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Register a new userTheory of the thickness dependence of the charge density wave transition in 1T-TiTe$_2$
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Most metallic transition metal dichalcogenides undergo charge density wave (CDW) instabilities with similar or identical ordering vectors in bulk and in single layer, albeit with different critical temperatures. Metallic 1T-TiTe$_2$ is a remarkable exception as it shows no evidence of charge density wave formation in bulk, but it displays a stable $2times2$ reconstruction in single-layer form. The mechanism for this 3D-2D crossover of the transition is still unclear, although strain from the substrate and the exchange interaction have been pointed out as possible formation mechanisms. Here, by performing non-perturbative anharmonic calculations with gradient corrected and hybrid functionals, we explain the thickness behaviour of the transition in 1T-TiTe$_2$. We demonstrate that the occurrence of the CDW in single-layer TiTe$_2$ occurs from the interplay of non-perturbative anharmonicity and an exchange enhancement of the electron-phonon interaction, larger in the single layer than in the bulk. Finally, we study the electronic and structural properties of the single-layer CDW phase and provide a complete description of its electronic structure, phonon dispersion as well as infrared and Raman active phonon modes.
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In Ti-intercalated self-doped $1T$-TiSe$_2$ crystals, the charge density wave (CDW) superstructure induces two nonequivalent sites for Ti dopants. Recently, it has been shown that increasing Ti doping dramatically influences the CDW by breaking it into phase-shifted domains. Here, we report scanning tunneling microscopy and spectroscopy experiments that reveal a dopant-site dependence of the CDW gap. Supported by density functional theory, we demonstrate that the loss of the longrange phase coherence introduces an imbalance in the intercalated-Ti site distribution and restrains the CDW gap closure. This local resilient behavior of the $1T$-TiSe$_2$ CDW reveals a novel mechanism between CDW and defects in mutual influence.
In this study, using low-temperature scanning tunneling microscopy (STM), we focus on understanding the native defects in pristine textit{1T}-TiSe$_2$ at the atomic scale. We probe how they perturb the charge density waves (CDWs) and lead to local domain formation. These defects influence the correlation length of CDWs. We establish a connection between suppression of CDWs, Ti intercalation, and show how this supports the exciton condensation model of CDW formation in textit{1T}-TiSe$_2$.
We study the impact of Cu intercalation on the charge density wave (CDW) in 1T-Cu$_{text{x}}$TiSe$_{text{2}}$ by scanning tunneling microscopy and spectroscopy. Cu atoms, identified through density functional theory modeling, are found to intercalate randomly on the octahedral site in the van der Waals gap and to dope delocalized electrons near the Fermi level. While the CDW modulation period does not depend on Cu content, we observe the formation of charge stripe domains at low Cu content (x$<$0.02) and a breaking up of the commensurate order into 2$times$2 domains at higher Cu content. The latter shrink with increasing Cu concentration and tend to be phase-shifted. These findings invalidate a proposed excitonic pairing as the primary CDW formation mechanism in this material.
We report a rectangular charge density wave (CDW) phase in strained 1T-VSe$_2$ thin films synthesized by molecular beam epitaxy on c-sapphire substrates. The observed CDW structure exhibits an unconventional rectangular 4a{times}{sqrt{3a}} periodicity, as opposed to the previously reported hexagonal $4atimes4a$ structure in bulk crystals and exfoliated thin layered samples. Tunneling spectroscopy shows a strong modulation of the local density of states of the same $4atimessqrt{3}a$ CDW periodicity and an energy gap of $2Delta_{CDW}=(9.1pm0.1)$ meV. The CDW energy gap evolves into a full gap at temperatures below 500 mK, indicating a transition to an insulating phase at ultra-low temperatures. First-principles calculations confirm the stability of both $4atimes4a$ and $4atimessqrt{3}a$ structures arising from soft modes in the phonon dispersion. The unconventional structure becomes preferred in the presence of strain, in agreement with experimental findings.
The momentum-dependent orbital character in crystalline solids, referred to as orbital texture, is of capital importance in the emergence of symmetry-broken collective phases such as charge density waves as well as superconducting and topological states of matter. By performing extreme ultraviolet multidimensional angle-resolved photoemission spectroscopy for two different crystal orientations linked to each other by mirror symmetry, we isolate and identify the role of orbital texture in photoemission from the transition metal dichalcogenide 1T-TiTe$_2$. By comparing our experimental results with theoretical calculations based on both a quantitative one-step model of photoemission and an intuitive tight-binding model, we unambiguously demonstrate the link between the momentum-dependent orbital orientation and the emergence of strong intrinsic linear dichroism in the photoelectron angular distributions. Our results represent an important step towards going beyond band structure (eigenvalues) mapping and learn about electronic wavefunction and orbital texture of solids by exploiting matrix element effects in photoemission spectroscopy.
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