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Register a new userTopological theory of inversion-breaking charge-density-wave monolayer 1textit{T}-TiSe$_2$
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A charge density wave (CDW) of a nonzero ordering vector $mathbf{q}$ couple electronic states at $mathbf{k}$ and $mathbf{k}+mathbf{q}$ statically, giving rise to a reduced Brillouin zone (RBZ) due to the band folding effect. Its structure, in terms of an irreducible representation of the little group of $mathbf{q}$, would change the symmetry of the system and electronic structure accompanying possible change of band inversion, offering a chance of the topological phase transition. Monolayer 1textit{T}-TiSe$_2$ is investigated for it shows an unconventional CDW phase having a triple-$q$ $M_1^-$ structure. Moreover, the coupling between the triple-$q$ component of the $M_1^-$ CDW will inevitably produce a small $M_1^+$ CDW. The CDW yields a band inversion in 1textit{T}-TiSe$_2$ but different types of CDW can affect the electronic structure and system topology differently. The impact of CDW of different types was studied by utilizing a symmetrization-antisymmetrization technique to extract the $M_1^-$ and $M_1^+$ CDW contributions in the DFT-based tight-binding model and study their effects. The results are consistent with the parity consideration, improving understanding of topology for a CDW system with and without parity.
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Despite the progress made in successful prediction of many classes of weakly-correlated topological materials, it is not clear how a topological order can emerge from interacting orders and whether or not a charge ordered topological state can exist in a two-dimensional (2D) material. Here, through first-principles modeling and analysis, we identify a 2$times$2 charge density wave (CDW) phase in monolayer $2H$-NbSe$_2$ that harbors coexisting quantum spin Hall (QSH) insulator, topological crystalline insulator (TCI) and topological nodal line (TNL) semimetal states. The topology in monolayer NbSe$_2$ is driven by the formation of the CDW and the associated symmetry-breaking periodic lattice distortions and not via a pre-existing topology. Our finding of an emergent triple-topological state in monolayer $2H$-NbSe$_2$ will offer novel possibilities for exploring connections between different topologies and a unique materials platform for controllable CDW-induced topological states for potential applications in quantum electronics and spintronics and Majorana-based quantum computing.
The transition metal dichalcogenide 1$T$-TiSe$_2$ is a quasi-two-dimensional layered material undergoing a commensurate 2 $times$ 2 $times$ 2 charge density wave (CDW) transition with a weak periodic lattice distortion (PLD) below $approx$ 200 K. Scanning tunneling microscopy (STM) combined with intentionally introduced interstitial Ti atoms allows to go beyond the usual spatial resolution of STM and to intimately probe the three-dimensional character of the PLD. Furthermore, the inversion-symmetric, achiral nature of the CDW in the $z$-direction is revealed, contradicting the claimed existence of helical CDW stacking and associated chiral order. This study paves the way to a simultaneous real-space probing of both charge and structural reconstructions in CDW compounds.
In this study, using low-temperature scanning tunneling microscopy (STM), we focus on understanding the native defects in pristine textit{1T}-TiSe$_2$ at the atomic scale. We probe how they perturb the charge density waves (CDWs) and lead to local domain formation. These defects influence the correlation length of CDWs. We establish a connection between suppression of CDWs, Ti intercalation, and show how this supports the exciton condensation model of CDW formation in textit{1T}-TiSe$_2$.
A variety of experiments have been carried out to establish the origin of the chiral charge-density wave transition in 1T-TiSe$_2$, which in turn has led to contradictory conclusions on the origin of this transition. Some studies suggest the transition is a phonon-driven structural distortion while other studies suggest it is an excitonic insulator phase transition that is accompanied by a lattice distortion. First, we propose these interpretations can be reconciled if one analyzes the available experimental and theoretical data within a formal definition of what constitutes an excitonic insulator as initially proposed by Keldysh and Kopaev. Next, we present pump-probe measurements of circularly polarized optical transitions and first-principles calculations where we highlight the importance of accounting for structural distortions to explain the finite chirality of optical transitions in the CDW phase. We show that at the elevated electronic temperature that occurs upon photoexcitation, there is a non-centrosymmetric structure that is near-degenerate in energy with the centrosymmetric charge density wave structure, which explains the finite chirality of the optical transitions observed in the CDW phase of TiSe$_2$.
In Ti-intercalated self-doped $1T$-TiSe$_2$ crystals, the charge density wave (CDW) superstructure induces two nonequivalent sites for Ti dopants. Recently, it has been shown that increasing Ti doping dramatically influences the CDW by breaking it into phase-shifted domains. Here, we report scanning tunneling microscopy and spectroscopy experiments that reveal a dopant-site dependence of the CDW gap. Supported by density functional theory, we demonstrate that the loss of the longrange phase coherence introduces an imbalance in the intercalated-Ti site distribution and restrains the CDW gap closure. This local resilient behavior of the $1T$-TiSe$_2$ CDW reveals a novel mechanism between CDW and defects in mutual influence.
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