition between a uniform metallic phase at high-temperature and a dimerized insulating phase at low temperature as well as the existence of a metastable uniform state below the critical temperature.

Diminishing in the concentration of quenching defects during thermocycling of orthorhombic TaS$_3$ samples in the temperature range below the Peierls transition temperature $T, Comment: LaTeX, 6 pages, 5 figures

The Su-Schrieffer-Heeger (SSH) model was introduced to describe the electron-phonon interactions leading to Peierls distortion in polyacetylene (PA). The same model was recently predicted to give rise to unique polaronic effects, including sharp transitions in polaron properties, quasi-self-trapping due to polaron interactions, and the formation of strongly bound yet light bipolarons, at strong electron-phonon coupling in the single and two-polaron limit. This suggests that organic polyenes with strong electron-phonon coupling may exhibit qualitatively different conduction properties from those with weak coupling. In order to observe this, it is necessary to design materials with a range of SSH electron-phonon coupling. Here, we use gradient-corrected density-functional-theory calculations to predict the SSH model parameters for a variety of polyenes, derived from PA by the substitution of the hydrogen atoms with molecular groups. We show that even though the calculations do not accurately reproduce the band gaps, the derivatives of the band structure parameters giving the phonon-induced couplings can be computed with good accuracy. We show that the electron-phonon coupling in such polyenes correlates with the Hammett constant of the substituted molecular group and that some substitutions enhance the coupling strength by as much as a factor of 2. We also find that the electron-phonon coupling in conjugated systems with heavier atoms (such as Si) is much weaker than in PA despite the lower phonon frequencies.

In this work, V1&minus, xZrxO2 powder (x = 0, 0.01, 0.02, 0.04) was synthesized by two step hydrothermal method. The micro-topography, magnetic and phase transition properties have been investigated using various measurement techniques. All prepared V1&minus, xZrxO2 powder samples exhibit monoclinic structure at room temperature. With the Zr4+ ions doping concentration increased, the shapes of VO2 particles change from spherical to rectangular slice. Besides, the saturation magnetic moment of the samples decrease with the increase of doped Zr4+ ions concentration, while their phase transition temperature increase gradually with Zr ions doping at a rate of around 2 &deg, C/at% on average. We investigated the Zr doping effects on V-V dimers and confirmed the role of V-V dimers in phase transition. We speculate that more V-V dimers form with Zr doping by magnetic measurements, which result in the monoclinic phase of Zr-doped VO2 sample is more stable than rutile phase. Therefore the phase transition temperature is elevated by Zr doping in our experiment. We further consider that the VO2 phase transition should be ascribed to Peierls transition caused by the changing of V-V dimers.

On the basis of first-principles DFT calculations the wave-vector and temperature dependencies of the Lindhard response function of the blue bronze K0.3MoO3 have been calculated. The kIF+ kIIF interband component of the response, which is responsible for the Peierls instability, has been quantitatively analyzed. It is found that (i) the electron-hole coherence length of this response determines the length scale of the experimental intrachain CDW correlations, and (ii) the intrachain q dependence of such a response also determines the shape of the Kohn anomaly experimentally measured. These findings provide compelling evidence that the Peierls transition of the blue bronze K0.3MoO3 follows the weak electron-phonon coupling scenario in the adiabatic approximation, something that had not yet been proved on the basis of first-principles calculations for a real material. It is proposed that the CDW interchain coupling occurs through a Coulomb coupling between dipolar CDWs. The nature of the phonon mode leading to the dipolar nature of the CDWs is also discussed, and the relevance of these results to rationalize the CDW instabilities in other oxides and bronzes is pointed out. These findings are also contrasted with recent results for other CDW materials like chalcogenides and tellurides., This work was supported by Spanish MINECO (the Severo Ochoa Centers of Excellence Program under Grants No. SEV-2017-0706 and No. SEV-2015-0496), Spanish MICIU, AEI and EU FEDER (Grants No. PGC2018-096955-B-C43 and No. PGC2018-096955-B-C44), Generalitat de Catalunya (Grant No. 2017SGR1506 and the CERCA Programme), and the European Union MaX Center of Excellence (EU-H2020 Grant No. 824143).

Using first-principles calculations, we predict a strong coupling of lattice, charge, and spin degrees of freedom in Ruddlesden-Popper phase ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$, which enables a phase control with epitaxial strain. While the bulk ground state is metallic, moderate compressive strain is found to trigger a Peierls transition to an insulating state in concurrence with a breathing distortion of ${\mathrm{NiO}}_{6}$ octahedra. The Peierls transition is microscopically interpreted as a band-gap opening arising from lifting and lowering of the Ni $d\ensuremath{-}{e}_{g}$ states due to the octahedral breathing.

${\mathrm{Ta}}_{2}{\mathrm{NiSe}}_{5}$ is considered a promising excitonic insulator (EI) candidate, in which the EI state is due to Coulomb interaction between electrons and holes. In ${\mathrm{Ta}}_{2}{\mathrm{NiSe}}_{5}$, the role of phonons is significant since the EI transition is accompanied by an orthorhombic-to-monoclinic structural transition at ${T}_{\mathrm{s}}=328\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. Our inelastic x-ray scattering measurements reveal that the transverse acoustic mode exhibits strong softening just above ${T}_{\mathrm{s}}$. Furthermore, the transverse optical mode exhibits linewidth broadening caused by strong electron--optical-phonon coupling above ${T}_{\mathrm{s}}$. Density functional theory calculations indicate that the coupled optical modes arise due to the vibration of Ta ions. Consequently, in the monoclinic phase, the coupled optical modes are ``frozen'' such that Ta and Se approach each other, forming atomic-displacement-type electric dipoles that are obviously different from a Peierls transition or Jahn--Teller distortion. The characteristic of electronic toroidal moment formation by the antiferroelectric arrangements of the electric dipoles forms the common feature between ${\mathrm{Ta}}_{2}{\mathrm{NiSe}}_{5}$ and $1T\ensuremath{-}\mathrm{TiS}{\mathrm{e}}_{2}$.

Ultrafast electron diffraction is employed for study of structural dynamics at surfaces in the time domain. Experiments are performed in a pump probe setup with fs-laser excitation and subsequent probing through diffraction of a fs electron pulse at a temporal resolution of 350 fs. The system of interest is one atomic layer of indium atoms on a Si(111) surface: Through self-assembly In atomic wires and form which exhibits a Peierls-like, insulator to metal phase transition which can be driven non-thermally through a femtosecond-laser pulse. Through the transient intensity of the diffraction spots we observe the lifting of the Peierls transition and melting of a charge density wave in only 700 fs, heating of the surface in 6 ps, and formation of a metastable and supercooled phase which exists for nanoseconds.

The magnetoresistance of a TbTe3 two-dimensional conductor with a charge-density wave (CDW) has been measured in a wide temperature range and in magnetic fields of up to 17 T. At temperatures well below the Peierls transition temperature and in high magnetic fields, the magnetoresistance exhibits a linear dependence on the magnetic field caused by the scattering of normal charge carriers by “hot” spots of the Fermi surface. In the sliding CDW regime in low magnetic fields, a qualitative change in the magnetoresistance has been observed associated with the strong scattering of carriers by the sliding CDW.

Nanoelectromechanical systems (NEMS) that operate in the megahertz (MHz) regime allow energy transducibility between different physical domains. For example, they convert optical or electrical signals into mechanical motions and vice versa. This coupling of different physical quantities leads to frequency-tunable NEMS resonators via electromechanical non-linearities. NEMS platforms with single- or low-degrees of freedom have been employed to demonstrate quantum-like effects, such as mode cooling, mechanically induced transparency, Rabi oscillation, two-mode squeezing and phonon lasing. Periodic arrays of NEMS resonators with architected unit cells enable fundamental studies of lattice-based solid-state phenomena, such as bandgaps, energy transport, non-linear dynamics and localization, and topological properties, directly transferrable to on-chip devices. Here we describe one-dimensional, non-linear, nanoelectromechanical lattices (NEML) with active control of the frequency band dispersion in the radio-frequency domain (10–30 MHz). The design of our systems is inspired by NEMS-based phonon waveguides and includes the voltage-induced frequency tuning of the individual resonators. Our NEMLs consist of a periodic arrangement of mechanically coupled, free-standing nanomembranes with circular clamped boundaries. This design forms a flexural phononic crystal with a well-defined bandgap, 1.8 MHz wide. The application of a d.c. gate voltage creates voltage-dependent on-site potentials, which can significantly shift the frequency bands of the device. Additionally, a dynamic modulation of the voltage triggers non-linear effects, which induce the formation of a phononic bandgap in the acoustic branch, analogous to Peierls transition in condensed matter. The gating approach employed here makes the devices more compact than recently proposed systems, whose tunability mostly relies on materials’ compliance and mechanical non-linearities.

We study a one-dimensional system of strongly correlated bosons on a dynamical lattice. To this end, we extend the standard Bose-Hubbard Hamiltonian to include extra degrees of freedom on the bonds of the lattice. We show that this minimal model exhibits phenomena reminiscent of fermion-phonon models. In particular, we discover a bosonic analog of the Peierls transition, where the translational symmetry of the underlying lattice is spontaneously broken. This provides a dynamical mechanism to obtain a topological insulator in the presence of interactions, analogous to the Su-Schrieffer-Heeger model for electrons. We characterize the phase diagram numerically, showing different types of bond order waves and topological solitons. Finally, we study the possibility of implementing the model using atomic systems.

The Peierls structural transition in quasi-one-dimensional organic crystals of TTF-TCNQ is investigated in the frame of a more complete physical model. The two most important electron-phonon interaction mechanisms are taken into account simultaneously. One is similar of that of deformation potential and the other is of polaron type. For simplicity, the 2D crystal model is considered. The renormalized phonon spectrum and the phonon polarization operator are calculated in the random phase approximation for different temperatures. The effects of interchain interaction on renormalized acoustic phonons and on the Peierls critical temperature are analyzed.

The Peierls transition of polycrystalline CuGeO3 samples was investigated by thermal and magnetic investigations. We find that spin disorder induced by chain breaking and grain boundaries has similar effects to doping but without suppressing the spin-Peierls transition temperature or the spin-Peierls gap.

Impurities and defects are known to affect the properties of the charge density wave (CDW) state but the influence of impurities on the density of states inside the Peierls gap remains largely unexplored. Here we present an experimental study of the effect of indium impurities on photoconduction spectra of CDW compound orthorhombic TaS$_3$. We use the temperature diffusion method to introduce indium into a sample from preliminary attached In contacts. The concentration of In after 23 hours of diffusion is found to be nonuniform and strongly dependent on the distance to the contacts. The diffusion affects the spectral range 0.15-0.25 eV, increasing the photoconduction amplitude linearly with diffusion time. The optical gap value obtained from the measurements is $2\Delta = 0.25$ eV and the tail of states below $2\Delta$ is associated with the impurities in agreement with the T\"{u}tt\"{o}-Zawadowski theory. Diffusion-induced modification of current-voltage characteristics and decrease of the Peierls temperature are also observed. Neither changes in photoconduction spectra nor in the Peierls transition temperature of the control sample with Au contacts are found., Comment: 6 pages, 6 figures. To be published in Physica B

We show that the isotropic conductivity in the normal state of rare-earth tritelluride RTe3 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 momentum-dependent CDW gap as determined by angle-resolved photoemission spectroscopy (ARPES). Nonlinear transport properties in TbTe3 and GdTe3 have been studied along different crystallographic orientations. The pronounced effect of collective CDW motion is observed along c-axis and is absent completely in the perpendicular direction demonstrating the unidirectional character of the CDW. The threshold electric field for CDW sliding is linearly temperature dependent in a wide range of temperature.

Physical properties for the late-lanthanide-based $R{\mathrm{NiC}}_{2}$ ($R=\mathrm{Dy}$, Ho, Er, and Tm) ternary compounds are reported. All the compounds show antiferromagnetic ground state with the N\'eel temperature ranging from 3.4 K for ${\mathrm{HoNiC}}_{2}$ to 8.5 K for ${\mathrm{ErNiC}}_{2}$. The results of the transport and galvanomagnetic properties confirm a charge density wave state at and above room temperature with transition temperatures ${T}_{\mathrm{CDW}}=284$, 335, 366, and 394 K for ${\mathrm{DyNiC}}_{2}$, ${\mathrm{HoNiC}}_{2}$, ${\mathrm{ErNiC}}_{2}$, and ${\mathrm{TmNiC}}_{2}$, respectively. The Peierls temperature ${T}_{\mathrm{CDW}}$ scales linearly with the unit cell volume. A similar linear dependence has been observed for the temperature of the lock-in transition ${T}_{1}$ as well. Beyond the intersection point of the trend lines, the lock-in transition is no longer observed. In this Rapid Communication we demonstrate an extended phase diagram for the $R{\mathrm{NiC}}_{2}$ family.

Ultrafast electron diffraction has been employed for the study of structural dynamics at surfaces in the time domain. Experiments were performed in a pump-probe setup with femtosecond-laser excitation and subsequent probing through diffraction of a femtosecond electron pulse at a temporal resolution of 350 fs. The system of interest is one atomic layer of indium atoms on a Si(111) surface. Through self-assembly, indium atomic wires form and exhibit a Peierls-like, insulator-to-metal phase transition that can be driven nonthermally through a femtosecond laser pulse. The transient intensity of the diffraction spots indicates the lifting of the Peierls transition and melting of a charge-density wave in only 700 fs, heating of the surface in 6 ps, and formation of a metastable and supercooled phase, which exists for nanoseconds.

Due to a strong spin-orbit interaction (SOI), the surface states of Sb (111) are similar to those for topological insulators (TI) Sugawara et al. (2006). The surface states are protected by time-reversal symmetry and energy dispersion is a linear function of momentum. Defects in crystal structure lead to a local break of the surface translational symmetry and can modify surface states. It is the primary reason to study defects of Sb crystal structure and their effect on the surface states dispersion. Etching of the Sb (111) surface using Ar + ions is a common way to create defects both in a bulk and on the surface of the crystal. Sb (111) ion etching at room temperature reveals anomalous behavior of surface crystal structure. It results in formation of flat terraces of 2 nm in size. Investigation of electronic structure of the etched Sb (111) surface has demonstrated increase of density of states (DOS) at the Fermi level. The results are discussed in terms of local break of conditions of Peierls transition.

The Peierls structural transition is studied in quasi-one-dimensional (Q1D) organic crystals of the tetrathiofulvalene-tetracyanoquinodimethane (TTF-TCNQ) type in a more complete 2D physical model. Unlike the previous investigations, two electron-phonon interactions are considered: one is of the deformation potential type and the other is similar to that of polaron. The method of temperature Green functions is applied and the analytic expression for the polarization operator is obtained in the random phase approximation. The polarization operator as a function of temperature is calculated numerically for different values of the ratio d of the transfer energy in the direction transversal to conductive chains to the transfer energy along the conductive chains. The Peierls critical temperature T p is determined for different values of the parameter d in two cases: 1) when the dimensionless Fermi momentum is k F = 0.59π/2, and 2) when the Fermi momentum is k F = 0.59π/2 ± δ, where δ represents the variation of the Fermi momentum, determined by the increase or by the decrease of carrier concentration. It is found that in the first case the T p strongly decreases with the increase of the parameter d and for a certain value of the parameter d the Peierls transition does not take place on the whole. In the second case, the T p with the increase of carrier concentration n also decreases and for some value of n the transition disappears too. But with the decrease of carrier concentration the T p strongly increases. In both these cases the physical interpretations of such behavior of the Peierls transition are presented and discussed.

The alpha-(Per)(2)[M(mnt)(2)] compounds with M = Pt and Au are isostructural two-chain solids that in addition to partially oxidized conducting perylene chains also contain anionic chains that can be either paramagnetic in the case of M = Pt or diamagnetic for M = Au. The electrical transport and magnetic properties of the solid solutions (Per)(2)[Pt-x-Au(1-x)(mnt)(2)] were investigated. The incorporation of paramagnetic [Pt(mnt)(2)] impurities in the diamagnetic chains, and the effect of breaking the paramagnetic chains with diamagnetic centers for the low and high Pt range of concentrations were respectively probed. In the low Pt concentration range, there is a fast decrease of the metal-to-insulator transition from 12.4 K in the pure Au compound to 9.7 K for x = 0.1 comparable to the 8.1 K in the pure Pt compound. In the range x = 0.5-0.95, only beta-phase crystals could be obtained. The spin-Peierls transition of the pure Pt compound, simultaneous with metal-to-insulator (Peierls) transition is still present for 2% of diamagnetic impurities (x = 0.98) with transition temperature barely affected. Single crystal X-ray diffraction data obtained a high-quality structural refinement of the alpha- phase of the Au and Pt compounds. The beta-phase structure was found to be composed of ordered layers with segregated donors and anion stacks, which alternate with disordered layers. The semiconducting properties of the beta-phase are due to the disorder localization effects. info:eu-repo/semantics/publishedVersion

Department of Education and Learning, Northern Ireland (Investigators Programme No. 15/1A/3160.)

We show how tuning the proximity to the soft optical mode phase transition via chemical composition affects the lattice thermal conductivity κ of Pb1-xGexTe alloys. Using first-principles virtual-crystal simulations, we find that the anharmonic contribution to κ is minimized at the phase transition due to the maximized acoustic-optical anharmonic interaction. Mass disorder significantly lowers and flattens the dip in the anharmonic κ over a wide composition range, thus shifting the κ minimum away from the phase transition. The total κ and its anharmonic contribution vary continuously between the rocksalt and rhombohedral phases as expected for the second-order phase transition. The actual phase and its strength of resonant bonding play a less prominent role in reducing the κ of Pb1-xGexTe alloys than the proximity to the phase transition and the atomic mass. Our results show that alloys with soft optical mode transitions are promising materials for achieving low thermal conductivity and possibly high thermoelectric efficiency.

The finite-temperature entanglement entropy for an alternating spin-1/2 chain with multi-spin interactions is investigated by means of Green’s function theory combined with Jordan-Wigner transformation, to identify the spin-Peierls (SP) transition. It is found that the two-site thermal entanglement entropy is a useful tool to characterize theSPtransition. In addition, the competition between multi-spin interaction and Peierls-dimerization plays a central role in the critical phenomenon of the system.

CuGeO3, a quasi-one-dimensional S = 1/2 antiferromagnet, is the first inorganic material to display a spin-Peierls transition (SP) in which the lattice of the S = 1/2 antiferromagnetic 1-D chain system undergoes dimerization below the transition temperature to give a singlet ground state. The size-dependent magnetic properties and SP transitions of CuGeO3 are little understood. In this paper, we report the size-controlled synthesis of CuGeO3 nanorods by a hydrothermal method via adjustment of the reaction conditions. The size-effect on their magnetic properties has been investigated. In smaller crystalline CuGeO3 nanorods (ca. 2 μm length) show a weak SP transition. These findings demonstrate that size tuning is an effective tuning parameter for controlling the ground state properties of CuGeO3 and other magnetic materials where spin–lattice interactions are important.

α-MoO3 nanosheets were synthesized by a water bath method using ammonium heptamolybdenum tetrahydrate and concentrated nitric acid as precursors. Hydrogen was doped by a chemical reduction in aqueous acidic media, with hydrazine hydrate used as the reducing agent. Temperature dependent resistance showed that the low temperature Peierls transition of H-doped MoO3 nanosheets breaks below 50 K, and its resistance is satisfied at temperatures lower than 37 K (37–10 K). This phenomenon was induced by thermal disturbance and the dominance of defects in low temperature transport, which was confirmed by photoresponse measurements taken before and after the break of the new phase.

In this work, we present a numerical simulation study of the dynamic properties of the charge density waves (CDW) in one-dimensional system. We present firstly, the results obtained within the classical model where the CDW is assimilated to a rigid particle. While this model explains qualitatively the CDW conductivity field dependence, a smooth discordance with the experimental results is observed. We present also the results obtained in the context of the deformable model where the CDW is considered as a continuum medium in interaction with the randomly distributed impurities in the lattice. The results obtained within this mode are in good concordance with the experimental ones which showing that the internal degrees of freedom play a capital role in the CDW dynamic properties.

Joule-heating induced conductance-switching is studied in VO2 , a Mott insulator. Complementary in situ techniques including optical characterization, blackbody microscopy, scanning transmission X-ray microscopy (STXM) and numerical simulations are used. Abrupt redistribution in local temperature is shown to occur upon conductance-switching along with a structural phase transition, at the same current.