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.
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