X-ray studies of phonon softening in tise2

Incoherence-to-coherence crossover observed in charge-density-wave material 1T-TiSe2

Analogous to the condensation of Cooper pairs in superconductors, the Bose-Einstein condensation (BEC) of electron-hole pairs in semiconductors and semimetals leads to an emergence of an exotic ground state - the excitonic insulator state. In this paper, we study the electronic structure of 1T-TiSe2 utilizing angle-resolved photoemission spectroscopy and alkali-metal deposition. Alkali-metal adatoms are deposited in-situ on the sample surface, doping the system with electrons. The conduction bands of 1T-TiSe2 are thereby pushed down below the Fermi energy, which enables us to characterize its temperature dependence with precision. We found that the formation of the charge density wave (CDW) in 1T-TiSe2 at ~ 205 K is accompanied by a significant increase of the band gap, supporting the existence of excitonic pairing in the CDW state of 1T-TiSe2. More importantly, by analyzing the linewidth of the single-particle excitation spectrum, we unveiled an incoherence-to-coherence crossover at 165 K, which could be attributed to a possible exciton condensation that occurs beneath the CDW transition in 1T-TiSe2. Our results not only explain the exotic transport properties of 1T-TiSe2, but also highlight the possible existence of an excitonic condensate in this semiconducting material.

Lifshitz transition enabling superconducting dome around a charge-order critical point

Superconductivity often emerges as a dome around a quantum critical point (QCP) where long-range order is suppressed to zero temperature, mostly in magnetically ordered materials. However, the emergence of superconductivity at charge-order QCPs remains shrouded in mystery, despite its relevance to high-temperature superconductors and other exotic phases of matter. Here, we present resistance measurements proving that a dome of superconductivity surrounds the putative charge-density-wave QCP in pristine samples of titanium diselenide tuned with hydrostatic pressure. In addition, our quantum oscillation measurements combined with electronic structure calculations show that superconductivity sets in precisely when large electron and hole pockets suddenly appear through an abrupt change of the Fermi surface topology, also known as a Lifshitz transition. Combined with the known repulsive interaction, this suggests that unconventional s± superconductivity is mediated by charge-density-wave fluctuations in titanium diselenide. These results highlight the importance of the electronic ground state and charge fluctuations in enabling unconventional superconductivity.

Plasmon Excitations across the Charge-Density-Wave Transition in Single-Layer TiSe2

1T-TiSe2 is believed to possess a soft electronic mode, i.e., plasmon or exciton, that might be responsible for the exciton condensation and charge-density-wave (CDW) transition. Here, we explore collective electronic excitations in single-layer 1T-TiSe2 by using the ab initio electromagnetic linear response and unveil intricate scattering pathways of the two-dimensional (2D) plasmon mode near the CDW phase. We found the dominant role of plasmon-phonon scattering, which in combination with the CDW gap excitations leads to the anomalous temperature dependence of the plasmon line width across the CDW transition. Below the transition temperature TCDW a strong hybridization between the 2D plasmon and CDW excitations is obtained. These optical features are highly tunable due to temperature-dependent CDW-related modifications of electronic structure and electron-phonon coupling and make CDW-bearing systems potentially interesting for applications in optoelectronics and low-loss plasmonics.

Emergence of two distinct phase transitions in monolayer CoSe2 on graphene

Dimensional modifications play a crucial role in various applications, especially in the context of device miniaturization, giving rise to novel quantum phenomena. The many-body dynamics induced by dimensional modifications, including electron-electron, electron-phonon, electron-magnon and electron-plasmon coupling, are known to significantly affect the atomic and electronic properties of the materials. By reducing the dimensionality of orthorhombic CoSe2 and forming heterostructure with bilayer graphene using molecular beam epitaxy, we unveil the emergence of two types of phase transitions through angle-resolved photoemission spectroscopy and scanning tunneling microscopy measurements. We disclose that the 2 × 1 superstructure is associated with charge density wave induced by Fermi surface nesting, characterized by a transition temperature of 340 K. Additionally, another phase transition at temperature of 160 K based on temperature dependent gap evolution are observed with renormalized electronic structure induced by electron-boson coupling. These discoveries of the electronic and atomic modifications, influenced by electron-electron and electron-boson interactions, underscore that many-body physics play significant roles in understanding low-dimensional properties of non-van der Waals Co-chalcogenides and related heterostructures.

An electronic origin of charge order in infinite-layer nickelates

A charge order (CO) with a wavevector [Formula: see text] is observed in infinite-layer nickelates. Here we use first-principles calculations to demonstrate a charge-transfer-driven CO mechanism in infinite-layer nickelates, which leads to a characteristic Ni1+-Ni2+-Ni1+ stripe state. For every three Ni atoms, due to the presence of near-Fermi-level conduction bands, Hubbard interaction on Ni-d orbitals transfers electrons on one Ni atom to conduction bands and leaves electrons on the other two Ni atoms to become more localized. We further derive a low-energy effective model to elucidate that the CO state arises from a delicate competition between Hubbard interaction on Ni-d orbitals and charge transfer energy between Ni-d orbitals and conduction bands. With physically reasonable parameters, [Formula: see text] CO state is more stable than uniform paramagnetic state and usual checkerboard antiferromagnetic state. Our work highlights the multi-band nature of infinite-layer nickelates, which leads to some distinctive correlated properties that are not found in cuprates.

Evidence of high-temperature exciton condensation in a two-dimensional semimetal

Electrons and holes can spontaneously form excitons and condense in a semimetal or semiconductor, as predicted decades ago. This type of Bose condensation can happen at much higher temperatures in comparison with dilute atomic gases. Two-dimensional (2D) materials with reduced Coulomb screening around the Fermi level are promising for realizing such a system. Here we report a change in the band structure accompanied by a phase transition at about 180 K in single-layer ZrTe₂ based on angle-resolved photoemission spectroscopy (ARPES) measurements. Below the transition temperature, gap opening and development of an ultra-flat band top around the zone center are observed. This gap and the phase transition are rapidly suppressed with extra carrier densities introduced by adding more layers or dopants on the surface. The results suggest the formation of an excitonic insulating ground state in single-layer ZrTe₂, and the findings are rationalized by first-principles calculations and a self-consistent mean-field theory. Our study provides evidence for exciton condensation in a 2D semimetal and demonstrates strong dimensionality effects on the formation of intrinsic bound electron-hole pairs in solids.

Dramatic Plasmon Response to the Charge-Density-Wave Gap Development in 1T-TiSe_{2}

1T-TiSe_{2} is one of the most studied charge density wave (CDW) systems, not only because of its peculiar properties related to the CDW transition, but also due to its status as a promising candidate of exciton insulator signaled by the proposed plasmon softening at the CDW wave vector. Using high-resolution electron energy loss spectroscopy, we report a systematic study of the temperature-dependent plasmon behaviors of 1T-TiSe_{2}. We unambiguously resolve the plasmon from phonon modes, revealing the existence of Landau damping to the plasmon at finite momentums, which does not support the plasmon softening picture for exciton condensation. Moreover, we discover that the plasmon lifetime at zero momentum responds dramatically to the band gap evolution associated with the CDW transition. The interband transitions near the Fermi energy in the normal phase are demonstrated to serve as a strong damping channel of plasmons, while such a channel in the CDW phase is suppressed due to the CDW gap opening, which results in the dramatic tunability of the plasmon in semimetals or small-gap semiconductors.

Light-induced dimension crossover dictated by excitonic correlations

In low-dimensional systems with strong electronic correlations, the application of an ultrashort laser pulse often yields novel phases that are otherwise inaccessible. The central challenge in understanding such phenomena is to determine how dimensionality and many-body correlations together govern the pathway of a non-adiabatic transition. To this end, we examine a layered compound, 1T-TiSe2, whose three-dimensional charge-density-wave (3D CDW) state also features exciton condensation due to strong electron-hole interactions. We find that photoexcitation suppresses the equilibrium 3D CDW while creating a nonequilibrium 2D CDW. Remarkably, the dimension reduction does not occur unless bound electron-hole pairs are broken. This relation suggests that excitonic correlations maintain the out-of-plane CDW coherence, settling a long-standing debate over their role in the CDW transition. Our findings demonstrate how optical manipulation of electronic interaction enables one to control the dimensionality of a broken-symmetry order, paving the way for realizing other emergent states in strongly correlated systems.

Role of Equilibrium Fluctuations in Light-Induced Order

Engineering novel states of matter with light is at the forefront of materials research. An intensely studied direction is to realize broken-symmetry phases that are "hidden" under equilibrium conditions but can be unleashed by an ultrashort laser pulse. Despite a plethora of experimental discoveries, the nature of these orders and how they transiently appear remain unclear. To this end, we investigate a nonequilibrium charge density wave (CDW) in rare-earth tritellurides, which is suppressed in equilibrium but emerges after photoexcitation. Using a pump-pump-probe protocol implemented in ultrafast electron diffraction, we demonstrate that the light-induced CDW consists solely of order parameter fluctuations, which bear striking similarities to critical fluctuations in equilibrium despite differences in the length scale. By calculating the dynamics of CDW fluctuations in a nonperturbative model, we further show that the strength of the light-induced order is governed by the amplitude of equilibrium fluctuations. These findings highlight photoinduced fluctuations as an important ingredient for the emergence of transient orders out of equilibrium. Our results further suggest that materials with strong fluctuations in equilibrium are promising platforms to host hidden orders after laser excitation.

The effect of finite-temperature and anharmonic lattice dynamics on the thermal conductivity of ZrS2monolayer: self-consistent phonon calculations

Two-dimensional (2D) ZrS₂monolayer (ML) has emerged as a promising candidate for thermoelectric (TE) device applications due to its high TE figure of merit, which is mainly contributed by its inherently low lattice thermal conductivity (LTC). This work investigates the effect of the lattice anharmonicity driven by the temperature-dependent phonon dispersions on the thermal transport of ZrS₂ML. The calculations are based on the self-consistent phonon (SCP) theory to calculate the thermodynamic parameters along with the LTC. The higher-order (quartic) force constants were extracted by using an efficient compressive sensing lattice dynamics technique, which estimates the necessary data based on the emerging machine learning program as an alternative of computationally expensive density functional theory calculations. Resolve of the degeneracy and hardening of the vibrational frequencies of low-energy optical modes were predicted upon including the quartic anharmonicity. As compared to the conventional Boltzmann transport equation (BTE) approach, the LTC of the optimized ZrS₂ML unit cell within SCP + BTE approach is found to be significantly enhanced (e.g., by 21% at 300 K). This enhancement is due to the relatively lower value of phonon linewidth contributed by the anharmonic frequency renormalization included in the SCP theory. Mainly, the conventional BTE approach neglects the temperature dependence of the phonon frequencies due to the consideration of harmonic lattice dynamics and treats the normal process of three-phonon scattering incorrectly due to the use of quasi-particle lifetimes. These limitations are addressed in this work within the SCP + BTE approach, which signifies the validity and accuracy of this approach.

Revealing momentum-dependent electron-phonon and phonon-phonon coupling in complex materials with ultrafast electron diffuse scattering

ABSTRACT

Despite their fundamental role in determining many important properties of materials, detailed momentum-dependent information on the strength of electron-phonon and phonon-phonon coupling across the entire Brillouin zone has remained elusive. Ultrafast electron diffuse scattering (UEDS) is a recently developed technique that is making a significant contribution to these questions. Here, we describe both the UEDS methodology and the information content of ultrafast, photoinduced changes in phonon-diffuse scattering from single-crystal materials. We present results obtained from Ni, WSe₂, and TiSe₂, materials that are characterized by a complex interplay between electronic (charge, spin) and lattice degrees of freedom. We demonstrate the power of this technique by unraveling carrier-phonon and phonon-phonon interactions in both momentum and time and following nonequilibrium phonon dynamics in detail on ultrafast time scales. By combining ab initio calculations with ultrafast diffuse electron scattering, insights into electronic and magnetic dynamics that impact UEDS indirectly can also be obtained.

Mechanisms of electron-phonon coupling unraveled in momentum and time: The case of soft phonons in TiSe2

The complex coupling between charge carriers and phonons is responsible for diverse phenomena in condensed matter. We apply ultrafast electron diffuse scattering to unravel electron-phonon coupling phenomena in 1T-TiSe₂ in both momentum and time. We are able to distinguish effects due to the real part of the many-body bare electronic susceptibility, [Formula: see text], from those due to the electron-phonon coupling vertex, g _q , by following the response of semimetallic (normal-phase) 1T-TiSe₂ to the selective photo-doping of carriers into the electron pocket at the Fermi level. Quasi-impulsive and wave vector-specific renormalization of soft zone-boundary phonon frequencies (stiffening) is observed, followed by wave vector-independent electron-phonon equilibration. These results unravel the underlying mechanisms driving the phonon softening that is associated with the charge density wave transition at lower temperatures.

Direct observation of excitonic instability in Ta2NiSe5

Coulomb attraction between electrons and holes in a narrow-gap semiconductor or a semimetal is predicted to lead to an elusive phase of matter dubbed excitonic insulator. However, direct observation of such electronic instability remains extremely rare. Here, we report the observation of incipient divergence in the static excitonic susceptibility of the candidate material Ta2NiSe5 using Raman spectroscopy. Critical fluctuations of the excitonic order parameter give rise to quasi-elastic scattering of B2g symmetry, whose intensity grows inversely with temperature toward the Weiss temperature of TW ≈ 237 K, which is arrested by a structural phase transition driven by an acoustic phonon of the same symmetry at TC = 325 K. Concurrently, a B2g optical phonon becomes heavily damped to the extent that its trace is almost invisible around TC, which manifests a strong electron-phonon coupling that has obscured the identification of the low-temperature phase as an excitonic insulator for more than a decade. Our results unambiguously reveal the electronic origin of the phase transition.

Weak Dimensionality Dependence and Dominant Role of Ionic Fluctuations in the Charge-Density-Wave Transition of NbSe_{2}

Contradictory experiments have been reported about the dimensionality effect on the charge-density-wave transition in 2H NbSe_{2}. While scanning tunneling experiments on single layers grown by molecular beam epitaxy measure a charge-density-wave transition temperature in the monolayer similar to the bulk, around 33 K, Raman experiments on exfoliated samples observe a large enhancement of the transition temperature up to 145 K. By employing a nonperturbative approach to deal with anharmonicity, we calculate from first principles the temperature dependence of the phonon spectra both for bulk and monolayer. In both cases, the charge-density-wave transition temperature is estimated as the temperature at which the phonon energy of the mode driving the structural instability vanishes. The obtained transition temperature in the bulk is around 59 K, in rather good agreement with experiments, and it is just slightly increased in the single-layer limit to 73 K, showing the weak dependence of the transition on dimensionality. Environmental factors could motivate the disagreement between the transition temperatures reported by experiments. Our analysis also demonstrates the predominance of ionic fluctuations over electronic ones in the melting of the charge-density-wave order.

Fermi Surface Reconstruction and Electron Dynamics at the Charge-Density-Wave Transition in TiSe_{2}

The evolution of the charge carrier concentrations and mobilities are examined across the charge-density-wave (CDW) transition in TiSe_{2}. Combined quantum oscillation and magnetotransport measurements show that a small electron pocket dominates the electronic properties at low temperatures while an electron and hole pocket contribute at room temperature. At the CDW transition, an abrupt Fermi surface reconstruction and a minimum in the electron and hole mobilities are extracted from two-band and Kohler analysis of magnetotransport measurements. The minimum in the mobilities is associated with the overseen role of scattering from the softening CDW mode. With the carrier concentrations and dynamics dominated by the CDW and the associated bosonic mode, our results highlight TiSe_{2} as a prototypical system to study the Fermi surface reconstruction at a density-wave transition.

Ultrafast charge ordering by self-amplified exciton-phonon dynamics in TiSe2

The origin of charge density waves (CDWs) in TiSe\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_{2}$$\end{document}2 has long been debated, mainly due to the difficulties in identifying the timescales of the excitonic pairing and electron–phonon coupling (EPC). Without a time-resolved and microscopic mechanism, one has to assume simultaneous appearance of CDW and periodic lattice distortions (PLD). Here, we accomplish a complete separation of ultrafast exciton and PLD dynamics and unravel their interplay in our real-time time-dependent density functional theory simulations. We find that laser pulses knock off the exciton order and induce a homogeneous bonding–antibonding transition in the initial 20 fs, then the weakened electronic order triggers ionic movements antiparallel to the original PLD. The EPC comes into play after the initial 20 fs, and the two processes mutually amplify each other leading to a complete inversion of CDW ordering. The self-amplified dynamics reproduces the evolution of band structures in agreement with photoemission experiments. Hence we resolve the key processes in the initial dynamics of CDWs that help elucidate the underlying mechanism.

The physical origins of charge density waves in 1T-TiSe2 and their response to ultrafast excitation have long been a topic of theoretical and experimental debate. Here the authors present an ab initio theory that successfully captures the observed dynamics of charge density wave formation.

Orbital- and k_{z}-Selective Hybridization of Se 4p and Ti 3d States in the Charge Density Wave Phase of TiSe_{2}

We revisit the enduring problem of the 2×2×2 charge density wave (CDW) order in TiSe_{2}, utilizing photon energy-dependent angle-resolved photoemission spectroscopy to probe the full three-dimensional high- and low-temperature electronic structure. Our measurements demonstrate how a mismatch of dimensionality between the 3D conduction bands and the quasi-2D valence bands in this system leads to a hybridization that is strongly k_{z} dependent. While such a momentum-selective coupling can provide the energy gain required to form the CDW, we show how additional "passenger" states remain, which couple only weakly to the CDW and thus dominate the low-energy physics in the ordered phase of TiSe_{2}.

Phonon Collapse and Second-Order Phase Transition in Thermoelectric SnSe

Since 2014 the layered semiconductor SnSe in the high-temperature Cmcm phase is known to be the most efficient intrinsic thermoelectric material. Making use of first-principles calculations we show that its vibrational and thermal transport properties are determined by huge nonperturbative anharmonic effects. We show that the transition from the Cmcm phase to the low-symmetry Pnma is a second-order phase transition driven by the collapse of a zone border phonon, whose frequency vanishes at the transition temperature. Our calculations show that the spectral function of the in-plane vibrational modes are strongly anomalous with shoulders and double-peak structures. We calculate the lattice thermal conductivity obtaining good agreement with experiments only when nonperturbative anharmonic scattering is included. Our results suggest that the good thermoelectric efficiency of SnSe is strongly affected by the nonperturbative anharmonicity.

Reproduction of the Charge Density Wave Phase Diagram in 1T-TiSe_{2} Exposes its Excitonic Character

Recent experiments suggest that excitonic degrees of freedom play an important role in precipitating the charge density wave (CDW) transition in 1T-TiSe_{2}. Through systematic calculations of the electronic and phonon spectrum based on density functional perturbation theory, we show that the predicted critical doping of the CDW phase overshoots the experimental value by 1 order of magnitude. In contrast, an independent self-consistent many-body calculation of the excitonic order parameter and renormalized band structure is able to capture the experimental phase diagram in extremely good qualitative and quantitative agreement. This demonstrates that electron-electron interactions and the excitonic instability arising from direct electron-hole coupling are pivotal to accurately describe the nature of the CDW in this system. This has important implications to understand the emergence of superconductivity within the CDW phase of this and related systems.

Unique Gap Structure and Symmetry of the Charge Density Wave in Single-Layer VSe_{2}

Single layers of transition metal dichalcogenides (TMDCs) are excellent candidates for electronic applications beyond the graphene platform; many of them exhibit novel properties including charge density waves (CDWs) and magnetic ordering. CDWs in these single layers are generally a planar projection of the corresponding bulk CDWs because of the quasi-two-dimensional nature of TMDCs; a different CDW symmetry is unexpected. We report herein the successful creation of pristine single-layer VSe_{2}, which shows a (sqrt[7]×sqrt[3]) CDW in contrast to the (4×4) CDW for the layers in bulk VSe_{2}. Angle-resolved photoemission spectroscopy from the single layer shows a sizable (sqrt[7]×sqrt[3]) CDW gap of ∼100  meV at the zone boundary, a 220 K CDW transition temperature twice the bulk value, and no ferromagnetic exchange splitting as predicted by theory. This robust CDW with an exotic broken symmetry as the ground state is explained via a first-principles analysis. The results illustrate a unique CDW phenomenon in the two-dimensional limit.

The effects of two-dimensional TiSe2 on the thermoelectric, electronic and optical response of Yb14MnSb11/AlSb9Yb11 heterostructures - A theoretical study

Two-dimensional TiSe₂, with Yb₁₄MnSb₁₁ and AlSb₉Yb₁₁ thermoelectric materials, were used to generate heterostructures. The electronic and optical calculations were done using the Materials Studio 2018 modelling software package, employing the Cambridge Serial Total Energy Package code and using the generalised gradient approximation with Perdew-Burke-Ernzerhof exchange-correlation functionals. However, the electronic results obtained revealed a reduction in the calculated band gap and an increase in the slope of the density of state at the Femi level, as well as the energy bands of the generated heterostructures was reported. Partial density of states showed that various orbitals were present in the thermoelectric materials. The thermal transport and electronic properties are compared using the Boltzmann transport theory and Mott derived equations, which were expressed in the maximum attainable figure of merit. A variation in the electric potential of the layers is observed. The dielectric function is found to decrease in both thermoelectric layers generated and far more than the Yb₁₄MnSb₁₁-TiSe₂ layer, which was more negative. The reduction in reflectivity of AlSb₉Yb₁₁TiSe₂ layer and elevation of the Yb₁₄MnSb₁₁-TiSe₂ layer is observed. Upon forming heterostructures with TiSe₂, the conductivity reduced in the high frequency, due to the generated complex multicomponent compounds.

van der Waals Metallic Transition Metal Dichalcogenides

Transition metal dichalcogenides are layered materials which are composed of transition metals and chalcogens of the group VIA in a 1:2 ratio. These layered materials have been extensively investigated over synthesis and optical and electrical properties for several decades. It can be insulators, semiconductors, or metals revealing all types of condensed matter properties from a magnetic lattice distorted to superconducting characteristics. Some of these also feature the topological manner. Instead of covering the semiconducting properties of transition metal dichalcogenides, which have been extensively revisited and reviewed elsewhere, here we present the structures of metallic transition metal dichalcogenides and their synthetic approaches for not only high-quality wafer-scale samples using conventional methods (e.g., chemical vapor transport, chemical vapor deposition) but also local small areas by a modification of the materials using Li intercalation, electron beam irradiation, light illumination, pressures, and strains. Some representative band structures of metallic transition metal dichalcogenides and their strong layer-dependence are reviewed and updated, both in theoretical calculations and experiments. In addition, we discuss the physical properties of metallic transition metal dichalcogenides such as periodic lattice distortion, magnetoresistance, superconductivity, topological insulator, and Weyl semimetal. Approaches to overcome current challenges related to these materials are also proposed.

Hidden Order and Dimensional Crossover of the Charge Density Waves in TiSe2

Charge density wave (CDW) formation, a key physics issue for materials, arises from interactions among electrons and phonons that can also lead to superconductivity and other competing or entangled phases. The prototypical system TiSe₂, with a particularly simple (2 × 2 × 2) transition and no Kohn anomalies caused by electron-phonon coupling, is a fascinating but unsolved case after decades of research. Our angle-resolved photoemission measurements of the band structure as a function of temperature, aided by first-principles calculations, reveal a hitherto undetected but crucial feature: a (2 × 2) electronic order in each layer sets in at ~232 K before the widely recognized three-dimensional structural order at ~205 K. The dimensional crossover, likely a generic feature of such layered materials, involves renormalization of different band gaps in two stages.

Dimensional Effects on the Charge Density Waves in Ultrathin Films of TiSe2

Charge density wave (CDW) formation in solids is a critical phenomenon involving the collective reorganization of the electrons and atoms in the system into a wave structure, and it is expected to be sensitive to the geometric constraint of the system at the nanoscale. Here, we study the CDW transition in TiSe₂, a quasi-two-dimensional layered material, to determine the effects of quantum confinement and changing dimensions in films ranging from a single layer to multilayers. Of key interest is the characteristic length scale for the transformation from a two-dimensional case to the three-dimensional limit. Angle-resolved photoemission spectroscopy (ARPES) measurements of films with thicknesses up to six layers reveal substantial variations in the energy structure of discrete quantum well states; however, the temperature-dependent band gap renormalization converges at just three layers. The results indicate a layer-dependent mixture of two transition temperatures and a very-short-range CDW interaction within a three-dimensional framework.

Charge density wave transition in single-layer titanium diselenide

A single molecular layer of titanium diselenide (TiSe₂) is a promising material for advanced electronics beyond graphene—a strong focus of current research. Such molecular layers are at the quantum limit of device miniaturization and can show enhanced electronic effects not realizable in thick films. We show that single-layer TiSe₂ exhibits a charge density wave (CDW) transition at critical temperature T_C=232±5 K, which is higher than the bulk T_C=200±5 K. Angle-resolved photoemission spectroscopy measurements reveal a small absolute bandgap at room temperature, which grows wider with decreasing temperature T below T_C in conjunction with the emergence of (2 × 2) ordering. The results are rationalized in terms of first-principles calculations, symmetry breaking and phonon entropy effects. The observed Bardeen-Cooper-Schrieffer (BCS) behaviour of the gap implies a mean-field CDW order in the single layer and an anisotropic CDW order in the bulk.

Single molecular layers of TiSe₂ are promising for advanced electronic applications, and it is therefore important to characterize their phases. Here, the authors use ARPES to detect a charge density wave transition without Fermi surface nesting and that takes place at a temperature higher than in bulk.

Impact of electron-hole correlations on the 1T-TiSe_{2} electronic structure

Several experiments have been performed on 1T-TiSe_{2} in order to identify whether the electronic structure is semimetallic or semiconducting without reaching a consensus. In this Letter, we theoretically study the impact of electron-hole and electron-phonon correlations on the bare semimetallic and semiconducting electronic structure. The resulting electron spectral functions provide a direct comparison of both cases and demonstrate that 1T-TiSe_{2} is of predominant semiconducting character with some spectral weight crossing the Fermi level.

Thermal diffuse scattering as a probe of large-wave-vector phonons in silicon nanostructures

Large-wave-vector phonons have an important role in determining the thermal and electronic properties of nanoscale materials. The small volumes of such structures, however, have posed significant challenges to experimental studies of the phonon dispersion. We show that synchrotron x-ray thermal diffuse scattering can be adapted to probe phonons with wave vectors spanning the entire Brillouin zone of nanoscale silicon membranes. The thermal diffuse scattering signal from flat Si nanomembranes with thicknesses from 315 to 6 nm, and a sample volume as small as 5 μm(3), has the expected linear dependence on the membrane thickness and also exhibits excess intensity at large wave vectors, consistent with the scattering signature expected from low-lying large-wave-vector modes of the membranes.

Electron-phonon coupling and the soft phonon mode in TiSe2

We report high-resolution inelastic x-ray measurements of the soft phonon mode in the charge-density-wave compound TiSe(2). We observe a complete softening of a transverse optic phonon at the L point, i.e., q=(0.5, 0, 0.5), at T≈T(CDW). Detailed ab initio calculations for the electronic and lattice dynamical properties of TiSe(2) are in quantitative agreement with experimental frequencies for the soft phonon mode. The observed broad range of renormalized phonon frequencies, (0.3, 0, 0.5)≤q≤(0.5, 0, 0.5), is directly related to a broad peak in the electronic susceptibility stabilizing the charge-density-wave ordered state. Our analysis demonstrates that a conventional electron-phonon coupling mechanism can explain a structural instability and the charge-density-wave order in TiSe(2) although other mechanisms might further boost the transition temperature.

On the origin of charge-density waves in select layered transition-metal dichalcogenides

The occurrence of charge-density waves in three selected layered transition-metal dichalcogenides-1T-TaS(2), 2H-TaSe(2) and 1T-TiSe(2)-is discussed from an experimentalist's point of view with a particular focus on the implications of recent angle-resolved photoelectron spectroscopy results. The basic models behind charge-density-wave formation in low-dimensional solids are recapitulated, the experimental and theoretical results for the three selected compounds are reviewed, and their band structures and spectral weight distributions in the commensurate charge-density-wave phases are calculated using an empirical tight-binding model. It is explored whether the origin of charge-density waves in the layered transition-metal dichalcogenides can be understood in a unified way on the basis of a few measured and calculated parameters characterizing the interacting electron-lattice system. It is found that the predictions of the standard mean-field model agree only semi-quantitatively with the experimental data and that there is not one generally dominant factor driving charge-density-wave formation in this family of layer compounds. The need for further experimental and theoretical scrutiny is emphasized.

Charge-density wave and superconducting dome in TiSe2 from electron-phonon interaction

At low temperature TiSe2 undergoes a charge-density wave instability. Superconductivity is stabilized either by pressure or by Cu intercalation. We show that the pressure phase diagram of TiSe2 is well described by first-principles calculations. At pressures smaller than 4 GPa charge-density wave ordering occurs, in agreement with experiments. At larger pressures the disappearing of the charge-density wave is due to a stiffening of the short-range force constants and not to the variation of nesting with pressure. Finally, we show that the behavior of T(c) as a function of pressure is entirely determined by the electron-phonon interaction without need of invoking excitonic mechanisms. Our work demonstrates that phase diagrams with competing orders and a superconducting dome are also obtained in the framework of the electron-phonon interaction.

Exciton condensation driving the periodic lattice distortion of 1T-TiSe2

We address the lattice deformation of 1T-TiSe2 within the exciton condensate phase. We show that, at low temperature, condensed excitons influence the lattice through electron-phonon interaction. It is found that at zero temperature, in the exciton condensate phase of 1T-TiSe2, this exciton condensate exerts a force on the lattice generating ionic displacements comparable in amplitude to what is measured in experiment. This is thus the first quantitative estimation of the amplitude of the periodic lattice distortion observed in 1T-TiSe2 as a consequence of the exciton condensate phase.

Magnetic-field- and pressure-induced quantum phases in complex materials

This Progress Report presents temperature-, magnetic-field-, and pressure-dependent Raman measurements of strongly correlated materials such as the charge-ordering manganese perovskites, the multiferroic material TbMnO(3), and the charge-density wave (CDW) materials 1T-TiSe(2) and Cu(x)TiSe(2). These studies illustrate the rich array of phases and properties that can be accessed with field and pressure tuning in these materials, and demonstrate the efficacy of using magnetic-field- and pressure-dependent scattering methods to elucidate the microscopic changes associated with highly tunable behavior in complex materials.

Pressure induced superconductivity in pristine 1T-TiSe2

The interplay between superconductivity and the charge-density wave (CDW) state in pure 1T-TiSe(2) is examined through a high-pressure study extending up to pressures of 10 GPa between sub-Kelvin and room temperatures. At a critical pressure of 2 GPa a superconducting phase sets in and persists up to pressures of 4 GPa. The maximum superconducting transition temperature is 1.8 K. These findings complement the recent discovery of superconductivity in copper-intercalated 1T-TiSe(2). The comparisons of the normal state and superconducting properties of the two systems reveal the possibility that the emergent electronic state qualitatively depends on the manner in which the CDW state is destabilized, making this a unique example where two different superconducting domes are obtained by two different methods from the same parent compound.

Determination of phonon dispersion relations by X-ray thermal diffuse scattering

Thermal diffuse scattering (TDS) of X-rays from crystals contains information on phonons. This paper reviews the general theory of TDS and some recent experiments aimed at further developing TDS into a useful and efficient method for studying phonon dispersion relations.

3D imaging of the Fermi surface by thermal diffuse scattering

We use thermal diffuse scattering of x rays to visualize the lens-shaped portions of the Fermi surface in metallic zinc. Our interpretation of the nature of the observed scattered intensity anomalies is supported by the incorporation of inelastic x-ray scattering measurements as well as ab initio calculations of the electronic structure and lattice dynamics. Our work demonstrates that thermal diffuse scattering complements well-established techniques and is a powerful tool in its own right for studying the shape of the Fermi surface through the associated electron-phonon coupling.

Quantum and classical mode softening near the charge-density-wave-superconductor transition of CuxTiSe2

Temperature- and x-dependent Raman scattering studies of the charge-density-wave (CDW) amplitude modes in Cu(x)TiSe(2) show that the amplitude mode frequency omega(0) exhibits identical power-law scaling with the reduced temperature T/T(CDW) and the reduced Cu content x/x(c), i.e., omega(0) approximately (1-p)(0.15) for p=T/T(CDW) or x/x(c), suggesting that mode softening is independent of the control parameter used to approach the CDW transition. We provide evidence that x-dependent mode softening in Cu(x)TiSe(2) is associated with the reduction of the electron-phonon coupling constant, and that x-dependent "quantum" (T approximately 0) mode softening suggests the presence of a quantum critical point within the superconductor phase of Cu(x)TiSe(2).

Anomalous Metallic State of Cu0.07TiSe2: an optical spectroscopy study

We report an optical spectroscopy study on the newly discovered superconductor Cu0.07TiSe2. Consistent with the development from a semimetal or semiconductor with a very small indirect energy gap upon doping TiSe2, it is found that the compound has a low carrier density. Most remarkably, the study reveals a substantial shift of the screened plasma edge in reflectance towards high energy with decreasing temperature. This phenomenon, rarely seen in metals, indicates either a sizable increase of the conducting carrier concentration or/and a decrease of the effective mass of carriers with reducing temperature. We attribute the shift primarily to the latter effect.

Evidence for an excitonic insulator phase in 1T-TiSe2

We present a new high-resolution angle-resolved photoemission study of 1T-TiSe2 in both its room-temperature, normal phase and its low-temperature, charge-density wave phase. At low temperature the photoemission spectra are strongly modified, with large band renormalizations at high-symmetry points of the Brillouin zone and a very large transfer of spectral weight to backfolded bands. A calculation of the theoretical spectral function for an excitonic insulator phase reproduces the experimental features with very good agreement. This gives strong evidence in favor of the excitonic insulator scenario as a driving force for the charge-density wave transition in 1T-TiSe2.

Emergence of Fermi pockets in a new excitonic charge-density-wave melted superconductor

A superconducting state (T(c) approximately 4.2 K) has very recently been observed upon successful doping of the charge-density-wave (CDW) ordered triangular lattice TiSe(2), with copper. Using state-of-the-art photoemission spectroscopy we identify, for the first time, momentum-space locations of doped electrons that form the Fermi sea of the superconductor. With doping, we find that kinematic nesting volume increases, whereas coherence of the CDW collective order sharply drops. In superconducting doping, as chemical potential rises, we observe the emergence of a large density of states in the form of a narrow electron pocket near the L point of the Brillouin zone with d-like character. The k-space spectral evolution directly demonstrates, for the first time, that the CDW order parameter microscopically competes with superconductivity in the same band.

Dynamic fluctuations and static speckle in critical X-ray scattering from SrTiO3

We report a study of critical x-ray scattering from SrTiO3 near the antiferrodistortive structural phase transition at T(C) approximately 105 K. A line shape analysis of the thermal diffuse scattering results in the most precise experimental determination to date of the critical exponent gamma. The microscopic mechanism behind the anomalous "central peak" critical scattering component is clarified here by the first-ever observation of a static coherent diffraction pattern (speckle pattern) within the anomalous critical scattering of SrTiO3. This observation allows us to directly attribute the origins of the central peak to Bragg diffraction from remnant static disorder above T(C).

Electron-hole coupling and the charge density wave transition in TiSe2

Angle-resolved photoemission is employed to measure the band structure of TiSe2 in order to clarify the nature of the ( 2 x 2 x 2) charge density wave transition. The results show a very small indirect gap in the normal phase transforming into a larger indirect gap at a different location in the Brillouin zone. Fermi surface topology is irrelevant in this case. Instead, electron-hole coupling together with a novel indirect Jahn-Teller effect drives the transition.