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Register a new userCoexisting charge-ordered states with distinct driving mechanisms in monolayer VSe$_2$
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Thinning crystalline materials to two dimensions (2D) creates a rich playground for electronic phases, including charge, spin, superconducting and topological order. Bulk materials hosting charge density waves (CDWs), when reduced to ultrathin films, have shown CDW enhancement and tunability. However, charge order confined to only 2D remains elusive. Here we report a distinct charge ordered state emerging in the monolayer limit of 1T-VSe$_2$. Systematic scanning tunneling microscopy experiments reveal that bilayer VSe$_2$ largely retains the bulk electronic structure, hosting a tri-directional CDW. However, monolayer VSe$_2$ exhibits a dimensional crossover, hosting two CDWs with distinct wavelengths. Electronic structure calculations reveal that while one CDW is bulk-like and arises from the well-known Peierls mechanism, the other is decidedly unconventional. The observed CDW-lattice decoupling and the emergence of a flat band suggest that the new CDW arises from enhanced electron-electron interactions in the 2D limit. These findings establish monolayer-VSe$_2$ as the first host of coexisting charge orders with distinct origins, opening the door to tailoring electronic phenomena via emergent interactions in 2D materials.
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We have investigated the chiral charge-density wave (CDW) in $1T$-VSe$_2$ using scanning tunneling microscopy (STM) measurements and optical polarimetry measurements. With the STM mesurements, we revealed that the CDW intensities along each triple-$q$ directions are different. Thus the rotational symmetry of $1T$-VSe$_2$ is lower than that in typical two-dimentional triple-$q$ CDWs. We found that the CDW peaks form a kagome lattice rather than a triangular lattice. The Friedel oscillations have the chirality and the periodicity reflected properties of the background CDW. With the optical measurements in $1T$-VSe$_2$, we also observed a lower rotational symmetry with the polarization dependence of the transient reflectivity variation, which is consistent with the STM result on a microscopic scale. Both $1T$-TiSe$_2$ and $1T$-VSe$_2$ show chiral CDWs, which implies that such waves are usual for CDWs with the condition $H_mathrm{CDW} equiv q_{1}cdot(q_{2} times q_{3}) eq0$.
Using the Lanczos exact-diagonalization and density-matrix renormalization group methods, we study the extended Hubbard model at quarter filling defined on the anisotropic triangular lattice. We focus on charge ordering (CO) phenomena induced by onsite and intersite Coulomb interactions. We determine the ground-state phase diagram including three CO phases, i.e., diagonal, vertical, and three-fold CO phases, based on the calculated results of the hole density and double occupancy. We also calculate the dynamical density-density correlation functions and find possible coexistence of the diagonal and three-fold charge fluctuations in a certain parameter region where the onsite and intersite interactions compete. Furthermore, the characteristic features of the optical conductivity for each CO phase are discussed.
To gain insight into the mechanism of charge-ordering transitions, which conventionally are pictured as a disproportionation of an ion M as 2M$^{n+}$ $rightarrow$ M$^{(n+1)+}$ + M$^{(n-1)+}$, we (1) review and reconsider the charge state (or oxidation number) picture itself, (2) introduce new results for the putative charge ordering compound AgNiO$_2$ and the dual charge state insulator AgO, and (3) analyze cationic occupations of actual (not formal) charge, and work to reconcile the conundrums that arise. We establish that several of the clearest cases of charge ordering transitions involve no disproportion (no charge transfer between the cations, hence no charge transfer), and that the experimental data used to support charge ordering can be accounted for within density functional based calculations that contain no charge transfer between cations. We propose that the charge state picture retains meaning and importance, at least inn many cases, if one focuses on Wannier functions rather than atomic orbitals. The challenge of modeling charge ordering transitions with model Hamiltonians is discussed.
The capability to isolate one to few unit-cell thin layers from the bulk matrix of layered compounds opens fascinating prospects to engineer novel electronic phases. However, a comprehensive study of the thickness dependence and of potential extrinsic effects are paramount to harness the electronic properties of such atomic foils. One striking example is the charge density wave (CDW) transition temperature in layered dichalcogenides whose thickness dependence remains unclear in the ultrathin limit. Here we present a detailed study of the thickness and temperature dependences of the CDW in VSe$_2$ by scanning tunnelling microscopy (STM). We show that mapping the real-space CDW periodicity over a broad thickness range unique to STM provides essential insight. We introduce a robust derivation of the local order parameter and transition temperature based on the real space charge modulation amplitude. Both quantities exhibit a striking non-monotonic thickness dependence that we explain in terms of a 3D to 2D dimensional crossover in the FS topology. This finding highlights thickness as a true tuning parameter of the electronic ground state and reconciles seemingly contradicting thickness dependencies determined in independent transport studies.
We present a detailed study of the bulk electronic structure of high quality VSe$_{2}$ single crystals using optical spectroscopy. Upon entering the charge density wave phase below the critical temperature of 112 K, the optical conductivity of VSe$_2$ undergoes a significant rearrangement. A Drude response present above the critical temperature is suppressed while a new interband transition appears around 0.07,eV. From our analysis, we estimate that part of the spectral weight of the Drude response is transferred to a collective mode of the CDW phase. The remaining normal state charge dynamics appears to become strongly damped by interactions with the lattice as evidenced by a mass enhancement factor m$^{*}$/m$approx$3. In addition to the changes taking place in the electronic structure, we observe the emergence of infrared active phonons below the critical temperature associated with the 4a x 4a lattice reconstruction.
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