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Carrier Mobility Modulation in Cu 2 Se Composites Using Coherent Cu 4 TiSe 4 Inclusions Leads to Enhanced Thermoelectric Performance
Carrier transport engineering in bulk semiconductors using inclusion phases often results in the deterioration of carrier mobility (μ) owing to enhanced carrier scattering at phase boundaries. Here, we show by leveraging the temperature-induced structural transition between the α-Cu 2 Se and β-Cu 2 Se polymorphs that the incorporation of Cu 4 TiSe 4 inclusions within the Cu 2 Se matrix results in a gradual large drop in the carrier mobility at temperatures below 400 K (α-Cu 2 Se), whereas the carrier mobility remains unchanged at higher temperatures, where the β-Cu 2 Se polymorph dominates. The sharp discrepancy in the electronic transport within the α-Cu 2 Se and β-Cu 2 Se matrices is associated with the formation of incoherent α-Cu 2 Se/Cu 4 TiSe 4 interfaces, owing to the difference in their atomic structures and lattice parameters, which results in enhanced carrier scattering. In contrast, the similarity of the Se sublattices between β-Cu 2 Se and Cu 4 TiSe 4 gives rise to coherent phase boundaries and good band alignment, which promote carrier transport across the interfaces. Interestingly, the different cation arrangements in Cu 4 TiSe 4 and β-Cu 2 Se contribute to enhanced phonon scattering at the interfaces, which leads to a reduction in the lattice thermal conductivity. The large reduction in the total thermal conductivity while preserving the high power factor of β-Cu 2 Se in the (1–x)Cu 2 Se/(x)Cu 4 TiSe 4 composites results in an improved ZT of 1.2 at 850 K, with an average ZT of 0.84 (500–850 K) for the composite with x = 0.01. Furthermore, this work highlights the importance of structural similarity between the matrix and inclusions when designing thermoelectric materials with improved energy conversion efficiency.
Intercalation induced quasi-freestanding layer in TiSe 2
Angle-resolved photoemission spectroscopy is employed to study the electronic structure of bulk TiSe 2 before and after doping with potassium impurities. A splitting in the conduction band into two branches is observed after room-temperature deposition. The splitting energy increases to approximately 130 meV when the sample is cooled to 40 K. One branch exhibits a nondispersive two-dimensional feature, while the other shows the characteristics of three-dimensional bulk band dispersion. Core-level spectroscopy suggests that the K impurities predominantly occupy the intercalated sites within the van der Waals gap. Furthermore, the results indicate the formation of a quasi-freestanding TiSe 2 layer. Additionally, doping completely suppresses the periodic lattice distortion in the surface region. These findings are further supported by density functional theory calculations, which compare the band structure of monolayer and bulk TiSe 2 with experimental data. Thus, the dimensional and intrinsic electronic properties of 1𝑇−TiSe 2 can be controlled through the intercalation procedure used in this work.
Two-step charge density wave transition and hidden transient phase in 1 T – TiSe 2
Using variable temperature atomic pair distribution function analysis, we study the emergence of charge density wave (CDW) order in 1T-TiSe 2 and find that it takes place via a two-step transition. First, upon decreasing temperature to about 235(3) K, CDW related lattice distortions emerge in the individual TiSe 2 layers alone. Then, upon further decreasing the temperature, the two-dimensional distortions in the layers couple and the widely recognized three-dimensional 2a o x 2a o x 2c o superstructure emerges at about 205(3) K. Because two different band gaps are known to emerge at the same temperatures, the finding indicates the presence of strong electron-phonon coupling. The transient phase between the two steps lacks inversion symmetry and may serve as a precursor of the debated chiral 1T-TiSe 2 phase. Finally, our findings are important for the understanding of the enigmatic CDW transition in 1T-TiSe 2 and CDW instabilities in van der Waals materials in general.
TiSe 2 is a band insulator created by lattice fluctuations, not an excitonic insulator
TiSe 2 is a narrow-gap insulator with a rich array of unique properties. In addition to being a superconductor under certain modifications, it is commonly thought to be a rare realisation of an excitonic insulator. Below 200 K, TiSe 2 undergoes a transition from a high-symmetry ($P\bar{3}m1$) phase to a low-symmetry ($P\bar{3}c1$) charge density wave (CDW). Here we establish that it is indeed an insulator in both $P\bar{3}m1$ and $P\bar{3}c1$ phases. However, the insulating state is driven not by excitonic effects but by symmetry-breaking. In the CDW phase it is static. At high temperature, thermally driven instantaneous deviations from $P\bar{3}m1$ break the symmetry on the characteristic time scale of a phonon. Even though the time-averaged lattice structure assumes $P\bar{3}m1$ symmetry, the time-averaged energy band structure is closer to the CDW phase - a rare instance of a metal-insulator transition induced by dynamical symmetry breaking. We establish these conclusions from quasiparticle self-consistent GW (QSGW) and many-body calculations (QS$G\widehat{W}$), in combination with molecular dynamics simulations to capture the effects of thermal disorder. The many-body theory includes explicitly ladder diagrams in the polarizability, which incorporates excitonic effects in an ab initio manner. We find that the excitonic modification to the potential is weak, ruling out the possibility that TiSe 2 is an excitonic insulator.
Orbital selective band re-normalization induced Lifshitz transition in TiSe 2
A Lifshitz transition is a sudden change in Fermi surface topology, often linked to quantum phenomena, with major impact on transport and sometimes superconductivity. Here we demonstrate a Lifshitz transition in TiSe 2 using micro–angle-resolved photoemission spectroscopy. At low temperatures an electron pocket appears at the Brillouin-zone center, whereas at higher temperatures spectral weight from a hole-like valence band dominates the Fermi level. Unlike previously reported cases typically driven by rigid band shifts, in TiSe 2 an orbital-selective strong band renormalization induces the crossover near 160 K. This mechanism naturally explains the longstanding resistivity anomaly of TiSe 2 , which peaks around 160 K. Our results clarify its puzzling transport behavior and open avenues to investigate how periodic lattice distortions interact with strong electronic correlations.
Charge density wave activated excitons in TiSe 2 –MoSe 2 heterostructures
Layered materials enable the assembly of a new class of heterostructures where lattice-matching is no longer a requirement. Interfaces in these heterostructures therefore become a fertile ground for unexplored physics as dissimilar phenomena can be coupled via proximity effects. In this article, we identify an unexpected photoluminescence (PL) peak when MoSe 2 interacts with TiSe 2 . A series of temperature-dependent and spatially resolved PL measurements reveal that this peak is unique to the TiSe 2 –MoSe 2 interface, is higher in energy compared to the neutral exciton, and exhibits exciton-like characteristics. The feature disappears at the TiSe 2 charge density wave transition, suggesting that the density wave plays an important role in the formation of this new exciton. We present several plausible scenarios regarding the origin of this peak that individually capture some aspects of our observations but cannot fully explain this feature. These results therefore represent a fresh challenge for the theoretical community and provide a fascinating way to engineer excitons through interactions with charge density waves.
Materials Data on TiSe by Materials Project
TiSe is lead oxide structured and crystallizes in the tetragonal P4/nmm space group. The structure is two-dimensional and consists of one TiSe sheet oriented in the (0, 0, 1) direction. Ti2+ is bonded to four equivalent Se2- atoms to form a mixture of edge and corner-sharing TiSe4 tetrahedra. All Ti–Se bond lengths are 2.53 Å. Se2- is bonded in a 4-coordinate geometry to four equivalent Ti2+ atoms.
Efficient simulations of charge density waves in the transition metal Dichalcogenide TiSe 2
Charge density waves (CDWs) in transition metal dichalcogenides are the subject of growing scientific interest due to their rich interplay with exotic phases of matter and their potential technological applications. Here, using density functional theory with advanced meta-generalized gradient approximations (meta-GGAs) and linear response time-dependent density functional theory (TDDFT) with state-of-the-art exchange-correlation kernels, we investigate the electronic, vibrational, and optical properties in 1T-TiSe 2 with and without CDW. In both bulk and monolayer TiSe 2 , the electronic bands and phonon dispersions in either normal or CDW (semiconducting) phase are described well via meta-GGAs, which separate the valence and conduction bands just as HSE06 does but with significantly more computational feasibility. The experimentally observed humps of electron energy loss spectroscopy are successfully reproduced in TDDFT. Our work opens the door to simulating these complexities in CDW compounds from first principles by revealing meta-GGAs as an accurate low-cost alternative to HSE06.
Aspects of symmetry and topology in the charge density wave phase of 1T–TiSe 2
Abstract The charge density wave (CDW) in 1 T –TiSe 2 harbors a nontrivial symmetry configuration. It is important to understand this underlying symmetry both for gaining a handle on the mechanism of CDW formation and for probing the CDW experimentally. Here, based on first-principles computations within the framework of the density functional theory, we unravel the connection between the symmetries of the normal and CDW states and the electronic structure of 1 T –TiSe 2 . Our analysis highlights the key role of irreducible representations of the electronic states and the occurrence of band gaps in the system in driving the CDW. By showing how symmetry-related topology can be obtained directly from the electronic structure, our study provides a practical pathway in search of topological CDW insulators.
Evidence for pseudo–Jahn-Teller distortions in the charge density wave phase of 1$\textit{T}-\text{TiSe}_2$
Here, the charge density wave (CDW) instability in 1$\textit{T}-\text{TiSe}_2$ is revisited to investigate its electronic and structural origins using angle resolved photoemission spectroscopy (ARPES), neutron diffraction, and density functional theory (DFT) calculations. The evidence for Jahn-Teller (JT)-like distortions in the CDW state is provided from the local structure analysis that shows splitting of the Ti-Se bonds into short and long. The magnitude of the split is inconsistent with the commonly accepted Di Salvo model for the structural distortions in the CDW phase. From the APRES data, it is deduced that a nontrivial temperature-dependent energy shift of the Se $4\textit{p}$ valence bands occurs, but is absent for the Ti $3\textit{d}$ conduction bands. Collectively, these observations suggest that a JT-like mechanism is most likely central to the CDW instability in 1$\textit{T}-\text{TiSe}_2$.
Gapless surface electronic structure of $1T–$$\mathrm{TiSe_2}$ in the distorted phase
Here, low temperature, high resolution angle resolved photoemission experiments performed on bulk $1T–$$\mathrm{TiSe_2}$ samples display conspicuous band folding as the only prominent signature of the periodic lattice distortion. The presence of a bulk electronic gap supporting a charge density wave phase is not confirmed in light of the new data. These observations cast serious doubts on the common belief of an electronic instability as the likely origin for the observed structural transition in $\mathrm{TiSe_2}$.
Ultrafast creation of a light-induced semimetallic state in strongly excited 1T-TiSe 2
Screening, a ubiquitous phenomenon associated with the shielding of electric fields by surrounding charges, has been widely adopted as a means to modify a material’s properties. While most studies have relied on static changes of screening through doping or gating thus far, here we demonstrate that screening can also drive the onset of distinct quantum states on the ultrafast timescale. By using time- and angle-resolved photoemission spectroscopy, we show that intense optical excitation can drive 1T-TiSe 2 , a prototypical charge density wave material, almost instantly from a gapped into a semimetallic state. By systematically comparing changes in band structure over time and excitation strength with theoretical calculations, we find that the appearance of this state is likely caused by a dramatic reduction of the screening length. In summary, this work showcases how optical excitation enables the screening-driven design of a nonequilibrium semimetallic phase in TiSe 2 , possibly providing a general pathway into highly screened phases in other strongly correlated materials.
Materials Data on TiSe by Materials Project
TiSe is Tungsten Carbide-like structured and crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. Ti2+ is bonded to six equivalent Se2- atoms to form a mixture of distorted corner and edge-sharing TiSe6 pentagonal pyramids. All Ti–Se bond lengths are 2.64 Å. Se2- is bonded to six equivalent Ti2+ atoms to form a mixture of corner, edge, and face-sharing SeTi6 octahedra. The corner-sharing octahedral tilt angles are 44°.
Materials Data on TiSe by Materials Project
TiSe is Tungsten Carbide-like structured and crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. Ti2+ is bonded to six equivalent Se2- atoms to form a mixture of corner, edge, and face-sharing TiSe6 octahedra. The corner-sharing octahedral tilt angles are 44°. All Ti–Se bond lengths are 2.61 Å. Se2- is bonded to six equivalent Ti2+ atoms to form a mixture of distorted corner and edge-sharing SeTi6 pentagonal pyramids.
Materials Data on TiSe by Materials Project
TiSe is Modderite structured and crystallizes in the orthorhombic Pnma space group. The structure is three-dimensional. Ti2+ is bonded to six equivalent Se2- atoms to form a mixture of distorted face, edge, and corner-sharing TiSe6 octahedra. The corner-sharing octahedra tilt angles range from 41–55°. There are a spread of Ti–Se bond distances ranging from 2.55–2.77 Å. Se2- is bonded in a 6-coordinate geometry to six equivalent Ti2+ atoms.
In-Plane Anisotropy of Charge Density Wave Fluctuations in 1𝑇−TiSe 2
We report measurements of anisotropic triple-𝑞 charge density wave (CDW) fluctuations in the transition metal dichalcogenide 1𝑇−TiSe 2 over a large volume of reciprocal space with x-ray diffuse scattering. Above the transition temperature, 𝑇 CDW , the in-plane diffuse scattering is marked by ellipses which reveal that the in-plane fluctuations are anisotropic. In addition, the out-of-plane diffuse scattering is characterized by rodlike structures which indicate that the CDW fluctuations in neighboring layers are largely decoupled. Furthermore, our analysis of the diffuse scattering line shapes and orientations suggests that the three charge density wave components contain independent phase fluctuations with a hierarchy of length scales, leading to intricate fluctuation patterns that go beyond the conventional 2D-to-3D crossover picture.
Emergent surface resonance from charge density wave symmetry breaking in TiSe 2
Surface confined electronic states provide a fertile ground for discovering emergent phenomena that have no counterpart in the bulk, offering new routes to manipulate correlations, symmetry breaking, and dimensionality at the atomic scale. Here, in this study, we show that charge density wave (CDW) symmetry breaking can yield surface states in 1T−TiSe 2 . Micro–angle-resolved photoemission spectroscopy (µ-ARPES) resolves a sharp, two-dimensional surface resonant state (SRS) that emerges within the CDW reconstructed low energy spectrum. The SRS exhibits notable temperature dependence and its spectral weight collapses around ∼ 160 K, while CDW transition temperature 𝑇 CDW is commonly reported as ≈ 202 K. Slab DFT + 𝑈 calculations reproduce a surface localized resonance when CDW folding brings valence and conduction states into near degeneracy, suggesting a correlation tuned, surface selective origin. These results point to a form of correlation-tuned surface resonance in a layered CDW compound and suggest a framework for engineering low-dimensional quantum states in van der Waals materials via symmetry breaking and electronic structure tuning.