Incommensurate Phase Research Articles

Atomic structure and Mott nature of the insulating charge density wave phase of 1T-TaS2

Using x-ray pair distribution function (PDF) analysis and computer modeling, we explore structure models for the complex charge density wave (CDW) phases of layered 1T-TaS2 that both well capture their atomic-level features and are amenable to electronic structure calculations. The models give the most probable position of constituent atoms in terms of 3D repetitive unit cells comprising a minimum number of Ta–S layers. Structure modeling results confirm the emergence of star-of-David (SD) like clusters of Ta atoms in the high-temperature incommensurate (IC) CDW phase and show that, contrary to the suggestions of recent studies, the low-temperature commensurate (C) CDW phase expands upon cooling thus reducing lattice strain. The C-CDW phase is also found to preserve the stacking sequence of Ta–S layers found in the room temperature, nearly commensurate (NC) CDW phase to a large extent. DFT based on the PDF refined model shows that bulk C-CDW 1T-TaS2 also preserves the insulating state of individual layers of SD clusters, favoring the Mott physics description of the metal-to-insulator (NC-CDW to C-CDW) phase transition in 1T-TaS2. Our work highlights the importance of using precise crystal structure models in determining the nature of electronic phases in complex materials.

Reduced crystal symmetry as the origin of the ferroelectric polarization within the incommensurate magnetic phase of TbMn2O5

The precise crystal symmetry, and hence the emergence of the electric polarization, still remains an open question in multiferroic $R$Mn${}_{2}$O${}_{5}$ ($R$=rare earth, Bi, Y). While previous diffraction studies have indicated the centrosymmetric space group $P\phantom{\rule{0}{0ex}}b\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}m$, an atomic displacement allowing for electric polarization would require a noncentrosymmetric symmetry. Here, single-crystal neutron diffraction experiments on TbMn${}_{2}$O${}_{5}$ provide direct evidence of a reduced crystallographic symmetry with the polar space group $P1211$ already above the multiferroic phase transition, indicating that a symmetric ${\mathbf{S}}_{\mathbf{i}}\ensuremath{\cdot}{\mathbf{S}}_{\mathbf{j}}$ spin coupling, i.e., magnetostriction is the dominant mechanism in the commensurate magnetic phase.

Calculation of charge density wave phase diagram by interacting eigenmodes method

Patterns and periods of charge density waves (CDWs) in transition metal dichalcogenides exhibit complex phase diagrams that depend on pressure, temperature, metal intercalation, or chalcogen alloying. The phase diagrams have been understood in the context of Landau free energy model which explains the lock-in behavior in the commensurate–incommensurate phase transition and rotational symmetry breaking (stripe phase) in CDW phase. Here, we present that our interatomic potential energy function has not only reproduced the above behaviors in the temperature-dependent phase diagram of monolayer H-TaSe2 without adjustable parameters, but also predict a new commensurate–commensurate phase transition. For the calculation, eigenmodes of the lattice potential were used for variables in the interatomic potential and CDWs are obtained as ground states of interacting eigenmodes. Unlike Landau model, the parameters in our potential energy function are directly calculated from first-principles. Our work explicitly shows how the aforementioned behaviors in CDW phase transition are related with the lattice anharmonicity.

Non-Hermitian topological mobility edges and transport in photonic quantum walks.

In non-Hermitian quasicrystals, mobility edges (ME) separating localized and extended states in the complex energy plane can arise as a result of non-Hermitian terms in the Hamiltonian. Such ME are of topological nature, i.e., the energies of localized and extended states exhibit distinct topological structures in the complex energy plane. However, depending on the origin of non-Hermiticity, i.e., asymmetry of hopping amplitudes or complexification of the incommensurate potential phase, different winding numbers are introduced, corresponding to different transport features in the bulk of the lattice: while ballistic transport is allowed in the former case, pseudo-dynamical localization is observed in the latter case. The results are illustrated by considering non-Hermitian photonic quantum walks in synthetic mesh lattices.

Tunable Domain Switching Features of Incommensurate Antiferroelectric Ceramics Realizing Excellent Energy Storage Properties.

An incommensurate modulated antiferroelectric phase is a key part of ideal candidate materials for the next generation of dielectric ceramics with excellent energy storage properties. However, there is less research carried out when considering its relatively low polarization response. Here, the incommensurate phase is modulated by stabilizing the antiferroelectric phase and the energy storage performance of the incommensurate phase under ultrahigh electric field is studied. The tape-casting method is applied to construct dense and thin ceramics. La3+ doping induces a room-temperature incommensurate antiferroelectric orthorhombic matrix. With little Cd2+ , the extremely superior energy storage performances arose as follows: when 0.03, the recoverable energy storage density reaches ≈19.3 J cm-3 , accompanying an ultrahigh energy storage efficiency of ≈91% (870kV cm-1 ); also, a giant discharge energy density of ≈15.4 J cm-3 emerges during actual operation. In situ observations demonstrate that these superior energy storage properties originate from the phase transition from the incommensurate antiferroelectric orthorhombic phase to the induced rhombohedral relaxor ferroelectric one. The adjustable incommensurate period affects the depolarization response. The revealed phase-transition mechanism enriches the existing antiferroelectric-ferroelectric transition. Attention to the incommensurate phase can provide a reference for the selection of the next generation of high-performance antiferroelectric materials.

Quantum orders in the frustrated Ising model on the bathroom tile lattice

We determine the zero and finite temperature phase diagram of the fully frustrated quantum Ising model on the bathroom tile (4-8) lattice. The phase diagram exhibits a wealth of 2+1d physics, including 1. classical Coulomb dimer liquids of both square and triangular lattice types; 2. quantum order-by-disorder induced phases breaking $\mathbb{Z}_4$, $\mathbb{Z}_6$, and $\mathbb{Z}_8$ symmetries; 3. finite temperature Kosterlitz-Thouless (KT) phases floating over the $\mathbb{Z}_6$ and $\mathbb{Z}_8$ orders; and, 4. staircases of (in)-commensurate symmetry breaking phases at intermediate coupling. We establish this elaborate phase diagram using a combination of dimer model mapping, perturbation theory, Landau analysis and Stochastic Series Expansion Quantum Monte Carlo (QMC-SSE). Our results provide a baseline for studying frustrated magnetism with D-Wave architecture annealers, where the 4-8 lattice can be embedded naturally without `cloning', reducing the number of competing energy scales. Simulations with the D-Wave 2000Q demonstrate qualitative agreement with the high temperature portion of the phase diagram, but are unable to access the low temperature phases.

Hybrid improper dipolar density wave in NaLaCoWO6

Hybrid improper ferroelectricity (HIF) allows the generation of an electrical polarization in the AA${}^{\ensuremath{'}}$BB${}^{\ensuremath{'}}{\mathrm{O}}_{6}$ double perovskite materials thanks to the combination of two nonpolar octahedral distortions. Nevertheless, for selected combination of the A/A${}^{\ensuremath{'}}$ cations a nonpolar incommensurate phase is observed with average symmetry $C2/m$. Thanks to a detailed crystallographic description of the incommensurate phase, based on electron, neutron, and x-ray diffraction data, we show that the incommensurate modulation is related to an abrupt change of the out-of-phase tilting along the $a$ and $c$ axis, whereas the tilting along the $b$ axis remains constant across the structure. By using group theory and symmetry analysis we show that we observe an incommensurate analog of HIF, which induces a hybrid improper dipolar density wave in ${\mathrm{NaLaCoWO}}_{6}$. The dipolar ordering is due also in this case to a trilinear invariant involving the commensurate and incommensurate octahedra tilting.

Incommensurate lamellar phase from long chain Mannosides: Investigation by X-Ray scattering and replica exchange molecular dynamics (REMD)

We report the synthesis and phase behaviour of two anhydrous mannosides (αManC18 and αManC18:1) with stearyl and monounsaturated oleyl hydrocarbon chains that can be obtained from vegetable sources. These mannosides have been characterised by differential scanning calorimetry, polarised optical microscopy and small- and wide-angle X-ray scattering. The two compounds exhibited multiple d-spacing bilayer structures. αManC18:1 gives a distinct incommensurate lamellar that persists until high temperature. On the other hand, αManC18 forms an incommensurate gel phase only at low temperature but undergoes a transition into the lamellar (Lα) liquid crystal phases on heating. The results were confirmed by replica exchange molecular dynamics (REMD). The average hydrocarbon chain/headgroup tilt angles 〈ϕ〉/〈θ〉, and average chain bending angle 〈ψ〉 were calculated for the simulated bilayer systems at ∼ 25 °C. The multiple averaged headgroup tilt angles 〈θ〉 explain the observed incommensurate bilayer structures with different bilayer thicknesses in these long hydrocarbon chain of mannosides. Moreover, different tilting angles of the headgroup result in different surface areas per lipid. Relating the incommensurate phase properly to molecular parameters is important especially in multi-component membranes, where the interplay of different molecule types is difficult to predict on intuitive grounds.

Thermodynamic Driving Forces for Substrate Atom Extraction by Adsorption of Strong Electron Acceptor Molecules.

A quantitative structural investigation is reported, aimed at resolving the issue of whether substrate adatoms are incorporated into the monolayers formed by strong molecular electron acceptors deposited onto metallic electrodes. A combination of normal-incidence X-ray standing waves, low-energy electron diffraction, scanning tunnelling microscopy, and X-ray photoelectron spectroscopy measurements demonstrate that the systems TCNQ and F4TCNQ on Ag(100) lie at the boundary between these two possibilities and thus represent ideal model systems with which to study this effect. A room-temperature commensurate phase of adsorbed TCNQ is found not to involve Ag adatoms, but to adopt an inverted bowl configuration, long predicted but not previously identified experimentally. By contrast, a similar phase of adsorbed F4TCNQ does lead to Ag adatom incorporation in the overlayer, the cyano end groups of the molecule being twisted relative to the planar quinoid ring. Density functional theory (DFT) calculations show that this behavior is consistent with the adsorption energetics. Annealing of the commensurate TCNQ overlayer phase leads to an incommensurate phase that does appear to incorporate Ag adatoms. Our results indicate that the inclusion (or exclusion) of metal atoms into the organic monolayers is the result of both thermodynamic and kinetic factors.

Observation of multiple charge density wave phases in epitaxial monolayer 1T-VSe2 film

As a special order of electronic correlation induced by spatial modulation, the charge density wave (CDW) phenomena in condensed matters attract enormous research interests. Here, using scanning–tunneling microscopy in various temperatures, we discover a hidden incommensurate stripe-like CDW order besides the () CDW phase at low-temperature of 4 K in the epitaxial monolayer 1T-VSe2 film. Combining the variable-temperature angle-resolved photoemission spectroscopic (ARPES) measurements, we discover a two-step transition of an anisotropic CDW gap structure that consists of two parts Δ 1 and Δ 2. The gap part Δ 1 that closes around ∼ 150 K is accompanied with the vanish of the () CDW phase. While another momentum-dependent gap part Δ 2 can survive up to ∼ 340 K, and is suggested to the result of the incommensurate CDW phase. This two-step transition with anisotropic gap opening and the resulted evolution in ARPES spectra are corroborated by our theoretical calculation based on a phenomenological form for the self-energy containing a two-gap structure Δ 1 + Δ 2, which suggests different forming mechanisms between the () and the incommensurate CDW phases. Our findings provide significant information and deep understandings on the CDW phases in monolayer 1T-VSe2 film as a two-dimensional (2D) material.

TMDs as a platform for spin liquid physics: A strong coupling study of twisted bilayer WSe2

The advent of twisted moiré heterostructures as a playground for strongly correlated electron physics has led to a plethora of experimental and theoretical efforts seeking to unravel the nature of the emergent superconducting and insulating states. Among these layered compositions of two-dimensional materials, transition metal dichalcogenides are now appreciated as highly tunable platforms to simulate reinforced electronic interactions in the presence of low-energy bands with almost negligible bandwidth. Here, we focus on the twisted homobilayer WSe2 and the insulating phase at half-filling of the flat bands reported therein. More specifically, we explore the possibility of realizing quantum spin liquid (QSL) physics on the basis of a strong coupling description, including up to second-nearest neighbor Heisenberg couplings J1 and J2 as well as Dzyaloshinskii–Moriya (DM) interactions. Mapping out the global phase diagram as a function of an out-of-plane displacement field, we indeed find evidence for putative QSL states, albeit only close to SU(2) symmetric points. In the presence of finite DM couplings and XXZ anisotropy, long-range order is predominantly present with a mix of both commensurate and incommensurate magnetic phases.

Incommensurate Phase in Λ-cobalt (III) Sepulchrate Trinitrate Governed by Highly Competitive N-H⋅⋅⋅O and C-H⋅⋅⋅O Hydrogen Bond Networks.

Phase transitions in molecular crystals are often determined by intermolecular interactions. The cage complex of [Co(C12H30N8)]3+ ⋅ 3 NO3 − is reported to undergo a disorder‐order phase transition at T c1 ≈133 K upon cooling. Temperature‐dependent neutron and synchrotron diffraction experiments revealed satellite reflections in addition to main reflections in the diffraction patterns below T c1. The modulation wave vector varies as function of temperature and locks in at T c3≈98 K. Here, we demonstrate that the crystal symmetry lowers from hexagonal to monoclinic in the incommensurately modulated phases in T c1<T<T c3. Distinctive levels of competitions: trade‐off between longer N−H⋅⋅⋅O and shorter C−H⋅⋅⋅O hydrogen bonds; steric constraints to dense C−H⋅⋅⋅O bonds give rise to pronounced modulation of the basic structure. Severely frustrated crystal packing in the incommensurate phase is precursor to optimal balance of intermolecular interactions in the lock‐in phase.

Scalable production of single 2D van der Waals layers through atomic layer deposition: bilayer silica on metal foils and films

The self-limiting nature of atomic layer deposition (ALD) makes it an appealing option for growing single layers of two-dimensional van der Waals (2D-VDW) materials. In this paper it is demonstrated that a single layer of a 2D-VDW form of SiO2 can be grown by ALD on Au and Pd polycrystalline foils and epitaxial films. The silica was deposited by two cycles of bis(diethylamino) silane and oxygen plasma exposure at 525 K. Initial deposition produced a three-dimensionally disordered silica layer; however, subsequent annealing above 950 K drove a structural rearrangement resulting in 2D-VDW. The annealing could be performed at ambient pressure. Surface spectra recorded after annealing indicated that the two ALD cycles yielded close to the silica coverage obtained for 2D-VDW silica prepared by precision SiO deposition in ultra-high vacuum (UHV). Analysis of ALD-grown 2D-VDW silica on a Pd(111) film revealed the co-existence of amorphous and incommensurate crystalline 2D phases. In contrast, ALD growth on Au(111) films produced predominantly the amorphous phase while SiO deposition in UHV led to only the crystalline phase, suggesting that the choice of Si source can enable phase control.

Dynamical crossover behavior in the relaxation of quenched quantum many-body systems

A crossover between different power-law relaxation behaviors of many-body periodically driven integrable systems has come to light in recent years. We demonstrate using integrable quantum systems, that similar kinds of dynamical transitions may also occur in the relaxation of such systems following a sudden quench. Particularly, we observe two distinct power-law relaxation behaviors following a sudden quench in the integrable XY model, depending upon whether the quenched Hamiltonian lies in the commensurate or the incommensurate phase. The relaxation behavior for quenches at and near the boundary line, called the disorder line (DL), separating these phases is also characterized. The relaxation at the DL shows a new scaling exponent previously unexplored. The transitions occur through a crossover from the commensurate/incommensurate scaling behavior to the DL scaling behavior. The crossover time diverges like a power law as the parameters of the final quenched Hamiltonian approach the DL. The transitions are also observed to be robust under weak integrability breaking perturbations but disappear following strongly chaotic quenches.

Magnetic phase transitions in the LiNi0.9 M 0.1PO4 (M = Mn, Co) single crystals

The LiNiPO4, LiNi0.9Mn0.1PO4, and LiNi0.9Co0.1PO4 single crystals are studied with heat capacity and neutron diffraction measurements over the temperature interval (10–30) K. Two peaks are observed on the temperature dependence of heat capacity for LiNiPO4, and LiNi0.9Co0.1PO4 samples. One peak indicates the first order phase transition from an antiferromagnetic commensurate (C) structure to an incommensurate (IC) one upon heating. According to neutron diffraction, in LiNiPO4 the IC ordering is described by the propagation vector k = 2π/b(0, 0.080, 0) at the Néel temperature T N = 20.8 K, and k = 2π/b(0, 0.098, 0) at T N = 20.2(1) K for LiNi0.9Co0.1PO4. A further increase in temperature leads to the second order phase transition to a paramagnetic state at critical temperature T IC = 21.7 K and 21.1 K for LiNiPO4 and LiNi0.9Co0.1PO4, respectively. The C and IC phases coexist over the temperature interval (20.6–20.8) K and (20.2–21.2) K in LiNiPO4 and LiNi0.9Co0.1PO4, respectively. In the LiNi0.9Mn0.1PO4 the magnetic phase transition occurs at T N = 22.7 K, but a magnetic scattering is observed up to 24.6 K.

Fisher zeros and persistent temporal oscillations in nonunitary quantum circuits

We present a quantum circuit with measurements and post-selection that exhibits a panoply of space- and/or time-ordered phases, from ferromagnetic order to spin-density waves to time crystals. Unlike the time crystals that have been found in unitary models, those that occur here are \emph{incommensurate} with the drive frequency. The period of the incommensurate time-crystal phase may be tuned by adjusting the circuit parameters. We demonstrate that the phases of our quantum circuit, including the inherently non-equilibrium dynamical ones, correspond to complex-temperature equilibrium phases of the exactly solvable square-lattice anisotropic Ising model.

Ferroelectric to incommensurate fluctuations crossover in PbHfO3−PbSnO3

Perovskite solid solutions PbHfO3-PbSnO3 offer valuable opportunities for studying the formation mechsnisms of incommensurate phases, owing to the presence of an intermediate (between cubic and incommensurate) phase, which is stabilized in PbHfO3 upon PbSnO3 admixture. Here, x-ray diffuse scattering signal is used to quantify the evolution of susceptibilities related to different modes of distortion (ferroelectric, incommensurate, antiferrodistortive) as a function of temperature and the results are critically compared to the predictions of a minimal symmetry-based Landau-like model with two coupled order parameters (ferroelectric and antiferrodistortive) and incommensurate order parameter being interpreted as inhomogeneous polarization. Experimentally, we observe a Curie-Weiss-like linear dependence of ferroelectric stiffness (inverse of susceptibility related to homogeneous polarization fluctuations) in the cubic phase down to about 50 K above the transition to the intermediate phase, where this dependence nearly saturates. Upon cooling down to the intermediate phase, the maximum of susceptibility shifts gradually to the non-zero wavevector, where another Curie-Weiss-like linear stiffness trend is established, but with respect to the incommensurate order parameter. Symmetry of diffuse scattering distributions indicates an orthorhombic symmetry of the intermediate phase. A notable temperature dependence of the constant that describes the energy of polarization inhomogeneities is observed experimentally, which is in disagreement with the model expectations. Specifics of this dependence suggest the presence of a nearly temperature-independent characteristic length scale for inhomogeneities across several phases. Other differences with the model suggest that the incommensurate order parameter cannot be straightforwardly identified with weakly-inhomogeneous ferroelectric polarization.

Phase diagrams of lattice models on Cayley tree and chandelier network: a review

The main purpose of this review paper is to give systematically all the known results on phase diagrams corresponding to lattice models (Ising and Potts) on Cayley tree (or Bethe lattice) and chandelier networks. A detailed survey of various modelling applications of lattice models is reported. By using Vannimenus's approach, the recursive equations of Ising and Potts models associated to a given Hamiltonian on the Cayley tree are presented and analyzed. The corresponding phase diagrams with programming codes in different programming languages are plotted. To detect the phase transitions in the modulated phase, we investigate in detail the actual variation of the wave-vector q with temperature and the Lyapunov exponent associated with the trajectory of our current recursive system. We determine the transition between commensurate (C) and incommensurate (I) phases by means of the Lyapunov exponents, wave-vector, and strange attractor for a comprehensive comparison. We survey the dynamical behavior of the Ising model on the chandelier network. We examine the phase diagrams of the Ising model corresponding to a given Hamiltonian on a new type of "Cayley-tree-like lattice", such as triangular, rectangular, pentagonal chandelier networks (lattices). Moreover, several open problems are discussed.

Normal to In-Commensurate Phase Transition in Sr2nb2o7 Single Crystal as Studied by Inelastic Light Scattering

Normal to In-Commensurate Phase Transition in Sr2nb2o7 Single Crystal as Studied by Inelastic Light Scattering

A one-dimensional high-order commensurate phase of tilted molecules.

We report on the formation of a high-order commensurate (HOC) structure of 5,14-dihydro-5,7,12,14-tetraazapentacene (DHTAP) molecules on the highly corrugated Cu(110)–(2 × 1)O surface. Scanning tunnelling microscopy shows that the DHTAP molecules form a periodic uniaxial arrangement in which groups of seven molecules are distributed over exactly nine substrate lattice spacings along the [1̄10] direction. DFT-calculations reveal that this peculiar arrangement is associated with different tilting of the seven DHTAP molecules within the quasi one-dimensional HOC unit cell. The orientational degree of freedom thus adds a new parameter, which can efficiently stabilize complex molecular structures on corrugated surfaces.