Polymorphic charge density waves, magnetism, and topologies in $1T\text{−}{\mathrm{TaTe}}_2$

Polymorphism in two-dimensional (2D) materials presents a fertile ground for introducing new functionalities and designing novel architectures. Here, using first-principles calculations, we investigate the polymorphs of monolayer $1T\text{−}{\mathrm{TaTe}}_2$, including the high-symmetry phase and various charge density wave (CDW) phases ($3\times 1, 4\times 1, 3\times 3, 2\sqrt{3}\times 2\sqrt{3}, \sqrt{13}\times \sqrt{13}, 4\times 4$, and $\sqrt{19}\times \sqrt{19}$) with diverse physical properties. The high-symmetry $1T$ phase is predicted to be a quantum anomalous Hall metal with ferromagnetism. However, after undergoing the CDW phase transitions, the ferromagnetism vanishes and the nontrivial topological properties are also altered. Particularly, the $4\times 4$ CDW phase with the second lowest total energy exhibits a novel topological insulating state, while the $3\times 3$ CDW phase, possessing the lowest total energy, behaves as a normal metal. We further propose that charge doping can effectively modulate the relative stability of the CDW phases. Upon introducing slight hole doping, the $4\times 4$ CDW becomes the most energetically stable state followed by the $3\times 3$ CDW phase. These findings show the rich landscape of structures and properties of $1T\text{−}{\mathrm{TaTe}}_2$, which will strongly stimulate further investigations and lay the foundation for the development of new electronic devices.

Figure 1

Crystal structures for $1\times 1, 3\times 1, 4\times 1, 3\times 3, 2\sqrt{3}\times 2\sqrt{3}, \sqrt{13}\times \sqrt{13}, 4\times 4$, and $\sqrt{19}\times \sqrt{19}$ CDW phases. The green and yellow balls represent Ta and Te atoms, respectively.

Figure 2

(a) Harmonic phonon dispersion at 0 K for the high-symmetry monolayer $1T\text{−}{\mathrm{TaTe}}_2$. (b),(c) Anharmonic phonon dispersion of monolayer $1T\text{−}{\mathrm{TaTe}}_2$ at 300 K and 500 K, respectively. (d) Frequency of the lowest phonon mode at $Q_{\mathrm{cdw}}$ as a function of temperature.

Figure 3

Relative total energies Δ$E$ of different polymorphs in $1T\text{−}{\mathrm{TaTe}}_2$ at the HSE06 level. Δ$E$ calculated without (cyan bars) and with SOC (blue bars) are both given.

Figure 4

Electronic structures (a) without and (b) with SOC effect in the high-symmetry phase. The solid and dashed lines represent the spin-up and spin-down channels, respectively. The shaded region in (b) indicates the continuous band gap below which the corresponding Chern number is calculated. The inset of Fig. 3 is a local enlargement of the band structure around the $M$ point. (c) DOS around the Fermi level for the high-symmetry phase and multiple CDW phases. (d) The calculated DOS at Fermi level (cyan bars) and the total magnetic moment (blue balls) for the $1\times 1$ and different CDW structures.

Figure 5

Electronic and topological properties in the $4\times 4$ CDW phase of monolayer $1T\text{−}{\mathrm{TaTe}}_2$. Electronic structures without (d) and with (e) SOC effects. (f) Topological edge states of the $4\times 4$ CDW phase.

Figure 6

Band structures of $\sqrt{13}\times \sqrt{13}$ and $2\sqrt{3}\times 2\sqrt{3}$ CDW phases at the GGA+SOC and HSE06+SOC levels in $1T\text{−}{\mathrm{TaTe}}_2$, respectively. The red balls represent the contributions of the central Ta $5d_{z^2}$ orbitals of the Star of David $\sqrt{13}\times \sqrt{13}$ phase.

Figure 7

(a) The CDW formation energies of the $3\times 1, 4\times 1, 3\times 3, 2\sqrt{3}\times 2\sqrt{3}, \sqrt{13}\times \sqrt{13}, 4\times 4$, and $\sqrt{19}\times \sqrt{19}$ CDW phases of monolayer $1T\text{−}{\mathrm{TaTe}}_2$ as a function of doping concentration. (b) Schematic illustration of band alignment for monolayer $1T\text{−}{\mathrm{TaTe}}_2$ in multiple CDW phases.