Chiral phase transition in charge ordered 1T-TiSe2

Observation of Circular Dichroism Induced by Electronic Chirality

Chiral phases of matter, characterized by a definite handedness, abound in nature, ranging from the crystal structure of quartz to spiraling spin states in helical magnets. In 1T-TiSe_{2} a source of chirality has been proposed that stands apart from these classical examples as it arises from combined electronic charge and quantum orbital fluctuations. This may allow its chirality to be accessed and manipulated without imposing either structural or magnetic handedness. However, direct bulk evidence that broken inversion symmetry and chirality are intrinsic to TiSe_{2} remains elusive. Here, employing resonant elastic x-ray scattering technique, we reveal the presence of circular dichroism, i.e., polarization dependence of the resonant diffraction intensity, up to ∼40% at forbidden Bragg peaks that emerge at the charge and orbital ordering transition. The dichroism varies dramatically with incident energy and azimuthal angle. Comparison to calculated scattering intensities traces its origin to bulk chiral electronic order in TiSe_{2} and establishes resonant elastic x-ray scattering as a sensitive probe to electronic chirality.

Unraveling Hidden Charge Density Wave Phases in 1T-TiSe_{2}

The unexpected chiral order observed in 1T-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 1T-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.

Chiral Charge Density Wave and Backscattering-Immune Orbital Texture in Monolayer 1T-TiTe2

Nontrivial electronic states are attracting intense attention in low-dimensional physics. Though chirality has been identified in charge states with a scalar order parameter, its intertwining with charge density waves (CDW), film thickness, and the impact on the electronic behaviors remain less well understood. Here, using scanning tunneling microscopy, we report a 2 × 2 chiral CDW as well as a strong suppression of the Te-5p hole-band backscattering in monolayer 1T-TiTe2. These exotic characters vanish in bilayer TiTe2 in a non-CDW state. Theoretical calculations prove that chirality comes from a helical stacking of the triple-q CDW components and, therefore, can persist at the two-dimensional limit. Furthermore, the chirality renders the Te-5p bands with an unconventional orbital texture that prohibits electron backscattering. Our study establishes TiTe2 as a promising playground for manipulating the chiral ground states at the monolayer limit and provides a novel path to engineer electronic properties from an orbital degree.

Optically Induced Symmetry Breaking Due to Nonequilibrium Steady State Formation in Charge Density Wave Material 1T-TiSe2

The strongly correlated charge density wave (CDW) phase of 1T-TiSe2 is of interest to verify the claims of a chiral order parameter. Characterization of the symmetries of 1T-TiSe2 is critical to understand the origin of its intriguing properties. Here we use very low-power, continuous wave laser excitation to probe the symmetries of 1T-TiSe2 by using the circular photogalvanic effect. We observe that the ground state of the CDW phase (D3d) is achiral. However, laser excitation above a threshold intensity transforms 1T-TiSe2 into a nonequilibrium chiral phase (C3), which changes the electronic correlations in the material. The inherent sensitivity of the photogalvanic technique to structural symmetries provides evidence of the different optically driven phase of 1T-TiSe2, which allows us to assign symmetry groups to these states. Our work demonstrates that optically induced phase change can occur at extremely low optical intensities in strongly correlated materials, providing a pathway to engineer new phases using light.

Spectroscopic visualization and phase manipulation of chiral charge density waves in 1T-TaS2

The chiral charge density wave is a many-body collective phenomenon in condensed matter that may play a role in unconventional superconductivity and topological physics. Two-dimensional chiral charge density waves provide the building blocks for the fabrication of various stacking structures and chiral homostructures, in which physical properties such as chiral currents and the anomalous Hall effect may emerge. Here, we demonstrate the phase manipulation of two-dimensional chiral charge density waves and the design of in-plane chiral homostructures in 1T-TaS₂. We use chiral Raman spectroscopy to directly monitor the chirality switching of the charge density wave-revealing a temperature-mediated reversible chirality switching. We find that interlayer stacking favours homochirality configurations, which is confirmed by first-principles calculations. By exploiting the interlayer chirality-locking effect, we realise in-plane chiral homostructures in 1T-TaS₂. Our results provide a versatile way to manipulate chiral collective phases by interlayer coupling in layered van der Waals semiconductors.

Circular Dichroism of Emergent Chiral Stacking Orders in Quasi-One-Dimensional Charge Density Waves

Chirality-driven optical properties in charge density waves are of fundamental and practical importance. Here, we investigate the interaction between circularly polarized light and emergent chiral stacking orders in quasi-one-dimensional (quasi-1D) charge-density waves (CDWs) with density-functional theory calculations. In our specific system, self-assembled In nanowires on a Si(111) surface, spontaneous mirror symmetry breaking leads to four symmetrically distinct degenerate quasi-1D CDW structures, which exhibit geometrical chirality. Such geometrical chirality may naturally induce optically active phenomena even when the quasi-1D CDW structures are stacked perpendicular to the CDW chain direction. Indeed, we find that left- and right-chiral stacking orders show distinct circular dichroism responses while a nonchiral stacking order has no circular dichroism. Such optical responses are attributed to the existence of glide mirror symmetry of the CDW stacking orders. Our findings suggest that the CDW chiral stacking orders can lead to diverse active optical phenomena such as chirality-dependent circular dichroism, which can be observed in scanning tunneling luminescence measurements with circularly polarized light.

Anomalous orbital structure in two-dimensional titanium dichalcogenides

Generally, lattice distortions play a key role in determining the electronic ground states of materials. Although it is well known that trigonal distortions are generic to most two dimensional transition metal dichalcogenides, the impact of this structural distortion on the electronic structure and topological properties has not been understood conclusively. Here, by using a combination of polarization dependent X-ray absorption spectroscopy (XAS), X-ray photoelectron spectroscopy (XPS) and atomic multiplet cluster calculations, we have investigated the electronic structure of titanium dichalcogenides TiX₂ (X = S, Se, Te), where the magnitude of the trigonal distortion increase monotonically from S to Se and Te. Our results reveal the presence of an anomalously large crystal field splitting. This unusual kind of crystal field splitting is likely responsible for the unconventional electronic structure of TiX₂ compounds and ultimately controls the degree of the electronic phase protection. Our findings also indicate the drawback of the distorted crystal field picture in explaining the observed electronic ground state and emphasize the key importance of trigonal symmetry, metal-ligand hybridization and electron-electron correlations in defining the electronic structures at the Fermi energy.

Local Real-Space View of the Achiral 1T-TiSe_{2} 2×2×2 Charge Density Wave

The transition metal dichalcogenide 1T-TiSe_{2}-two-dimensional layered material undergoing a commensurate 2×2×2 charge density wave (CDW) transition with a weak periodic lattice distortion (PLD) below ≈200  K. Scanning tunneling microscopy (STM) combined with intentionally introduced interstitial Ti atoms allows us 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.

Quantum Phase Transition in Few-Layer NbSe_{2} Probed through Quantized Conductance Fluctuations

We present the first observation of dynamically modulated quantum phase transition between two distinct charge density wave (CDW) phases in two-dimensional 2H-NbSe_{2}. There is recent spectroscopic evidence for the presence of these two quantum phases, but its evidence in bulk measurements remained elusive. We studied suspended, ultrathin 2H-NbSe_{2} devices fabricated on piezoelectric substrates-with tunable flakes thickness, disorder level, and strain. We find a surprising evolution of the conductance fluctuation spectra across the CDW temperature: the conductance fluctuates between two precise values, separated by a quantum of conductance. These quantized fluctuations disappear for disordered and on-substrate devices. With the help of mean-field calculations, these observations can be explained as to arise from dynamical phase transition between the two CDW states. To affirm this idea, we vary the lateral strain across the device via piezoelectric medium and map out the phase diagram near the quantum critical point. The results resolve a long-standing mystery of the anomalously large spectroscopic gap in NbSe_{2}.

Incommensurate Chirality Density Wave Transition in a Hybrid Molecular Framework

Using single-crystal x-ray diffraction we characterize the 235 K incommensurate phase transition in the hybrid molecular framework tetraethylammonium silver(I) dicyanoargentate, [NEt_{4}]Ag_{3}(CN)_{4}. We demonstrate the transition to involve spontaneous resolution of chiral [NEt_{4}]^{+} conformations, giving rise to a state in which molecular chirality is incommensurately modulated throughout the crystal lattice. We refer to this state as an incommensurate chirality density wave (XDW) phase, which represents a fundamentally new type of chiral symmetry breaking in the solid state. Drawing on parallels to the incommensurate ferroelectric transition of NaNO_{2}, we suggest the XDW state arises through coupling between acoustic (shear) and molecular rotoinversion modes. Such coupling is symmetry forbidden at the Brillouin zone center but symmetry allowed for small but finite modulation vectors q=[0,0,q_{z}]^{*}. The importance of long-wavelength chirality modulations in the physics of this hybrid framework may have implications for the generation of mesoscale chiral textures, as required for advanced photonic materials.

Thermal properties of Zn2(C8H4O4)2•C6H12N2 metal-organic framework compound and mirror symmetry violation of dabco molecules

Thermal properties of Zn₂(C₈H₄O₄)₂•C₆H₁₂N₂ metal-organic framework compound at 8-300 K suggest the possibility of subbarrier tunnelling transitions between left-twisted (S) and right-twisted (R) forms of C₆H₁₂N₂ dabco molecules with D₃ point symmetry. The data agree with those obtained for the temperature behavior of nuclear spin-lattice relaxation times. It is shown that there is a temperature range where the transitions are stopped. Therefore, Zn₂(C₈H₄O₄)₂•C₆H₁₂N₂ and related compounds are interesting objects to study the effect of spontaneous mirror-symmetry breaking and stabilization of chiral isomeric molecules in solids at low temperatures.

Modulation of doping and biaxial strain on the transition temperature of the charge density wave transition in 1T-TiSe2

We study the effects of charge doping and biaxial strains on the transition temperature of charge density wave (CDW) transition in TiSe₂.

Theoretical prediction of a time-reversal broken chiral superconducting phase driven by electronic correlations in a single TiSe₂ layer

Bulk TiSe2 is an intrinsically layered transition metal dichalcogenide hosting both superconducting and charge-density-wave ordering. Motivated by the recent progress in preparing two-dimensional transition metal dichalcogenides, we study these frustrated orderings in a single trilayer of TiSe2. Using a renormalization group approach, we find that electronic correlations can give rise to charge-density-wave order and two kinds of superconductivity. One possible superconducting state corresponds to unconventional s(+-) pairing. The other is particularly exciting as it is chiral, breaking time-reversal symmetry. Its stability depends on the precise strength and screening of the electron-electron interactions in two-dimensional TiSe2.