Unraveling Hidden Charge Density Wave Phases in $1T\text{\ensuremath{-}}{\mathrm{TiSe}}_{2}$

Unraveling Hidden Charge Density Wave Phases in $1 T − {TiSe}_{2}$

Zhengwei Nie, Yaxian Wang, Daqiang Chen, and Sheng Meng

Phys. Rev. Lett. 131, 196401 – Published 7 November 2023

Abstract

The unexpected chiral order observed in $1 T − {TiSe}_{2}$ represents an exciting area to explore chirality in condensed matter, while its microscopic mechanism remains elusive. Here, we have identified three metastable collective modes—the so-called single- $q$ modes—in single layer ${TiSe}_{2}$ , which originate from the unstable phonon eigenvectors at the zone boundary and break the threefold rotational symmetry. We show that polarized laser pulse is a unique and efficient tool to reconstruct the transient potential energy surface, so as to drive phase transitions between these states. By designing sequent layers with chiral stacking order, we propose a practical means to realize chiral charge density waves in $1 T − {TiSe}_{2}$ . Further, the constructed chiral structure is predicted to exhibit circular dichroism as observed in recent experiments. These facts strongly indicate the chirality transfer from photons to the electron subsystem, meanwhile being strongly coupled to the lattice degree of freedom. Our work provides new insights into understanding and modulating chirality in quantum materials that we hope will spark further experimental investigation.

Received 29 June 2023
Accepted 2 October 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.196401

Physics Subject Headings (PhySH)

Charge density waves

Transition metal dichalcogenides

Time-dependent DFT

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Zhengwei Nie^1,2, Yaxian Wang ^1,*, Daqiang Chen^1,2, and Sheng Meng ^1,2,3,†

¹Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
²School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
³Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China

^*Corresponding author: yaxianw@iphy.ac.cn
^†Corresponding author: smeng@iphy.ac.cn

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Vol. 131, Iss. 19 — 10 November 2023

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Figure 1
(a) First Brillouin zones of $1 \times 1$ (black line) and $2 \times 2$ (cyan line) ${TiSe}_{2}$ monolayer with corresponding high-symmetry points. (b) Phonon dispersion of the unit cell of monolayer ${TiSe}_{2}$ . (c)–(f) Visualization of the soft phonon mode at (d) $M_{1}$ , (e) $M_{2}$ , (f) $M_{3}$ point, and (c) their superposition. Purple and green balls represent Ti and Se atoms, respectively. Corresponding atomic displacements and the CDW transition vectors are denoted by the red and black arrows.
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Figure 2
(a) Schematics of the optical control of phase transition in monolayer ${TiSe}_{2}$ via a laser pulse [profile shown as the gray line in (b)] linearly polarized along the $M_{1}$ direction (red arrow). (b) Time evolution of the bonding strength calculated in a $2 \times 2$ ${TiSe}_{2}$ supercell. Differential charge density after illumination is shown in the inset. (c) False color representation of the momentum space distribution of the excited electrons after the laser pulse, showing the light selectivity of the three otherwise equivalent directions. (d) The potential energy surface (PES) along the three vibrational modes at $M$ . The upper (lower) panel represents with (without) laser excitations, in which black and colored lines correspondingly denote the ground state PES and nonequilibrium PES. (e) Projected vibrational amplitude of $M_{1}$ , $M_{2}$ , and $M_{3}$ phonon modes driven by the ultrafast laser pulse (gray line) with a fluence of $0.7 mJ / {cm}^{2}$ . (f) Schematic illustration of the CP-laser-driven chirality. The blue, green, and orange blocks represent three successive slices, which consist of $n_{1}$ , $n_{2}$ , and $n_{3}$ multilayers of ${TiSe}_{2}$ , respectively. When a CP light is propagating along the out-of-plane direction of the material, different slices undergo electric fields with varying directions due to the phase shift of the laser between layers.
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Figure 3
(a) Schematic representation of the three-layer model (left panel). The yellow, green, and blue planes correspond to single- $q$ patterns along the lowest energy phonon modes at $M_{1}$ , $M_{2}$ , and $M_{3}$ points, respectively. Charge density distributes in a corkscrew pattern (right panel). (b) Phonon spectrum of the three-layer model at a weak excitation intensity ( $0.47 \times 10^{21} e^{-} / {cm}^{3}$ , pink) and a strong excitation intensity ( $0.73 \times 10^{21} e^{-} / {cm}^{3}$ , red). (c) Evolution of the lowest phonon mode frequency at $Γ^{*}$ and CDW order as a function of excitation intensity $n$ . The strong dependence of both curves signals a chiral CDW transition at a critical point where atomic configuration is fully stabilized in a helical arrangement (shaded area).
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Figure 4
(a) Schematic illustration of the circular photogalvanic effect. A photocurrent $I$ along the $z$ direction is induced by a circularly polarized light. (b) Transient circular photogalvanic current as a function of time for an 800 nm pump. (c) Degree of chirality $(R_{r} - R_{l}) / R$ as a function of photon wavelength calculated for the three-layer model. The two gray markers denote experimental observations from Ref. [19]. (d) Simulated electron diffraction patterns for the achiral and chiral CDW phases.
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Physical Review Letters

Unraveling Hidden Charge Density Wave Phases in 1T−TiSe2

Zhengwei Nie, Yaxian Wang, Daqiang Chen, and Sheng Meng

Phys. Rev. Lett. 131, 196401 – Published 7 November 2023

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Unraveling Hidden Charge Density Wave Phases in $1 T − {TiSe}_{2}$