Electron-phonon driven charge density wave in CuTe

The compound CuTe (vulcanite) undergoes a quasi one dimensional charge density wave (CDW) at $T< T_{\mathrm{CDW}}=335$ K with a $5\times1\times2$ periodicity. The mechanism at its origin is debated. Several theoretical works claimed that semilocal functionals are unable to describe its occurrence and ascribed its formation only to strong electron-electron interaction. Moreover, the possible role of quantum anharmonicity has not been addressed. Here, by performing quantum anharmonic calculations, we show that semilocal functionals correctly describe the occurrence of a CDW in CuTe if ultradense electron momentum grids allowing for small electronic temperatures are used. The distortion is driven by the perfect nesting among 1D Fermi surface sheets extending in the $k_y$ direction. Quantum anharmonic effects are important and tend to suppress both the distortion and $T_{\mathrm{CDW}}$. The quantum anharmonic structural minimization of the CDW phase in the generalized gradient approximation leads, however, to distorted Te-Te bond lengths in the low temperature phase that are $21\%$ of the experimental ones at $T=20$ K. This suggests that, even if the electron-electron interaction is not crucial for the mechanism of CDW formation, it is relevant to accurately describe the structural data for the low-T phase. We assess the effect of correlation on the CDW by using the DFT+U+V approximation with parameters calculated from first principles. We find that correlation enhances the Te-Te distortion, T$_{CDW}$ and the total energy gain by the distortion.Comment: 9 pages, 8 figures, to appear on Phys. Rev.

Theory of the thickness dependence of the charge density wave transition in 1T-TiTe2_2

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 $2\times2$ 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.Comment: 11 pages, 10 picture

Variations on the “exact factorization” theme

International audienceIn a series of publications, Hardy Gross and co-workers have highlighted the interest of an “exact factorization” approach to the interacting electron-nuclei problem, be it time-independent or time-dependent. In this approach, an effective potential governs the dynamics of the nuclei such that the resulting N-body nuclear density is in principle exact. This contrasts with the more usual adiabatic approach, where the effective potential leads to an approximate nuclear density. Inspired by discussions with Hardy, we explore the factorization idea for arbitrary many-body Hamiltonians, generalizing the electron-nuclei case, with a focus on the static case. While the exact equations do not lead to any practical advantage, they are illuminating, and may therefore constitute a suitable starting point for approximations. In particular, we find that unitary transformations that diagonalize the coupling term for one of the sub-systems make exact factorization appealing. The algorithms by which the equations for the separate subsystems can be solved in the time-independent case are also explored. We illustrate our discussions using the two-site Holstein model and the quantum Rabi model. Two factorization schemes are possible: one where the boson field feels a potential determined by the electrons, and the reverse exact factorization, where the electrons feel a potential determined by the bosons; both are explored in this work. A comparison with a self-energy approach is also presented

Cumulant Green's function calculations of plasmon satellites in bulk sodium: Influence of screening and the crystal environment

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Anharmonic melting of the charge density wave in single-layer TiSe2

Low dimensional systems with a vanishing band-gap and a large electron-hole interaction have been proposed to be unstable towards exciton formation. As the exciton binding energy increases in low dimension, conventional wisdom suggests that excitonic insulators should be more stable in 2D than in 3D. Here we study the effects of the electron-hole interaction and anharmonicity in single-layer TiSe2. We find that, contrary to the bulk case and to the generally accepted picture, the electron-hole exchange interaction is much smaller in 2D than in 3D and it has negligible effects on phonon spectra. By calculating anharmonic phonon spectra within the stochastic self-consistent harmonic approximation, we obtain TCDW= 440K for an isolated and undoped single-layer and TCDW= 364K for an electron-doping n= 4.6 x 10^ 13 cm^{-2}, close to the experimental result of 200-280K on supported samples. Our work demonstrates that anharmonicity and doping melt the charge density wave in single-layer TiSe2

Anharmonic melting of the charge density wave in single-layer TiSe2

5 pages, 4 figuresLow dimensional systems with a vanishing band-gap and a large electron-hole interaction have been proposed to be unstable towards exciton formation. As the exciton binding energy increases in low dimension, conventional wisdom suggests that excitonic insulators should be more stable in 2D than in 3D. Here we study the effects of the electron-hole interaction and anharmonicity in single-layer TiSe2. We find that, contrary to the bulk case and to the generally accepted picture, the electron-hole exchange interaction is much smaller in 2D than in 3D and it has negligible effects on phonon spectra. By calculating anharmonic phonon spectra within the stochastic self-consistent harmonic approximation, we obtain TCDW = 440K for an isolated and undoped single-layer and TCDW = 364K for an electron-doping n = 4.6 x 10^13 cm^{-2} , close to the experimental result of 200-280K on supported samples. Our work demonstrates that anharmonicity and doping melt the charge density wave in single-layer TiSe2

Theory of the thickness dependence of the charge density wave transition in 1 T-TiTe2

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 1 T-TiTe2 is a remarkable exception as it shows no evidence of charge density wave formation in bulk, but it displays a stable 2 × 2 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 1 T-TiTe. We demonstrate that the CDW in single-layer TiTe2 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.Computational resources were granted by PRACE (Project No. 2017174186) and from IDRIS, CINES and TGCC (Grant eDARI 91202 and Grand Challenge Jean Zay). M C, F M, J S Z and L M acknowledge support from the European Union’s Horizon 2020 research and innovation programme Graphene Flagship under grant agreement No 881603.. M C and J S Z acknowledge support from Agence nationale de la recherche (Grant No. ANR-19-CE24-0028). F M and L M acknowledge support by the MIUR PRIN-2017 program, project number 2017Z8TS5B.Peer reviewe

Anharmonic melting of the charge density wave in single-layer TiSe2

5 pages, 4 figuresLow dimensional systems with a vanishing band-gap and a large electron-hole interaction have been proposed to be unstable towards exciton formation. As the exciton binding energy increases in low dimension, conventional wisdom suggests that excitonic insulators should be more stable in 2D than in 3D. Here we study the effects of the electron-hole interaction and anharmonicity in single-layer TiSe2. We find that, contrary to the bulk case and to the generally accepted picture, the electron-hole exchange interaction is much smaller in 2D than in 3D and it has negligible effects on phonon spectra. By calculating anharmonic phonon spectra within the stochastic self-consistent harmonic approximation, we obtain TCDW = 440K for an isolated and undoped single-layer and TCDW = 364K for an electron-doping n = 4.6 x 10^13 cm^{-2} , close to the experimental result of 200-280K on supported samples. Our work demonstrates that anharmonicity and doping melt the charge density wave in single-layer TiSe2