On the basis of first-principles DFT calculations the wave-vector and temperature dependencies of the Lindhard response function of the blue bronze K 0.3 MoO 3 have been calculated. The k I F + k II F interband component of the response, which is responsible for the Peierls instability, has been quantitatively analyzed. It is found that (i) the electron-hole coherence length of this response determines the length scale of the experimental intrachain CDW correlations, and (ii) the intrachain q dependence of such a response also determines the shape of the Kohn anomaly experimentally measured. These findings provide compelling evidence that the Peierls transition of the blue bronze K 0.3 MoO 3 follows the weak electron-phonon coupling scenario in the adiabatic approximation, something that had not yet been proved on the basis of first-principles calculations for a real material. It is proposed that the CDW interchain coupling occurs through a Coulomb coupling between dipolar CDWs. The nature of the phonon mode leading to the dipolar nature of the CDWs is also discussed, and the relevance of these results to rationalize the CDW instabilities in other oxides and bronzes is pointed out. These findings are also contrasted with recent results for other CDW materials like chalcogenides and tellurides.

We report the first-principles DFT calculation of the electron-hole Lindhard response function of the (TMTSF) 2 PF 6 Bechgaard salt using the real triclinic low-temperature structure. The Lindhard response is found to change considerably with temperature. Near the 2k F spin density wave (SDW) instability it has the shape of a broad triangular plateau as a result of the multiple nesting associated with the warped quasi-one-dimensional Fermi surface. The evolution of the 2k F broad maximum as well as the effect of pressure and deuteration is calculated and analyzed. The thermal dependence of the electron-hole coherence length deduced from these calculations compares very well with the experimental thermal evolution of the 2k F Bond Order Wave correlation length. The existence of a triangular plateau of maxima in the low-temperature electron-hole Lindhard response of (TMTSF) 2 PF 6 should favor a substantial mixing of q-dependent fluctuations which can have important consequences in understanding the phase diagram of the 2k F SDW ground state, the mechanism of superconductivity and the magneto-transport of this paradigmatic quasi-one-dimensional material. The first-principles DFT Lindhard response provides a very accurate and unbiased approach to the low-temperature instabilities of (TMTSF) 2 PF 6 which can take into account in a simple way 3D effects and subtle structural variations, thus providing a very valuable tool in understanding the remarkable physics of molecular conductors.

Bulk and single-layer 2H-NbSe 2 exhibit identical charge density wave order (CDW) with a quasi-commensurate 3×3 superlattice periodicity. Here we combine scanning tunnelling microscopy (STM) imaging at T = 1 K of 2H-NbSe 2 with firstprinciples density functional theory (DFT) calculations to investigate the structural atomic rearrangement of this CDW phase. Our calculations for single-layers reveal that six different atomic structures are compatible with the 3×3 CDW distortion, although all of them lie on a very narrow energy range of at most 3 meV per formula unit, suggesting the coexistence of such structures. Our atomically resolved STM images of bulk 2H-NbSe 2 unambiguously confirm this by identifying two of these structures. Remarkably, these structures differ from the X-ray crystal structure reported for the bulk 3×3 CDW which, in fact, is also one of the six DFT structures located for the single-layer. Our calculations also show that due to the minute energy difference between the different phases, the ground state of the 3×3 CDW could be extremely sensitive to doping, external strain or internal pressure within the crystal. The presence of multi-phase CDW order in 2H-NbSe 2 may provide further understanding of its low temperature state and the competition between different instabilities.

We present a Density Functional Theory study of the electronic structure of single-layer TiSe 2 , and focus on the Charge Density Wave (CDW) instability present on this 2D material. We explain the 2 × 2 periodicity of the CDW from the phonon band structure of the undistorted crystal, which is unstable under one of the phonon modes at the M point. This can be understood in terms of a partial band gap opening at the Fermi level, which we describe on the basis of the symmetry of the involved crystal orbitals, leading to an energy gain upon the displacement of the atoms following the phonon mode in a 2×1 structure. Furthermore, the combination of the corresponding phonons for the three inequivalent M points of the Brillouin zone leads to the 2×2 distortion characteristic of the CDW state. This leads to a further opening of a full gap, which reduces the energy of the 2×2 structure compared to the 2×1 one of a single M point phonon, and makes the CDW structure the most stable one. We also analyze the effect of charge injection into the layer on the structural instability. We predict that the 2×2 structure only survives for a certain range of doping levels, both for electrons and for holes, as doping reduces the energy gain due to the gap opening. We predict the transition from the commensurate 2×2 distortion to an incommensurate one with increasing wavelength upon increasing the doping level, followed by the appearance of the undistorted 1×1 structure for larger carrier concentrations.

A density functional theory study concerning the origin of the recently reported 2×2 charge density wave (CDW) instability in single-layer TiTe 2 is reported. It is shown that, whereas calculations employing the semi-local functional PBE favor the undistorted structure, the hybrid functional HSE06 correctly predicts the 2×2 distortion,. The study suggests that the magnitude of the semi-metallic overlap between the valence band top at Γ and the conduction band bottom at M is a key factor controlling the tendency towards the distortion. It is also shown that tensile strain stabilizes the 2×2 CDW, and we suggest that this fact could be further used to induce the instability in double-layers of TiTe 2 which in the absence of strain remain undistorted. The driving force for the CDW instability seems to be the same phonon mediated mechanism acting for singlelayer TiSe 2 , although in single-layer TiTe 2 the driving force is smaller, and the semimetallic character is kept below the transition temperature.