Exciton-phonon cooperative mechanism of the triple- q charge-density-wave and antiferroelectric electron polarization in TiSe 2

摘要: We investigate the microscopic mechanisms of charge-density-wave (CDW) formation in a monolayer ${\mathrm{TiSe}}_{2}$ using realistic multiorbital $d\ensuremath{-}p$ model with electron-phonon coupling and intersite Coulomb (excitonic) interactions. First, we estimate tight-binding bands Ti $3d$ Se $4p$ orbitals on basis first-principles band-structure calculations. thereby show orbital textures undistorted band structure near Fermi level. Next, derive approximation that softening occurs transverse phonon mode at $M$ point Brillouin zone. The stability triple-$q$ CDW state is thus examined to modes ${M}_{1}, {M}_{2}$, ${M}_{3}$ points are frozen simultaneously. Then, introduce interactions between nearest-neighbor atoms lead excitonic instability valence conduction bands. Treating mean-field approximation, cooperatively stabilize ${\mathrm{TiSe}}_{2}$. also calculate single-particle spectrum reproduce folding spectra observed photoemission spectroscopies. Finally, clarify nature state, examine electronic charge density distribution bond type induces vortexlike antiferroelectric polarization kagome network atoms.