Periodic Lattice Distortion Research Articles

Mapping Picometer Scale Periodic Lattice Distortions with Aberration Corrected Scanning Transmission Electron Microscopy

Mapping Picometer Scale Periodic Lattice Distortions with Aberration Corrected Scanning Transmission Electron Microscopy

Stable charge density wave phase in a 1T–TiSe2 monolayer

Charge density wave (CDW) phases are symmetry-reduced states of matter in which a periodic modulation of the electronic charge frequently leads to drastic changes of the electronic spectrum, including the emergence of energy gaps. We analyze the CDW state in a 1T-TiSe$_2$ monolayer within a density functional theory framework and show that, similarly to its bulk counterpart, the monolayer is unstable towards a commensurate $2{\times}2$ periodic lattice distortion (PLD) and CDW at low temperatures. Analysis of the electron and phonon spectrum establishes the PLD as the stable $T=0$ K configuration with a narrow bandgap, whereas the undistorted and semi-metalic state is stable only above a threshold temperature. The lattice distortions as well as the unfolded and reconstructed band structure in the CDW phase agree well with experimental results. We also address evidence in our results for the role of electron-electron interactions in the CDW instability of 1T-TiSe$_2$ monolayers.

Atomic lattice disorder in charge-density-wave phases of exfoliated dichalcogenides (1T-TaS2)

Charge-density waves (CDWs) and their concomitant periodic lattice distortions (PLDs) govern the electronic properties in several layered transition-metal dichalcogenides. In particular, 1T-TaS2 undergoes a metal-to-insulator phase transition as the PLD becomes commensurate with the crystal lattice. Here we directly image PLDs of the nearly commensurate (NC) and commensurate (C) phases in thin, exfoliated 1T-TaS2 using atomic resolution scanning transmission electron microscopy at room and cryogenic temperature. At low temperatures, we observe commensurate PLD superstructures, suggesting ordering of the CDWs both in- and out-of-plane. In addition, we discover stacking transitions in the atomic lattice that occur via one-bond-length shifts. Interestingly, the NC PLDs exist inside both the stacking domains and their boundaries. Transitions in stacking order are expected to create fractional shifts in the CDW between layers and may be another route to manipulate electronic phases in layered dichalcogenides.

Nature of charge density waves and superconductivity in1T−TaSe2−xTex

Transition-metal dichalcogenides (TMDs) $MX_2$ ($M$ = Ti, Nb, Ta; $X$ = S, Se, Te) exhibit a rich set of charge density wave (CDW) orders, which usually coexist and/or compete with superconductivity. The mechanisms of CDWs and superconductivity in TMDs are still under debate. Here we perform an investigation on a typical TMD system, 1\emph{T}-TaSe$_{2-x}$Te$_x$ ($0 \leq x \leq 2$). Doping-induced disordered distribution of Se/Te suppresses CDWs in 1\emph{T}-TaSe$_2$. A domelike superconducting phase with the maximum $T_\textrm{c}^{\textrm{onset}}$ of 2.5 K was observed near CDWs. The superconducting volume is very small inside the CDW phase and becomes very large instantly when the CDW phase is fully suppressed. The observations can be understood based on the strong \emph{\textbf{q}}-dependent electron-phonon coupling-induced periodic-lattice-distortion (PLD) mechanism of CDWs. The volume variation of superconductivity implies the emergence of domain walls in the suppressing process of CDWs. Our concluded scenario makes a fundamental understanding about CDWs and related superconductivity in TMDs.

Mapping Periodic Lattice Distortions in Exfoliated Dichalchogenides with Atomic Resolution cryo-STEM

Mapping Periodic Lattice Distortions in Exfoliated Dichalchogenides with Atomic Resolution cryo-STEM

Femtosecond dynamics of decoupled superlattice zones in 4Hb–TaSe2 single crystals

Strongly correlated electronic crystal systems marked by temperature-dependent phase transitions often feature an emergence of new structural periodicities, arising from an interplay between modulated electron density and periodic lattice distortion. We investigate the structural evolution of superlattice clusters in 4Hb–TaSe2 single crystals on a subpicosecond and atomic resolution via femtosecond electron diffraction (FED). The superlattice clusters comprise of two six-member rings each, related by a rotational symmetry and held in position by Coulombic mode repulsion. The two six-member rings are decoupled into two possible zones, which are further decoupled into respective site-specific satellite reflections in the reciprocal space. Governed by the interlayer interactions and the electron diffraction simulation analysis, FED measurements are used to demonstrate the suppression and dynamics of the decoupled superlattice zones. The simultaneous temporal evolution of the two CDW reflection orders are assigned to the decoupled Raman-active Ag and soft phonon modes previously reported on an isomorphic crystal structure (4Hb–TaS2). It is found that the charge density wave amplitude mode dominates over the corresponding phase mode.

Evolution of the charge density wave superstructure inZrTe3under pressure

The material ZrTe3 is a well-known example of an incommensurate periodic lattice distortion (PLD) at low temperatures due to a charge density wave (CDW). Previous studies have found a sharp boundary as a function of pressure between CDW below 5 GPa and bulk superconductivity above this value. We present a study of low-temperature-high-pressure single crystal x-ray diffraction along with ab initio density functional theory calculations. The modulation vector q(CDW) is found to change smoothly with pressure until the PLD is lost. Fermi surface calculations reproduce these changes, but neither these nor the experimental crystal lattice structure show a particular step change at 5 GPa, thus leading to the conclusion that the CDW is lost accidentally by tipping the balance of CDW formation in the Fermi surface nesting that stabilizes it.

Unconventional Charge-Density-Wave Transition in Monolayer 1T-TiSe2.

Reducing the dimension in materials sometimes leads to unexpected discovery of exotic and/or pronounced physical properties such as quantum Hall effect in graphene and high-temperature superconductivity in iron-chalcogenide atomically thin films. Transition-metal dichalcogenides (TMDs) provide a fertile ground for studying the interplay between dimensionality and electronic properties, since they exhibit a variety of electronic phases like semiconducting, superconducting, and charge-density-wave (CDW) states. Among TMDs, bulk 1T-TiSe2 has been a target of intensive studies due to its unusual CDW properties with the periodic lattice distortions characterized by the three-dimensional (3D) commensurate wave vector. Clarifying the ground states of its two-dimensional (2D) counterpart is of great importance not only to pin down the origin of CDW, but also to find unconventional physical properties characteristic of atomic-layer materials. Here, we show the first experimental evidence for the realization of 2D CDW phase without Fermi-surface nesting in monolayer 1T-TiSe2. Our angle-resolved photoemission spectroscopy (ARPES) signifies an electron pocket at the Brillouin-zone corner above the CDW-transition temperature (TCDW ∼ 200 K), while, below TCDW, an additional electron pocket and replica bands appear at the Brillouin-zone center and corner, respectively, due to the back-folding of bands by the 2 × 2 superstructure potential. Similarity in the spectral signatures to bulk 1T-TiSe2 implies a common driving force of CDW, i.e., exciton condensation, whereas the larger energy gap below TCDW in monolayer 1T-TiSe2 suggests enhancement of electron-hole coupling upon reducing dimensionality. The present result lays the foundation for the electronic-structure engineering based with atomic-layer TMDs.

Phase stability of transition metal dichalcogenide by competing ligand field stabilization and charge density wave

Transition metal dichalcogenides (TMDs) have been investigated extensively for potential application as device materials in recent years. TMDs are found to be stable in trigonal prismatic (H), octahedral (T), or distorted octahedral (Td) coordination of the transition metal. However, the detailed understanding of stabilities of TMDs in a particular phase is lacking. In this work, the detailed TMD phase stability using first-principles calculations based on density functional theory (DFT) has been investigated to clarify the mechanism of phase stabilities of TMDs, consistent with the experimental observation. Our results indicate that the phase stability of TMDs can be explained considering the relative strength of two competing mechanisms: ligand field stabilization of d-orbitals corresponding to transition metal coordination geometry, and charge density wave (CDW) instability accompanied by a periodic lattice distortion (PLD) causing the phase transition in particular TMDs.

CDW-gaps, soft-phonons and physical transitions in bulk single crystal of alpha-Uranium

An overview of three decades of studies of the low temperature structural behaviour of the bulk of alpha-Uranium (α-U) is presented. Combining high-resolution elastic and inelastic neutron scattering made it possible to observe and study, down to 5 K, the structural and lattice dynamical aspects of a series of three charge-density waves (CDWs) transition (43, 37 and 22 K). However at lower temperatures several physical quantities show anomalies such as a controversial superconductivity transition. This stresses the need for extra structural data down to very low temperatures. While this would be a challenge with neutrons due to fission sample heating, a new opportunity is offered by low temperature Laue diffraction with hard X- rays. For example a full locking of the periodic lattice distortion (PLD) can be expected related to the evolution of the CDW and/or the appearance of a SDW, this might help understand the physical behaviour of the material and clarify the role of sample impurities.

Coupling of rare earth moment and charge density wave ordering in a single crystal Er2Ir3Si5

Charge Density Wave (CDW) transitions are well known phenomena in a large variety of quasi-low dimensional conductors. Their appearance is basically due to the low dimensionality which facilitates Fermi surface nesting. We have shown that both Lu2Ir3Si5 and Er2Ir3Si5 are two new CDW compounds whose structure is 3-D in nature [1,2]. The nesting of Fermi surfaces leads to the appearance of a periodic lattice distortion with an accompanying energy gap opening at the Fermi level [3]. In this work, we report the bulk characterization of a high quality single crystal of Czochkralski pulled Er2Ir3Si5 using transport and magnetization measurements. These studies establish multiple charge density wave transitions in this crystal with coupling of the Er moments to the CDW ordering as evidenced by the magnetization measurement. Such a coupling is rather unusual in rare earth compounds that display CDW transition. Possibility of modulated magnetism of Er moments due to CDW will be discussed.

Sliding state of the quasi-two dimensional CDW system TbTe3 probed by coherent x-ray diffraction

Coherent x-ray diffraction experiments have been performed to probe the sliding state of a quasi-two dimensional charge density wave (CDW) in TbTe3. The 2kF satellite reflection associated with the CDW has been observed with respect to external dc currents, on both sides of the threshold current. These measurements illustrate how the periodic lattice distortion associated to the CDW supports the collective motion of a sliding CDW in a quasi-two dimensional system. A comparison with the quasi-one dimensional NbSe3 system is done.

Coherent structural dynamics of a prototypical charge-density-wave-to-metal transition.

Using femtosecond time-resolved x-ray diffraction, we directly monitor the coherent lattice dynamics through an ultrafast charge-density-wave-to-metal transition in the prototypical Peierls system K(0.3)MoO(3) over a wide range of relevant excitation fluences. While in the low fluence regime we directly follow the structural dynamics associated with the collective amplitude mode; for fluences above the melting threshold of the electronic density modulation we observe a transient recovery of the periodic lattice distortion. We can describe these structural dynamics as a motion along the coordinate of the Peierls distortion triggered by the prompt collapse of electronic order after photoexcitation. The results indicate that the dynamics of a structural symmetry-breaking transition are determined by a high-symmetry excited state potential energy surface distinct from that of the initial low-temperature state.

Microscopic evidence for strong periodic lattice distortion in two-dimensional charge-density wave systems

In the quasi-2D electron systems of the layered transition metal dichalcogenides (TMD) there is still a controversy about the nature of the transitions to charge-density wave (CDW) phases, i.e. whether they are described by a Peierls-type mechanism or by a lattice-driven model. By performing scanning tunneling microscopy (STM) experiments on the canonical TMD-CDW systems, we have imaged the electronic modulation and the lattice distortion separately in 2H-TaS$_2$, TaSe$_2$, and NbSe$_2$. Across the three materials, we found dominant lattice contributions instead of the electronic modulation expected from Peierls transitions, in contrast to the CDW states that show the hallmark of contrast inversion between filled and empty states. Our results imply that the periodic lattice distortion (PLD) plays a vital role in the formation of CDW phases in the TMDs and illustrate the importance of taking into account the more complicated lattice degree of freedom when studying correlated electron systems.

Chiral charge order in 1T-TiSe2: Importance of lattice degrees of freedom

We address the question of the origin of the recently discovered chiral property of the charge-density-wave phase in 1$T$-TiSe$_2$ which so far lacks a microscopic understanding. We argue that the lattice degrees of freedom seems to be crucial for this novel phenomenon. We motivate a theoretical model that takes into account one valence and three conduction bands, a strongly screened Coulomb interaction between the electrons, as well as the coupling of the electrons to a transverse optical phonon mode. The Falicov-Kimball model extended in this way possesses a charge-density-wave state at low temperatures, which is accompanied by a periodic lattice distortion. The charge ordering is driven by a lattice deformation and electron-hole pairing (excitonic) instability in combination. We show that both electron-phonon interaction and phonon-phonon interaction must be taken into account at least up to quartic order in the lattice displacement to achieve a stable chiral charge order. The chiral property is exhibited in the ionic displacements. Furthermore, we provide the ground-state phase diagram of the model and give an estimate of the electron-electron and electron-phonon interaction constants for 1$T$-TiSe$_2$.

Dynamic separation of electron excitation and lattice heating during the photoinduced melting of the periodic lattice distortion in 2H-TaSe2

The photoinduced structural dynamics in 2H-TaSe2 in the charge-density wave (CDW) state is investigated using MeV ultrafast electron diffraction. By simultaneously tracking both the melting of the periodic lattice distortion (PLD) associated with the CDW and the lattice heating, following an impulsive photoexcitation, the separate contributions of electronic excitation and lattice thermalization to the melting process are disentangled in the time domain. Two distinct time-constants, reflecting the corresponding individual dynamics of the subsystems, are observed. Our experimental results demonstrate that the PLD in 2H-TaSe2 is first suppressed promptly by the electronic excitation and scattering, and then subsequently by lattice thermalization through electron-phonon interaction, on a much longer time scale. This latter leads to the final, full melting of the PLD.

Dynamics of charge density wave order in the quasi one dimensional conductor (TaSe4)2I probed by femtosecond optical spectroscopy

Carrier and collective mode dynamics in the quasi one-dimensional charge density wave (CDW) system (TaSe4)2I have been investigated by means of time-resolved optical pump-probe spectroscopy. In the low excitation, linear, regime we focus on the temperature dependence of the collective amplitude modes, originating from linear coupling of the electronic modulation to phonons at q CDW. Numerous amplitude modes are observed, ranging from 100 GHz to several THz. The modes’ softening near T c is rather weak, which could be related to strong decoupling of electronic and lattice subsystems. Alternatively, the data could be reconciled also in case the CDW phase transition is of the first-order type where a nearly constant order parameter below T c would prevent softening. In the high excitation regime we investigated the energetics of the photoinduced CDW-normal phase transition. Similarly to the elaborately investigated one-dimensional CDW system K0.3MoO3 we observe two characteristic energy scales, related to melting the electronic modulation alone (100 meV per unit cell) and to the overall (electronic modulation and the periodic lattice distortion) collapse of the CDW (> 400 meV per unit cell). While the latter coincides with the thermal energy needed to heat the sample from 5 K above T c the former is consistent with the mean field estimate for the electronic condensation energy, suggesting that the weak coupling description of the CDW in (TaSe4)2I is appropriate.

Lattice constant anomaly in the Li1+xV1–xO2 system near x = 0

Polycrystalline powders of Li1+xV1-xO2 were prepared in the composition range -0.10 ≤ x ≤ 0.30 via the solid state technique. X-ray diffraction indicated single phase, layered R3ˉm structure material with the exception of some impurity phases for x ≥ 0.15. Analysis of powder X-ray diffraction patterns revealed an anomaly in the lattice parameters centered near x =0 . The c-axis of the hexagonal representation was at a maximum for this composition and the a-axis at a minimum. Careful X-ray diffraction scans observed the well-known superlattice peak, which is due to trimer formation in LiVO2 — a periodic lattice distortion within the plane of vanadium cations. Integrating the areas of the Li1+xV1-xO2 superlattice peaks revealed a strong correlation between composition, fraction of vanadium in the V3+ oxidation state, lattice parameter, and degree of trimer formation. These results may suggest the view of trimer formation as a consequence of vanadium t2g orbital ordering.

Driving force of phase transition in indium nanowires on Si(111).

The precise driving force of the phase transition in indium nanowires on Si(111) has been controversial whether it is driven by a Peierls instability or by a simple energy lowering due to a periodic lattice distortion. The present van der Waals (vdW) corrected hybrid density functional calculation predicts that the low-temperature 8×2 structure whose building blocks are indium hexagons is energetically favored over the room-temperature 4×1 structure. We show that the correction of self-interaction error and the inclusion of vdW interactions play crucial roles in describing the covalent bonding, band-gap opening, and energetics of hexagon structures. The results manifest that the formation of hexagons occurs by a simple energy lowering due to the lattice distortion, not by a charge density wave formation arising from Fermi surface nesting.

Comment on “Cleavage surface of the BaFe2−xCoxAs2and FeySe1−xTexsuperconductors: A combined STM plus LEED study”

Massee et al. [Phys. Rev. B 80, 140507(R) (2009)] found on the cleavage planes of BaFe${}_{2\ensuremath{-}x}$Co${}_{x}$As${}_{2}$ two different long-range ordered structures, i.e., a ($2\ifmmode\times\else\texttimes\fi{}1$) phase present only after cleavage at low temperature and a $\sqrt{2}\ifmmode\times\else\texttimes\fi{}\sqrt{2}$ phase observed after cleavage at room temperature. These results apply generally to 122 Fe-based superconductors, but have been discussed controversially [for a summary of the conflicting views, see Hoffman, Rep. Prog. Phys. 74, 124513 (2011)]. Here we support the interpretation of Massee et al. In addition, we argue that the existence of different long-range ordered structures corresponding to the same coverage in different temperature regimes is associated with the melting of a charge density wave and removal of an associated periodic lattice distortion (CDW/PLD) in the substrate as $T$ is increased. At sufficiently low temperature the fluctuating CDW/PLD order parameter is stabilized by the adsorbate in a lock-in type mechanism. Accordingly, we interpret the surface structures observed on the 122 Fe pnictide surfaces as evidence for the presence of CDW fluctuations at low temperature, but with a wave vector differing from that of the antiferromagnetic spin-density fluctuations.