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Register a new userExciton-phonon cooperative mechanism of the triple-$q$ charge-density-wave and antiferroelectric electron polarization in TiSe$_2$
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We investigate the microscopic mechanisms of the charge-density-wave (CDW) formation in a monolayer TiSe$_2$ using a realistic multiorbital $d$-$p$ model with electron-phonon coupling and intersite Coulomb (excitonic) interactions. First, we estimate the tight-binding bands of Ti $3d$ and Se $4p$ orbitals in the monolayer TiSe$_2$ on the basis of the first-principles band structure calculations. We thereby show orbital textures of the undistorted band structure near the Fermi level. Next, we derive the electron-phonon coupling using the tight-binding approximation and show that the softening occurs in the transverse phonon mode at the M point of the Brillouin zone. The stability of the triple-$q$ CDW state is thus examined to show that the transverse phonon modes at the M$_1$, M$_2$, and M$_3$ points are frozen simultaneously. Then, we introduce the intersite Coulomb interactions between the nearest-neighbor Ti and Se atoms that lead to the excitonic instability between the valence Se $4p$ and conduction Ti $3d$ bands. Treating the intersite Coulomb interactions in the mean-field approximation, we show that the electron-phonon and excitonic interactions cooperatively stabilize the triple-$q$ CDW state in TiSe$_2$. We also calculate a single-particle spectrum in the CDW state and reproduce the band folding spectra observed in photoemission spectroscopies. Finally, to clarify the nature of the CDW state, we examine the electronic charge density distribution and show that the CDW state in TiSe$_2$ is of a bond-type and induces a vortex-like antiferroelectric polarization in the kagome network of Ti atoms.
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The semimetallic or semiconducting nature of the transition metal dichalcogenide 1$T$-TiSe$_2$ remains under debate after many decades mainly due to the fluctuating nature of its 2 $times$ 2 $times$ 2 charge-density-wave (CDW) phase at room-temperature. In this letter, using angle-resolved photoemission spectroscopy, we unambiguously demonstrate that the 1$T$-TiSe$_2$ normal state is semimetallic with an electron-hole band overlap of $sim$110 meV by probing the low-energy electronic states of the perturbed CDW phase strongly doped by alkali atoms. Our study not only closes a long-standing debate but also supports the central role of the Fermi surface for driving the CDW and superconducting instabilities in 1$T$-TiSe$_2$.
Monolayer 2H-NbSe2 has recently been shown to be a 2-dimensional superconductor, with a coexisting charge-density wave (CDW). As both phenomena are intimately related to electron-lattice interaction, a natural question is how superconductivity and CDW are interrelated through electron-phonon coupling (EPC), which is important to the understanding of 2-dimensional superconductivity. This work investigates the superconductivity of monolayer NbSe2 in CDW phase using the anisotropic Migdal-Eliashberg formalism based on first principles calculations. The mechanism of the competition between and coexistence of the superconductivity and CDW is studied in detail by analyzing EPC. It is found that the intra-pocket scattering is related to superconductivity, leading to almost constant value of superconducting gaps on parts of the Fermi surface. The inter-pocket scattering is found to be responsible for CDW, leading to partial or full bandgap on the remaining Fermi surface. Recent experiment indicates that there is transitioning from regular superconductivity in thin-film NbSe2 to two-gap superconductivity in the bulk, which is shown here to have its origin in the extent of Fermi surface gapping of K and K pockets induced by CDW. Overall blue shifts of the phonons and sharp decrease of Eliashberg spectrum are found when the CDW forms.
Understanding collective electronic states such as superconductivity and charge density waves is pivotal for fundamental science and applications. The layered transition metal dichalcogenide 1T-TiSe2 hosts a unique charge density wave (CDW) phase transition whose origins are still not fully understood. Here, we present ultrafast time- and angle-resolved photoemission spectroscopy (TR-ARPES) measurements complemented by time-resolved reflectivity (TRR) which allows us to establish the contribution of excitonic and electron-phonon interactions to the CDW. We monitor the energy shift of the valence band (VB) and coupling to coherent phonons as a function of laser fluence. The VB shift, directly related to the CDW gap closure, exhibits a markedly slower recovery dynamics at fluences above Fth = 60 microJ cm-2. This observation coincides with a shift in the relative weight of coherently coupled phonons to higher frequency modes in time-resolved reflectivity (TRR), suggesting a phonon bottleneck. Using a rate equation model, the emergence of a high-fluence bottleneck is attributed to an abrupt reduction in coupled phonon damping and an increase in exciton dissociation rate linked to the loss of CDW superlattice phonons. Thus, our work establishes the important role of both excitonic and phononic interactions in the CDW phase transition and the advantage of combining complementary femtosecond techniques to understand the complex interactions in quantum materials.
We report high-resolution inelastic x-ray measurements of the soft phonon mode in the charge-density-wave compound TiSe$_2$. We observe a complete softening of a transverse optic phonon at the L point, i.e. q = (0.5, 0, 0.5), at T ~ T_{CDW}. Renormalized phonon energies are observed over a large wavevector range $(0.3, 0, 0.5) le mathbf{q} le (0.5, 0, 0.5)$. Detailed ab-initio calculations for the electronic and lattice dynamical properties of TiSe2 are in quantitative agreement with experimental frequencies for the phonon branch involving the soft mode. The observed broad range of renormalized phonon frequencies is directly related to a broad peak in the electronic susceptibility stabilizing the charge-density-wave ordered state. Our analysis demonstrates that a conventional electron-phonon coupling mechanism can explain a structural instability and the charge-density-wave order in TiSe_2 although other mechanisms might further boost the transition temperature.
Substrate engineering provides an opportunity to modulate the physical properties of quantum materials in thin film form. Here we report that TiSe$_2$ thin films grown on TiO$_2$ have unexpectedly large electron doping that suppresses the charge density wave (CDW) order. This is dramatically different from either bulk single crystal TiSe$_2$ or TiSe$_2$ thin films on graphene. The epitaxial TiSe$_2$ thin films can be prepared on TiO$_2$ via molecular beam epitaxy (MBE) in two ways: by conventional co-deposition using selenium and titanium sources, and by evaporating only selenium on reconstructed TiO$_2$ surfaces. Both growth methods yield atomically flat thin films with similar physical properties. The electron doping and subsequent suppression of CDW order can be explained by selenium vacancies in the TiSe$_2$ film, which naturally occur when TiO$_2$ substrates are used. This is due to the stronger interfacial bonding that changes the ideal growth conditions. Our finding provides a way to tune the chemical potential of chalcogenide thin films via substrate selection and engineering.
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